mm534
====
Subject: Re: distribution of an outlier?
> Bob,
Agreed
Any DELETION of outliers is a CRIME unless you can fully justify
its
> deletion.
This sounds a bit strong to me. As far as I can see, the argument is
> that outliers will always happen by chance, and as they are part of
the
> data, they shouldn't be removed. OK so far. If you can show that an
> outlier was created by a rogue process, then that's not what you're
> modelling, so the outlier can be removed. Again OK (given a suitable
> definition of a rogue process!).
But, what about the outlier that is created by a rogue process, but
not
> one that you are able to recognise? Objectively, it's just as much
an
> outlier as one for which you can see why it's acting oddly, so if you
> can be confident that it is from a rogue process, even if you can't
> identify the process, then it should be treated in the same way, and
> hence be deleted.
I suppose I'm worried by this absolute rule that an outlier can't be
> deleted unless you're omnipotent enough to know that it's an outlier.
> I'm also not sure if there's any hard and fast answer to this, so
that
> there will be cases (hopefully rare) where it makes sense to remove
an
> outlier.
Bob
>
Having hunted down a few outliers, let my put my two cents in.
One can test for outliers with statistics. That gives one an idea
of which are improbable values. To remove them from the sample
requires an argument based on something other than statistics.
Examples from my experience:
A) 12 inches of rain in 24 hours at a station in Florida  accepted
as real and left in the sample because there was a hurricane hitting
Florida during that period.
B) 1.22 inches of rain at a station  thrown out because rainfall
can not be negative and there were no indications of real rainfall
at adjacent stations on the date (decreasing the probability of
a sign error).
I don't think one needs to exactly know the rogue process (did
the observer in the second case forget his coffee, was the
transmission garbled, did someone set pizza on the form?) to
be reasonably sure something went wrong. If one can't be
reasonably sure something went wrong, then IMO it isn't a
rogue process, as far as one can tell. The datum may be wrong,
but we'll never know. Knowledge is limited.
Russell
====
Subject: I'm Dumb! Need Help! Stats Question
do1XYg0AAADDNFUW6acK0ZYthwIZ29bH
I have a series of 60 lines of data with the following 3 columns:
month, amount purchased with software (X), maximum price without using
software (Y).
Assume a business has 100 items that it buys from 10 vendors and it
orders various things throughout the month.
X = total dollar amount of items purchased in a month where the
business used the software and received the lowest price from each of
its vendors by comparing prices among the vendors it does business with
to generate the purchase orders.
Y = total dollar amount assuming the business paid the highest price
from each of its vendors to generate the purchase orders (idea being if
you don't compare prices with our software, you will pay higher prices)
I have X and Y for each business. I know the true savings by month is
not YX as even without the software the business would not likely pay
the highest price on each item from its vendor community.
What is a true statistical representation of savings by month? Please
help!
RI
====
Subject: Exceptionally nonnormal data?
I'm in a lab that has tested a number of subjects (N=88) on 60
stimuli, 20 of each of 3 types. Each subject sees the same 60
stimuli, and for each one gives a response which is marked as Correct
or Incorrect. The subjects are themselves evenly divided into a
patient group and a control group. We've calculated the proportion of
correct responses for each subject, for each stimulus type (thus 3
accuracy measures per subject), and would like to see whether there's
an interaction between stimulus type and subject group in predicting
accuracy.
If the accuracy measures or some transformation thereof were normally
distributed, I'd just run an ANOVA. However, it turns out that most
accuracies are quite high, and the higher the accuracy, the more often
it appears in our data. That is, a histogram of the data looks
something like this (using a fixedwidth font):
*
*
***
*****
********
0.4 1.0
I don't think any transformation is going to normalize this one. So
my questions are, is it possible or likely that tests which assume
normal distributions will give correct results on this data anyway?
And if not, is there some alternative method of running tests on the
data?
Chris
====
Subject: Re: Exceptionally nonnormal data?
I'm in a lab that has tested a number of subjects (N=88) on 60
> stimuli, 20 of each of 3 types. Each subject sees the same 60
> stimuli, and for each one gives a response which is marked as Correct
> or Incorrect. The subjects are themselves evenly divided into a
> patient group and a control group. We've calculated the proportion of
> correct responses for each subject, for each stimulus type (thus 3
> accuracy measures per subject), and would like to see whether there's
> an interaction between stimulus type and subject group in predicting
> accuracy.
>
Could you not model the probability that each individual gets each
stimulus correct, using logistic regression? At the simplest level, if
you could assume that the probability of getting a reaction correct is
the same for every question, and that the responses are independent (so
that they are all equally difficult and there is no learning), then the
number of stimuli correct would be binomially distributed, and things
get a lot easier. Even if this isn't the case, then knowing more
details about the system, we might be able to suggest something
appropriate (and perhaps spot a couple of pitfalls).
Bob

Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf H.8allstr.9amin katu 2b)
FIN00014 University of Helsinki
Finland
Telephone: +3589191 51479
Mobile: +358 50 599 0540
Fax: +3589191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results  EEB: www.jnreeb.org
====
Subject: Re: Exceptionally nonnormal data?
On Tue, 19 Apr 2005 19:11:25 +0300, Anon.
>Could you not model the probability that each individual gets each
>stimulus correct, using logistic regression? At the simplest level, if
>you could assume that the probability of getting a reaction correct is
>the same for every question, and that the responses are independent (so
>that they are all equally difficult and there is no learning), then the
>number of stimuli correct would be binomially distributed, and things
>get a lot easier. Even if this isn't the case, then knowing more
>details about the system, we might be able to suggest something
>appropriate (and perhaps spot a couple of pitfalls).
Bob
I actually have been trying to use a logistic mixed model (subjects
crossed with stimuli) to do what you've described, I think. I was
hoping to figure out an ANOVA method as well for two reasons. It's
more in line with what reviewers, publishers, and readers are familiar
with, even though it's a lesssensitive model. Also, the logistic
mixed model has been doing things I don't entirely understand, like
producing adjusted means that are uncomfortably different from
empirical probabilities. (Our local statistician says that the
adjusted means can't be interpreted in such a model, but without
understanding why not I find this difficult to completely believe.)
Anyway, all three replies in this thread are interesting and
sensiblesounding pieces of advice, and I am trying to follow up on
Chris
====
Subject: Re: Exceptionally nonnormal data?
j1mTRwwAAADzgndA_zkUptpIw3BECfQi
> I don't think any transformation is going to normalize this one. So
> my questions are, is it possible or likely that tests which assume
> normal distributions will give correct results on this data anyway?
> And if not, is there some alternative method of running tests on the
> data?
The beta distribution is sometimes used to model proportions. I think
some software packages handle regressions where the response is beta
distributed. A message at
http://tolstoy.newcastle.edu.au/R/help/04/06/1069.html says that STATA,
====
Subject: Re: Exceptionally nonnormal data?
Lf4ckgwAAAANkWQeq7i63ANW145yHLAd
>If the accuracy measures or some transformation thereof were normally
>distributed, I'd just run an ANOVA. However, it turns out that most
>accuracies are quite high,
Here is a classic paper discussing the analysis of percentage correct
data:
Murdock, B. B. Jr., & Ogilvie, J. C. (1968). Binomial variability in
shortterm memory. Psychological Bulletin, 70, 256260.
I think they recommend an arcsin transformation for your situation.
>would like to see whether there's an interaction between stimulus
type and
>subject group in predicting accuracy.
But this statement suggests that you may have a deeper problem to
address in your analysis, because it is tricky to infer interactions
from percentage correct data. For a discussion of this problem, see:
Loftus, G. R. (1978). On interpretation of interactions. Memory &
Cognition, 6, 312319.
Best of luck,
====
Subject: Joint Probability Distributions
XRFC2646: Format=Flowed; Original
The joint pmf of X1 and X2 is as given in the accompanying table.
X2
0 1 2 3
0 .08 .07 .04 .00
1 .06 .15 .05 .04
X1 2 .05 .04 .10 .06
3 .00 .03 .04 .07
4 .00 .01 .05 .06
Calculate V(X1 + X2)
I have the student solutions manual to this problem so here is the answer
provided:
V(X1 + X2) = V(X1) + V(X2) + 2 Cov(X1,X2) = 1.59 + 1.0875 + 2(.695) =
4.0675
I've already computed the covariance (.695) so I have no problem with that,
but I just don't understand where the 1.59 and 1.0875 came from. Can
someone just explain to me where the solutions manual got those numbers
from?
====
Subject: Re: Joint Probability Distributions
> The joint pmf of X1 and X2 is as given in the accompanying table.
X2
> 0 1 2 3
> 0 .08 .07 .04 .00
> 1 .06 .15 .05 .04
> X1 2 .05 .04 .10 .06
> 3 .00 .03 .04 .07
> 4 .00 .01 .05 .06
> Calculate V(X1 + X2)
But don't you need the actual values of X1 and X2 too to calculate this?
pj
====
Subject: Re: Joint Probability Distributions
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> The joint pmf of X1 and X2 is as given in the accompanying table.
X2
> 0 1 2 3
> 0 .08 .07 .04 .00
> 1 .06 .15 .05 .04
> X1 2 .05 .04 .10 .06
> 3 .00 .03 .04 .07
> 4 .00 .01 .05 .06
> Calculate V(X1 + X2)
But don't you need the actual values of X1 and X2 too to calculate
this?
You use the same book and have the same instructor as meyousikmann?
:)
X1 = 0,1,2,3,4; and X2 = 0,1,2,3.
Now the row sums are the probabilities of X1; column sums probabilites
of X2.
 Bob.
====
Subject: Re: Joint Probability Distributions
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> The joint pmf of X1 and X2 is as given in the accompanying table.
X2
> 0 1 2 3
> 0 .08 .07 .04 .00
> 1 .06 .15 .05 .04
> X1 2 .05 .04 .10 .06
> 3 .00 .03 .04 .07
> 4 .00 .01 .05 .06
> Calculate V(X1 + X2)
> I have the student solutions manual to this problem so here is the
answer
> provided:
Why do you need a student solution manual???
If you study the TEXT material, and tried to understand it, the
solution
would have been transparent and obvious.
V(X1 + X2) = V(X1) + V(X2) + 2 Cov(X1,X2) = 1.59 + 1.0875 + 2(.695) =
4.0675
I've already computed the covariance (.695) so I have no problem with
that,
> but I just don't understand where the 1.59 and 1.0875 came from. Can
> someone just explain to me where the solutions manual got those
numbers
> from?
You obviously did not know how to computer the variance of a random
variable from its probability distribution. 1.59 is the variance of
X1, and 1.0875 is the variance of X2, computed strictly according to
the variance definition (formula), once you add up the rows and
columns to get the MARGINAL probs. of X1 and X2.
Take my advice that I give to my students: BURN your Solution Manual!
Learn from your textbook and lecture material. You should not need
any solution manual, and your progress will be much faster WITHOUT it.
Trust me.
 Bob.
====
Subject: Re: Joint Probability Distributions
XRFC2646: Format=Flowed; Original
> The joint pmf of X1 and X2 is as given in the accompanying table.
>> X2
>> 0 1 2 3
>> 0 .08 .07 .04 .00
>> 1 .06 .15 .05 .04
>> X1 2 .05 .04 .10 .06
>> 3 .00 .03 .04 .07
>> 4 .00 .01 .05 .06
>> Calculate V(X1 + X2)
>> I have the student solutions manual to this problem so here is the
> answer
>> provided:
Why do you need a student solution manual???
If you study the TEXT material, and tried to understand it, the
> solution
> would have been transparent and obvious.
>> V(X1 + X2) = V(X1) + V(X2) + 2 Cov(X1,X2) = 1.59 + 1.0875 + 2(.695) =
> 4.0675
>> I've already computed the covariance (.695) so I have no problem with
> that,
>> but I just don't understand where the 1.59 and 1.0875 came from. Can
> someone just explain to me where the solutions manual got those
> numbers
>> from?
You obviously did not know how to computer the variance of a random
> variable from its probability distribution. 1.59 is the variance of
> X1, and 1.0875 is the variance of X2, computed strictly according to
> the variance definition (formula), once you add up the rows and
> columns to get the MARGINAL probs. of X1 and X2.
Take my advice that I give to my students: BURN your Solution Manual!
Learn from your textbook and lecture material. You should not need
> any solution manual, and your progress will be much faster WITHOUT it.
Trust me.
 Bob.
>
Let me just say thank you, Bob. While I agree with you about the solutions
manual, I hope we can agree that there are instructors out there that don't
know how to teach as well as textbooks that do not adequately cover the
material. In my unfortunate situation, I am stuck with both. I absolutely
loathe the textbook (it seems to leave the teaching part to the problems at
the end of the sections which forces the student to struggle with concepts
without adequate discussion or example) and the instructor seems to be
equally inept at teaching. Don't get me wrong, I am not questioning the
instructor's intelligence, just the teaching skills. Some people can be
absolutely brilliant but lack the skill to pass that brilliance to others in
a method that is understandable. Hence, in this particular situation, I am
forced to attempt to understand the material on my own. When I don't
understand, I consult the answer to see if I can work backwards to figure
out how the solution was derived. Believe me when I say this is the first
time that I have had to operate in this fashion and I honestly try as best I
can to work the problems before checking my results. Sometimes, it just
doesn't go that way.
Anyway, you gave me the key to figure this out. I, in fact, DO KNOW how to
compute the variance of a random variable from its probability distribution,
but there was no discussion in the text about how to do it with a joint
probability distribution. Your little hint about the marginal probabilities
====
Subject: Re: Joint Probability Distributions
<116ba73khsqpc23@corp.supernews.com>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> The joint pmf of X1 and X2 is as given in the accompanying table.
>> X2
>> 0 1 2 3
>> 0 .08 .07 .04 .00
>> 1 .06 .15 .05 .04
>> X1 2 .05 .04 .10 .06
>> 3 .00 .03 .04 .07
>> 4 .00 .01 .05 .06
>> Calculate V(X1 + X2)
>> I have the student solutions manual to this problem so here is the
> answer
>> provided:
Why do you need a student solution manual???
If you study the TEXT material, and tried to understand it, the
> solution
> would have been transparent and obvious.
>> V(X1 + X2) = V(X1) + V(X2) + 2 Cov(X1,X2) = 1.59 + 1.0875 +
2(.695) =
> 4.0675
>> I've already computed the covariance (.695) so I have no problem
with
> that,
>> but I just don't understand where the 1.59 and 1.0875 came from.
Can
> someone just explain to me where the solutions manual got those
> numbers
>> from?
You obviously did not know how to computer the variance of a random
> variable from its probability distribution. 1.59 is the variance
of
> X1, and 1.0875 is the variance of X2, computed strictly according
to
> the variance definition (formula), once you add up the rows and
> columns to get the MARGINAL probs. of X1 and X2.
Take my advice that I give to my students: BURN your Solution
Manual!
Learn from your textbook and lecture material. You should not need
> any solution manual, and your progress will be much faster WITHOUT
it.
Trust me.
 Bob.
> Let me just say thank you, Bob. While I agree with you about the
solutions
> manual, I hope we can agree that there are instructors out there that
don't
> know how to teach as well as textbooks that do not adequately cover
the
> material.
Unfortunately that is true, but I think poor instructors and
inattentive
students far outrank poorly written textbooks, as many such textbooks
there are.
> In my unfortunate situation, I am stuck with both. I absolutely
> loathe the textbook (it seems to leave the teaching part to the
problems at
> the end of the sections which forces the student to struggle with
concepts
> without adequate discussion or example) and the instructor seems to
be
> equally inept at teaching. Don't get me wrong, I am not questioning
the
> instructor's intelligence, just the teaching skills. Some people can
be
> absolutely brilliant but lack the skill to pass that brilliance to
others in
> a method that is understandable.
In your case, I am unable to judge who is more to blame, the book, the
instructor, or you. But it doesn't matter in a way.
> Hence, in this particular situation, I am
> forced to attempt to understand the material on my own.
And the way to do it is to go to the library, pick up another
elementary
book of the same level, and see how the same concepts are explained.
This is what you SHOULD NOT do, no matter how poor the book and
instructor are:
> When I don't
> understand, I consult the answer to see if I can work backwards to
figure
> out how the solution was derived. Believe me when I say this is the
first
> time that I have had to operate in this fashion and I honestly try as
best I
> can to work the problems before checking my results. Sometimes, it
just
> doesn't go that way.
This work backwards to figure out how the solution was derived is
the WORST practice a student can do.
1. Sometimes students figured the right answer for the wrong
reasons.
2. Sometimes students waste hours trying to figure how they could
get the WRONG answer in the book or manual (as in a case of an OP
asking about Poisson probabilities).
> Anyway, you gave me the key to figure this out. I, in fact, DO KNOW
how to
> compute the variance of a random variable from its probability
distribution,
> but there was no discussion in the text about how to do it with a
joint
> probability distribution. Your little hint about the marginal
probabilities
I am glad that little hint worked for you.
But my advice of BURN THE MANUAL still applies. :)
Consult a second (or third) book in the library if your instructor and
textbook are really that bad.
Good luck. You had the right spirit, but the wrong approach.
 Bob.
====
Subject: Box PlotsAcceptance?
It's been at least 15 years since I played with Box plots. I believe when
they
were introduced some 20 years ago they got something of a mild acceptance.
Are
they now widely use or have any changes been made to the original approach.
I used to have the orange ang green books on this subject. I think Box was
one
author. What were the titles of the books and who, if anyone, was the other
author?

Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
Obz Site: 39¡ 15' 7 N,
121¡ 2' 32 W, 2700 feet
Academic disputes are vicious because so little
is at stake.  Anonymous
Web Page:
====
Subject: Re: Box PlotsAcceptance?
XRFC2646: Format=Flowed; Response
> It's been at least 15 years since I played with Box plots. I believe when
> they were introduced some 20 years ago they got something of a mild
> acceptance. Are they now widely use or have any changes been made to the
> original approach.
Box plots are an accepted part of the Six Sigma methodology. I'm taking the
series of three oneweek green belt courses at this time as my employer,
Johns Hopkins Medicine, is implementing the Six/Lean Sigma approach. The
middle week was spent on statistical applications, using MiniTab software.
The box plots are part of the graphical package.
I've already used box plots in illustrating lengthofstay and direct cost
variations by diagnosis. It's an easy concept to explain to the medical and
administrative staff and it gives a good picture of what's going on.
Paul
====
Subject: Re: Box PlotsAcceptance?
It's been at least 15 years since I played with Box plots. I believe when
they
> were introduced some 20 years ago they got something of a mild acceptance.
Are
> they now widely use or have any changes been made to the original
approach.
I used to have the orange ang green books on this subject. I think Box was
one
> author. What were the titles of the books and who, if anyone, was the
other author?
They are teaching it to fifth or sixth graders (in advanced
math class) in the local school district I just moved from.
They were also used were I worked. I guess you can tell from
those to facts the level of my former job. ;)
I think the others who mentioned Tukey and Mosteller are right.
I remember the covers being somewhat garish for textbooks of the
period.
Russell

All too often the study of data requires care.
====
Subject: Re: Box PlotsAcceptance?
>
>>It's been at least 15 years since I played with Box plots. I believe when
they
>>were introduced some 20 years ago they got something of a mild acceptance.
Are
>>they now widely use or have any changes been made to the original
approach.
>>I used to have the orange ang green books on this subject. I think Box was
one
>>author. What were the titles of the books and who, if anyone, was the
other author?
> They are teaching it to fifth or sixth graders (in advanced
> math class) in the local school district I just moved from.
> They were also used were I worked. I guess you can tell from
> those to facts the level of my former job. ;)
I think the others who mentioned Tukey and Mosteller are right.
> I remember the covers being somewhat garish for textbooks of the
> period.
Russell
Do any current books cover this material plus any developments in the world
of
data analysis (exploratory)? I noticed EDA selling for $100 on Amazon. I
think I
donated my copies to a university library. I sure can't find them around the
house or garage.

Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
Obz Site: 39¡ 15' 7 N,
121¡ 2' 32 W, 2700 feet
Academic disputes are vicious because so little
is at stake.  Anonymous
Web Page:
====
Subject: Re: Box PlotsAcceptance?
>It's been at least 15 years since I played with Box plots. I believe
when they
>>were introduced some 20 years ago they got something of a mild
acceptance. Are
>>they now widely use or have any changes been made to the original
approach.
>>I used to have the orange ang green books on this subject. I think Box
was one
>>author. What were the titles of the books and who, if anyone, was the
other author?
> They are teaching it to fifth or sixth graders (in advanced
> math class) in the local school district I just moved from.
> They were also used were I worked. I guess you can tell from
> those to facts the level of my former job. ;)
I think the others who mentioned Tukey and Mosteller are right.
> I remember the covers being somewhat garish for textbooks of the
> period.
Russell
> Do any current books cover this material plus any developments in the
world of
> data analysis (exploratory)? I noticed EDA selling for $100 on Amazon. I
think I
> donated my copies to a university library. I sure can't find them around
the
> house or garage.
>
Sorry, I don't have any titles to recomend.
Russell

All too often the study of data requires care.
====
Subject: Re: Box PlotsAcceptance?
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
> It's been at least 15 years since I played with Box plots. I believe
when they
> were introduced some 20 years ago they got something of a mild
acceptance.
Box plots are older than that.
Tukey's boxplot dates back to at least the early 70s, though I think
his book wasn't published until 1977
(and I have seen boxplotlike constructs dating back at least to the
1940s).
> Are
> they now widely use or have any changes been made to the original
approach.
Depends on what you mean by widely. Many people have proposed
changes.
I have seen at least 5 different versions of the same basic construct.
> I used to have the orange ang green books on this subject. I think
Box was one
> author. What were the titles of the books and who, if anyone, was the
other author?
Do you mean Tukey's EDA (Exploratory Data Analysis)? That was
originally orange IIRC.
Tukey was also an authour on a green book. The book by Mosteller and
Tukey might have been green, but my memory isn't clear on what books
were what colour now.
Glen
> 
> Wayne T. Watson (Watson Adventures, Prop., Nevada City,
CA)
> Obz Site: 39¡ 15' 7 N,
121¡ 2' 32 W, 2700
feet
Academic disputes are vicious because so
little
> is at stake.  Anonymous
Web Page:
====
Subject: Re: Box PlotsAcceptance?
>
>>It's been at least 15 years since I played with Box plots. I believe
when they
>
>>were introduced some 20 years ago they got something of a mild
acceptance.
Box plots are older than that.
Tukey's boxplot dates back to at least the early 70s, though I think
> his book wasn't published until 1977
> (and I have seen boxplotlike constructs dating back at least to the
> 1940s).
>>Are
>>they now widely use or have any changes been made to the original
approach.
Depends on what you mean by widely. Many people have proposed
> changes.
> I have seen at least 5 different versions of the same basic construct.
>>I used to have the orange ang green books on this subject. I think
Box was one
>
>>author. What were the titles of the books and who, if anyone, was the
other author?
Do you mean Tukey's EDA (Exploratory Data Analysis)? That was
> originally orange IIRC.
Tukey was also an authour on a green book. The book by Mosteller and
> Tukey might have been green, but my memory isn't clear on what books
> were what colour now.
Glen
I suppose some gauge of how widely these have been accepted is whether they
still crop up in applications. Are there any recent practical applications
of
these methods that have proven useful? Maybe Google can answer this.
====
Subject: Re: Box PlotsAcceptance?
> I suppose some gauge of how widely these have been accepted is whether
they
> still crop up in applications. Are there any recent practical applications
of
> these methods that have proven useful? Maybe Google can answer this.
Oh, they're used quite a bit. But you don't see them much in mainstream
media.
Glen
====
Subject: Re: Box PlotsAcceptance?
ONSuJQ0AAABDeuDwQ9FnSh1VIzGh74o
At the risk of morphing this topic, the use of statistics in US
mainstream media is abysmal! You flip open the new york times and how
often do you see a bar chart, let alone scatter plots, box plots,
regression lines, etc.? Most of our newspapers are filled with text or
photographs. Same with TV: CNN, CNBC, etc. also tend to stay away from
charts... at most they provide a list of numbers.
Now we come to ESPN and the sports outlets. OMG, they keep posting
spurious correlations as insights (ABC team has never lost a game that
was played in Dome Y on the 19th day of a summer month when the
temperature was over 70 degrees and humidity over 80.3%).
Box plots are not often used in the mainstream because most lay people
are still preoccupied with means. It's only when one is concerned
with distributions then one would look at box plots and similar things.
====
Subject: Re: Box PlotsAcceptance?
At the risk of morphing this topic, the use of statistics in US
> mainstream media is abysmal! You flip open the new york times and how
> often do you see a bar chart, let alone scatter plots, box plots,
> regression lines, etc.? Most of our newspapers are filled with text or
> photographs. Same with TV: CNN, CNBC, etc. also tend to stay away from
> charts... at most they provide a list of numbers.
Now we come to ESPN and the sports outlets. OMG, they keep posting
> spurious correlations as insights (ABC team has never lost a game that
> was played in Dome Y on the 19th day of a summer month when the
> temperature was over 70 degrees and humidity over 80.3%).
Oh, yes. And things like They're 9 wins and 1 loss in games when
they've been ahead going into 9th inning really annoy me. Yeah,
and they've won 100% of the games when they were ahead at the end
of the game! Perhaps the commentators should pass this on as
a strategy tip to the managers: Pssst, you'll win more games if
you score more than the other team more often.
> Box plots are not often used in the mainstream because most lay people
> are still preoccupied with means. It's only when one is concerned
> with distributions then one would look at box plots and similar things.
Russell

All too often the study of data requires care.
====
Subject: Re: Box PlotsAcceptance?
> Oh, yes. And things like They're 9 wins and 1 loss in games when
> they've been ahead going into 9th inning really annoy me. Yeah,
> and they've won 100% of the games when they were ahead at the end
> of the game! Perhaps the commentators should pass this on as
> a strategy tip to the managers: Pssst, you'll win more games if
> you score more than the other team more often.
The comic strip _Tank McNamara_ periodically runs Great Moments In Sports
Analysis where the author comes up with a cartoon to match a reader
contributed example of a tautology actually uttered by a sportscaster.
====
Subject: Re: Box PlotsAcceptance?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> At the risk of morphing this topic, the use of statistics in US
> mainstream media is abysmal!
That's overrating it a tad. :) it's something between abysmal
and nadir.
> You flip open the new york times and how
> often do you see a bar chart, let alone scatter plots, box plots,
> regression lines, etc.?
Actually you see bar charts quite often, but most of them are
MISLEADINGLY scaled. For example, if you see something like this:
xxx
xxx
xxx
xxx
xxx
xxx
xxx
xxx xxx
xxx xxx
xxx xxx xxx

You obvious reaction is the dramatic increase or the expotential
graphic presentation of a set of nearly CONSTANT numbers, with minor
random fluctations from year to year, such as (985, 987, 994) for
those three years, while the preceding 10 years varied randomly from
980
to 1000. The absence of a VERTICAL scale, or an improperly truncated
vertical scale. are among the most common misleading graphical
reporesentations.
 Bob.
====
Subject: Re: Box PlotsAcceptance?
> Actually you see bar charts quite often, but most of them are
> MISLEADINGLY scaled. For example, if you see something like this:
xxx
> xxx
> xxx
> xxx
> xxx
> xxx
> xxx
> xxx xxx
> xxx xxx
> xxx xxx xxx
> 
You obvious reaction is the dramatic increase or the expotential
> graphic presentation of a set of nearly CONSTANT numbers, with minor
> random fluctations from year to year, such as (985, 987, 994) for
> those three years, while the preceding 10 years varied randomly from
> 980
> to 1000. The absence of a VERTICAL scale, or an improperly truncated
> vertical scale. are among the most common misleading graphical
> reporesentations.
See for a particularly
egregious example of this (which Darrell Huff called the geewhiz
graph; Tufte has also written about it). There the CNN graph visually
conveyed the impression that 90% of Democrats and 10% of Republicans
approved of having Terri Schiavo's feeding tube removed, whereas the
legends indicated that the real figures were 62% and 54% respectively
(the difference being within the poll's margin of error). If you read
the comments, you'll see that several people discovered that many common
graphing packages produce this sort of graph by default.
====
Subject: Re: Box PlotsAcceptance?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
Actually you see bar charts quite often, but most of them are
> MISLEADINGLY scaled. For example, if you see something like this:
xxx
> xxx
> xxx
> xxx
> xxx
> xxx
> xxx
> xxx xxx
> xxx xxx
> xxx xxx xxx
> 
You obvious reaction is the dramatic increase or the expotential
media's
> graphic presentation of a set of nearly CONSTANT numbers, with
minor
> random fluctations from year to year, such as (985, 987, 994) for
> those three years, while the preceding 10 years varied randomly
from
> 980
> to 1000. The absence of a VERTICAL scale, or an improperly
truncated
> vertical scale. are among the most common misleading graphical
> reporesentations.
See for a particularly
> egregious example of this
I was trying to convey in my post.
> (which Darrell Huff called the geewhiz
> graph; Tufte has also written about it).
Ah yes. Often called the geewhiz factor in graphs and charts.
Now I recall having a modest collection of those geewhiz graphs and
charts to make my lectures more interesting to those students whose
minds were on the football field and attended the class only because
they were required to, to keep their athletic scholorships,
where the term scholorship was later changed to grantinaid making
it clear scholorship had nothing to do with it. :)
Here is a true story about those scholars.
I recall once having an All American football player on a National
Championship football Team in my statistics class. Of course I
didn't know he was a football player, let alone an All American
until this episode took place and my colleagues informed me who
he was.
After the first quiz when he scored 20 out of 100, while the next
lowest score in the class of 40 was about 65, it was such an outlier
performance that I called him to my office to find out what the
story was, because he attended classes regularly, and even looked
attentive.
It was then that we realized he was suppsed to be enrolled in Mthsc
101, in Room 301; but went to Room 101 where Mthsc 301 was taught.
No, he didn't pass Mthsc 101 either, but he could sure play ball!!
 Bob.
====
Subject: Re: Box PlotsAcceptance?
zuiTXwwAAADHDQA2vQPjoyoWimvkgeWk
> Actually you see bar charts quite often, but most of them are
> > MISLEADINGLY scaled. For example, if you see something like
this:
> > xxx
> > xxx
> > xxx
> > xxx
> > xxx
> > xxx
> > xxx
> > xxx xxx
> > xxx xxx
> > xxx xxx xxx
> > 
> > You obvious reaction is the dramatic increase or the expotential
> media's
> > graphic presentation of a set of nearly CONSTANT numbers, with
> minor
> > random fluctations from year to year, such as (985, 987, 994) for
> > those three years, while the preceding 10 years varied randomly
> from
> > 980
> > to 1000. The absence of a VERTICAL scale, or an improperly
> truncated
> > vertical scale. are among the most common misleading graphical
> > reporesentations.
See for a particularly
> egregious example of this
I was trying to convey in my post.
> (which Darrell Huff called the geewhiz
> graph; Tufte has also written about it).
Ah yes. Often called the geewhiz factor in graphs and charts.
Now I recall having a modest collection of those geewhiz graphs and
> charts to make my lectures more interesting to those students whose
> minds were on the football field and attended the class only because
> they were required to, to keep their athletic scholorships,
> where the term scholorship was later changed to grantinaid making
> it clear scholorship had nothing to do with it. :)
> Here is a true story about those scholars.
I recall once having an All American football player on a National
> Championship football Team in my statistics class. Of course I
> didn't know he was a football player, let alone an All American
> until this episode took place and my colleagues informed me who
> he was.
After the first quiz when he scored 20 out of 100, while the next
> lowest score in the class of 40 was about 65, it was such an outlier
> performance that I called him to my office to find out what the
> story was, because he attended classes regularly, and even looked
> attentive.
It was then that we realized he was suppsed to be enrolled in Mthsc
> 101, in Room 301; but went to Room 101 where Mthsc 301 was taught.
> No, he didn't pass Mthsc 101 either, but he could sure play ball!!
 Bob.
I normally don't watch Drew Carey, but I just caught a bit of a
rerun flipping through channels. Drew was going back to grad school.
The prof walks in and says, Welcome to Statistical Modeling. So,
what is a statistic? Here's an example: 3% of students who sign up
for this clsss think it is about fashion modeling. You may leave
now. One handsome guy gets up and leaves.
Russell
====
Subject: Re: Box PlotsAcceptance?
ONSuJQ0AAABDeuDwQ9FnSh1VIzGh74o
USA Today I think is most guilty of such graphics  ironically they do
print statistics on the front page every day (if they are still doing
it)
====
Subject: Re: Box PlotsAcceptance?
>It's been at least 15 years since I played with Box plots. I believe
when they
>were introduced some 20 years ago they got something of a mild
acceptance.
Box plots are older than that.
Tukey's boxplot dates back to at least the early 70s, though I think
> his book wasn't published until 1977
> (and I have seen boxplotlike constructs dating back at least to the
> 1940s).
>>Are
>>they now widely use or have any changes been made to the original
approach.
Depends on what you mean by widely. Many people have proposed
> changes.
> I have seen at least 5 different versions of the same basic construct.
>>I used to have the orange ang green books on this subject. I think
Box was one
>author. What were the titles of the books and who, if anyone, was the
other author?
Do you mean Tukey's EDA (Exploratory Data Analysis)? That was
> originally orange IIRC.
Tukey was also an authour on a green book. The book by Mosteller and
> Tukey might have been green, but my memory isn't clear on what books
> were what colour now.
Glen
> I suppose some gauge of how widely these have been accepted is whether
they
> still crop up in applications. Are there any recent practical applications
of
> these methods that have proven useful? Maybe Google can answer this.
Hmmm, I don't know exactly what you mean by practical applications
and useful, but they are used. Here's an example from my former
employer:
http://www.cpc.ncep.noaa.gov/products/predictions/90day/SSTs/ .
Russell

All too often the study of data requires care.
====
Subject: Re: Box PlotsAcceptance?
>
>>I suppose some gauge of how widely these have been accepted is whether
they
>>still crop up in applications. Are there any recent practical applications
of
>>these methods that have proven useful? Maybe Google can answer this.
> Hmmm, I don't know exactly what you mean by practical applications
> and useful, but they are used. Here's an example from my former
> employer:
> http://www.cpc.ncep.noaa.gov/products/predictions/90day/SSTs/ .
Russell
from the real world as opposed to something concocted or artificial. Often
text
book examples, have little detail or are constructed in a way to illustrate
how
one calculates something.

Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
Obz Site: 39¡ 15' 7 N,
121¡ 2' 32 W, 2700 feet
Academic disputes are vicious because so little
is at stake.  Anonymous
Web Page:
====
Subject: Re: Box PlotsAcceptance?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> Do you mean Tukey's EDA (Exploratory Data Analysis)? That was
> originally orange IIRC.
The saying you can't tell a book by its cover now takes on a
new twist, you can't tell a book by its colour!
Mine wasn't orange! I had given this one away to either one of my
former grad students or one of the 10 libraries in China.
Tukey was also an authour on a green book. The book by Mosteller and
> Tukey might have been green, but my memory isn't clear on what books
> were what colour now.
Mine was maroon, NOTHING on the front or back cover, but on the 1inch
edge were MOSTELLER AND TUKEY on top, my initials at the bottom,
and the book title in the middle  the color maroon was chosen by
the book binder! :)
Permit me a bit of historical nostalgia here on DATA ANALYSIS.
Before this book was published, Tukey had given a 1week seminar on
Data Analysis, sponsord by the NSF, circa 1977, to researchers who
were professors at universities, expenses paid by NSF, whose
participants were selected on some competitive basis.
Since I had already been TEACHING my OWN graduate course in Data
Analysis
since 1970, some ideas in which were from John Hartigan (former
colleague
of John Tukey) in John's graduate Data Analysis course at Yale, many
of Tukey's ideas were deja vu. So, never one to turn down a free lunch
that holds promise for a paletable one, I applied and was selected to
be
one of the 40 or so participants in Tukey's seminar.
I should add I was invited to give a colloquium talk at the Princeton
Statistics Department in 1973, and what better way could I bring coal
to New Castle than to title my talk Interactive Data Analysis talking
about how DATA ANALYSIS should, and could, be done with a suitably
designed interactive/conversational software as a supporting
statistical package (which I had already had one implemented in 1972).
I recall Paul Velleman (designer and author of the very fine product
ActivStat was student at Princeton at the time, and so was Dave
Hoaglin,
who assisted Tukey in the seminar.
http://seamonkey.ed.asu.edu/~alex/teaching/WBI/EDA.html
who later coauthored the book, Velleman and Hoaglin (1981), Elements
of EDA.
I couldn't quite say Tukey attended my Princeton talk on DATA ANALYSIS
because he was down with a bad cold (a bug he said), but Paul
Velleman did take me to Tukey's home where I met Tukey for the first
time, and bantered a bit about Data Analysis.
That's a long digression (my patented RANT as my flamers likes
to call them) to document why MY copy of Mosteller and Tukey wasn't
orange or green, but maroon. :)
The Mosteller and Tukey book was one of the fringe benefits (hand outs
of the UNBOUND chapters of the book) at Tukey's research ocnference
seminar, but we had to send it to the binder ourselves.
Now I recall another book which was often refered to as the Green
Book
 and that was Greybill's Applied Linear Models textbook I had used
in my more advanced and theoretical courses at the graduate level.
 Bob.
====
Subject: Re: Box PlotsAcceptance?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
Do you mean Tukey's EDA (Exploratory Data Analysis)? That was
> originally orange IIRC.
The saying you can't tell a book by its cover now takes on a
> new twist, you can't tell a book by its colour!
Mine wasn't orange! I had given this one away to either one of my
> former grad students or one of the 10 libraries in China.
Sorry for this misleading statement about libraries in China! I didn't
mean to imply that there are only 10 libraries in China. :)
Here comes ANOTHER digression (a shorter miniRANT ).
Note added: Well, it started as a miniRANT, but ballooned into
a fullblown RANT, on the subject of STATISTICS dear to my heart.
I am a man (or fish if you prefer) who had led many lives! I told
some of my internet friends that I am just beginning my 10th life 
preaching statistics in USNET newsgroups  like this one!
One of my former lives was a professor of Statistics. When I had
it up to my ears with many folks who called themselves educators,
statisticians, and researchers (alas, some of them are HERE,
though not necessarily worse than some of those trained
statisticians in academia) and many tree stumps who call
themselves students, I voluntarily ended that 8th life cold
turkey, stopped going to the JMS annual meetings, and donated
nearly ALL of my statistics journals and books to 10 different
libraries in China! THOSE were the 10 libraries I meant. :)
The extent of my coldturkey termination of my academic life as
a statistician was that I dropped in the San Francisco annual
meeting a couple years ago, and it was the FIRST time I knew
Tukey had passed away, when I ran into Dave Hoaglin and asked
what the Tukey Memorial Lectures were about. :) I met four
former doctoral students of mine who were presenting papers
at that Meeting, but I left the Meeting before all the
interesting and boring talks began.
Ever since I started kipbitzing and participating in this ng,
I found it both interesting AND challenging, and a much better
(more efficient, more farreaching, and a more diverse audience
MOST of whom are actually interested in STATISTICS) forum to
discuss with other statisticians and educate the general public
on statistical matters.
hundreds of times, nay, thousands of times, in several different
USENET newsgroups, when I insisted that neither the median
nor mode is a statistical average. :)
THAT's how ignorant the general public is about statistics and
statistical matters!
One of my earliest encounters in ngs about what a MODE is, was with
one Professor Brannigan, a professor of law, who said he TAUGHT
and published statistics, yet didn't have the slightest idea of the
definition of a median or mode in staistics. :) This was one
of his posted gems:
====
Subject: Re: Statistical definitions (
VB> I took my whack at the misuse of statistics in Brannigan, Beier and
VB> Berg Risk, Statistical inference, and the Law of Evidence:
VB> the use of Epidemiological data in Toxic Tort cases J. of Risk
VB> Analysis Vol 12 #3 343351
VB> I am personally fascinated by people who are otherwise intelligent
VB> and who spout statistical nonsense.
I am not sure of the otherwise intelligent part, but Vince proceeded
to spout his own nonsense:
VB> e.g. If you have 6 chickens 12 cows and 24 horses you cannot
of posts and flamewar threads in which *I* participated, over this
simple fact. :)
Here is a fairly typical one actually:
>There is no textbook book in statistics at ANY LEVEL, ANYWHERE, that
>presents mean, mode, and median as three forms of
average,
> Webster's Collegiate Dictionary. You can view it online at
webster.com.
RF> Did you use that as a TEXTBOOK in the course you took that you
RF> aced but should have flunked?
Even for one who has never taken a statistics course, doesn't have a
statistics textbook, and chooses to use your webster.com to find out
the meaning of those STATISTICAL terms, said person would have found
the CORRECT meaning and usage by looking up those terms individually:
MODE:
*> 7 a : the most frequent value of a set of data b : a value of
*> a random variable for which a function of probabilities defined
*> on it achieves a relative maximum
That is NOT an average, as I explained to Lee, but could be any
value from the minimum to the maximum, as long as that value is the
most frequent value, of a set of data.
MEDIAN:
*> 2 a : a value in an ordered set of values below and above which
*> there is an equal number of values or which is the arithmetic
*> mean of the two middle values if there is no one middle number
That is NOT an average, as explained by ryan in what he was going
to lecture to his Psych 105 students (a Freshman course, I presume).
The median of a set of data can ALSO be the minimum or the
maximum value of a set of data  quite apart from an average!!
Here's my COUNTERflame
RF> So Jason, you not only should have flunked the course in statistics
RF> you took, you also flunked miserably in the proper use of an
English
RF> dictionary to find out the CORRECT meanings of statistical terms,
RF> as shown to you above. Those definitions and explanations are
RF> CORRECT.
Jason got a grade of A in a statistics taken at UCLA.
RF> For a supposedly educated person who supposedly took a course in
RF> statistics (and claimed that you aced it ), Jason,
RF> you certainly argue very much like a completely uneducated person
RF> who has never taken a course in statistics, or learned how to
RF> use a dictionary properly.
RF>
RF> As I said, it's a sad commentary on your school system, and YOU.
Hey, but don't let that stop you from your old self of being a
smug, smartass. This IS rec.scuba, you know, in which your
behavior is not unexpected, and you have already EARNED your
welldeserved title of an IDIOT here. :)))
 Bob.
And now I return you to the regular channel on outliers, colors
of books, and more RANTS on other factoids that interested ME.
> Tukey was also an authour on a green book. The book by Mosteller
and
> Tukey might have been green, but my memory isn't clear on what
books
> were what colour now.
Mine was maroon, NOTHING on the front or back cover, but on the
1inch
> edge were MOSTELLER AND TUKEY on top, my initials at the bottom,
> and the book title in the middle  the color maroon was chosen by
> the book binder! :)
Permit me a bit of historical nostalgia here on DATA ANALYSIS.
> Before this book was published, Tukey had given a 1week seminar on
> Data Analysis, sponsord by the NSF, circa 1977, to researchers who
> were professors at universities, expenses paid by NSF, whose
> participants were selected on some competitive basis.
Since I had already been TEACHING my OWN graduate course in Data
> Analysis
> since 1970, some ideas in which were from John Hartigan (former
> colleague
> of John Tukey) in John's graduate Data Analysis course at Yale, many
> of Tukey's ideas were deja vu. So, never one to turn down a free
lunch
> that holds promise for a paletable one, I applied and was selected to
> be
> one of the 40 or so participants in Tukey's seminar.
I should add I was invited to give a colloquium talk at the Princeton
> Statistics Department in 1973, and what better way could I bring coal
> to New Castle than to title my talk Interactive Data Analysis
talking
about how DATA ANALYSIS should, and could, be done with a suitably
> designed interactive/conversational software as a supporting
> statistical package (which I had already had one implemented in
1972).
I recall Paul Velleman (designer and author of the very fine product
> ActivStat was student at Princeton at the time, and so was Dave
> Hoaglin,
> who assisted Tukey in the seminar.
http://seamonkey.ed.asu.edu/~alex/teaching/WBI/EDA.html
who later coauthored the book, Velleman and Hoaglin (1981), Elements
> of EDA.
I couldn't quite say Tukey attended my Princeton talk on DATA
ANALYSIS
> because he was down with a bad cold (a bug he said), but Paul
> Velleman did take me to Tukey's home where I met Tukey for the first
> time, and bantered a bit about Data Analysis.
That's a long digression (my patented RANT as my flamers likes
> to call them) to document why MY copy of Mosteller and Tukey wasn't
> orange or green, but maroon. :)
The Mosteller and Tukey book was one of the fringe benefits (hand
outs
> of the UNBOUND chapters of the book) at Tukey's research ocnference
> seminar, but we had to send it to the binder ourselves.
Now I recall another book which was often refered to as the Green
> Book
>  and that was Greybill's Applied Linear Models textbook I had used
> in my more advanced and theoretical courses at the graduate level.
 Bob.
====
Subject: Re: Box PlotsAcceptance?
On 19 Apr 2005 11:26:22 0700, Reef Fish
[snip, a bunch]
hundreds of times, nay, thousands of times, in several different
> USENET newsgroups, when I insisted that neither the median
> nor mode is a statistical average. :)
THAT's how ignorant the general public is about statistics and
> statistical matters!
>
[snip, 20+ lines]
of posts and flamewar threads in which *I* participated, over this
> simple fact. :)
This question has come up in the sci.stat.* groups before.
It seemed noncontroversial to point out that mathematicians
use the word mean in a more general way, but not the
word average  harmonic mean, geometric mean, root
mean square.
As another extension, the 'average' is what minimizes the
squared deviations, the median minimizes the absolute
deviations, and the mode minimizes the count of deviations
(from grouped values).
I don't remember whether anyone else objected to calling
those 'means' or not; I don't.
[snip, bunch more]

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: Box PlotsAcceptance?
> It seemed noncontroversial to point out that mathematicians
> use the word mean in a more general way, but not the
> word average  harmonic mean, geometric mean, root
> mean square.
As another extension, the 'average' is what minimizes the
> squared deviations, the median minimizes the absolute
> deviations, and the mode minimizes the count of deviations
> (from grouped values).
To unify these ideas,
sum = Sigma_k  x_k  m ^n
The mean is the value of m which minimizes sum for n = 2. The median
is the value of m which minimizes the sum for n = 1. The mode is the
value of m which minimizes the sum in the limit that n > 0.
Scott

Scott Hemphill hemphill@alumni.caltech.edu
This isn't flying. This is falling, with style.  Buzz Lightyear
====
Subject: Re: Box PlotsAcceptance?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> On 19 Apr 2005 11:26:22 0700, Reef Fish
> [snip, a bunch]
hundreds of times, nay, thousands of times, in several different
> USENET newsgroups, when I insisted that neither the median
> nor mode is a statistical average. :)
THAT's how ignorant the general public is about statistics and
> statistical matters!
[snip, 20+ lines]
>
THOUSANDS
> of posts and flamewar threads in which *I* participated, over this
> simple fact. :)
This question has come up in the sci.stat.* groups before.
I would have to dig the sci.stat.math archives to see if it could
possibly sink as low as other ngs. I am highly doubtful.
It seemed noncontroversial to point out that mathematicians
> use the word mean in a more general way, but not the
> word average  harmonic mean, geometric mean, root
> mean square.
That was actually the IRRELEVANT issue, though some thought
it was and brought it up, in the other ngs.
As another extension, the 'average' is what minimizes the
> squared deviations, the median minimizes the absolute
> deviations, and the mode minimizes the count of deviations
> (from grouped values).
That was CERTAINLY not the issue in the nonstat newsgroups. It's
irrelevant even in this group because the controversy statement
in question was:
The mode is NOT an average.
It concerns what the mode IS, in statistics, and that it is
NOT an average, in any sense of the word average, or any kind
of definition of a mean.
I don't remember whether anyone else objected to calling
> those 'means' or not; I don't.
[snip, bunch more]

> Rich Ulrich, wpilib@pitt.edu
> http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: Box PlotsAcceptance?
>...
>The mode is NOT an average.
It concerns what the mode IS, in statistics, and that it is
>NOT an average, in any sense of the word average, or any kind
>of definition of a mean.
Communication would be simpler if average had a clear meaning,
but it doesn't, so I disagree (NB. I'm not trying to pick a fight!)
Average, according to Chambers' dictionary, originally meant
a customs duty or similar charge. As this has to be a realisible
value, maybe mode is actually closer in sense to average than is
arithmetic mean.
In my experience, if someone (statistician or otherwise) says
'mean', they mean mean. If they say 'typical', they mean typical.
But if they say 'average', then they could mean either.
So the mode is an average, in at least one sense of the word average'.
Also, can you clarify what you consider
any kind of definition of mean?
If you allow the weighted mean
w = sum(n_i * x_i) / sum(n_i)
to be a mean, then do you allow
w_p = sum(n_i^p * x_i) / sum(n_i^p) ?
What about w_infty = lim_(p>infinity) w_p ?

J.E.H.Shaw [Ewart Shaw] strgh@uk.ac.warwick TEL: +44 2476 523069
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
http://www.warwick.ac.uk/statsdept http://www.ewartshaw.co.uk
3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@:2^:2))&.>@]^:(i.@[) <#:3 6 2
====
Subject: Re: Box PlotsAcceptance?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
>...
>The mode is NOT an average.
It concerns what the mode IS, in statistics, and that it is
>NOT an average, in any sense of the word average, or any kind
>of definition of a mean.
Communication would be simpler if average had a clear meaning,
> but it doesn't, so I disagree (NB. I'm not trying to pick a fight!)
I think you're still missing the point that no matter HOW you describe
or define an average or mean, the MODE is NOT it, because the MODE
is the point of highest frequency (or the relative maximum of a pdf).
It has NOTHING to do with the mean or average of a set of data or a
pdf.
 Bob.
====
Subject: Re: Box PlotsAcceptance?
On 19 Apr 2005 18:47:50 0700, Reef Fish
On 19 Apr 2005 11:26:22 0700, Reef Fish
[...]
RU This question has come up in the sci.stat.* groups before.
RF I would have to dig the sci.stat.math archives to see if it could
> possibly sink as low as other ngs. I am highly doubtful.
IIRC, it was crossposted from some other group,
by someone wanting a referee.
RU It seemed noncontroversial to point out that mathematicians
> use the word mean in a more general way, but not the
> word average  harmonic mean, geometric mean, root
> mean square.
RF That was actually the IRRELEVANT issue, though some thought
> it was and brought it up, in the other ngs.
Well, it is irrelevant if your point is
I'm RIGHT and you're an IDIOT.
But it is intended to be educational.
I believe that it would be (usually) satisfying to intelligent
inquiry. It is not hard to see how the error would arise, since
the Great Unwashed have had few reasons to ever
distinguish between the two words. This lays out the
distinction, and *who* has made it, and why the confusion
as come up.
[snip, detail and repetition]

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: Box PlotsAcceptance?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
RF That was actually the IRRELEVANT issue, though some thought
> it was and brought it up, in the other ngs.
Well, it is irrelevant if your point is
> I'm RIGHT and you're an IDIOT.
> But it is intended to be educational.
No, your point is irrelevant because the issue is the
definition and meaning of a statistial MODE.
What's the relevance of your comment relative to the MODE definition?
> RU > It seemed noncontroversial to point out that mathematicians
> > use the word mean in a more general way, but not the
> > word average  harmonic mean, geometric mean, root
> > mean square
You need to be more focused.
The same kind of unfocused comments from you when the subject
was the meaning of the SIGN of a multiple regression coefficient,
and you went off the tangent to some irrelevant issues in
psychometrics, without discussing the meaning of the SIGN.
BTW, have you read Mosteller and Tukey on that WOES of Regression
yet?
 Bob.
====
Subject: Re: Box PlotsAcceptance?
On 20 Apr 2005 11:36:14 0700, Reef Fish
>
RF > That was actually the IRRELEVANT issue, though some thought
> > it was and brought it up, in the other ngs.
Well, it is irrelevant if your point is
> I'm RIGHT and you're an IDIOT.
> But it is intended to be educational.
No, your point is irrelevant because the issue is the
> definition and meaning of a statistial MODE.
What's the relevance of your comment relative to the MODE definition?
> hundreds of times, nay, thousands of times, in several different
> USENET newsgroups, when I insisted that neither the median
> nor mode is a statistical average. :)
THAT's how ignorant the general public is about statistics and
> statistical matters!
You have a point  that I missed the point  if the
posters really did not know the definitions, and could
not give proper examples, of median and mode.
I still read your previous post as describing a *semantic*
problem, which is solved by substituting the word
mean for average; and where it is meanspirited of
you to regard it as a gross ignorance.
Did you overlook that possibility entirely, then?
[snip, insults  beginning to remind me of W. Chambers]
> BTW, have you read Mosteller and Tukey on that WOES of Regression
> yet?
I mentioned elsewhere that I enjoyed the Tukey texts.
Googling groups shows that I have previously, on various
occasions, recommended (in sci.stat.*) that book, Tukey's
EDA, and the volume edited by Hoaglin, Mosteller, and Tukey.

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: A statistical MODE is NOT an Average
<5scd61tmj8dtqrgfge80e19g7gtlqrtdh1@4ax.com>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> On 20 Apr 2005 11:36:14 0700, Reef Fish
> No, your point is irrelevant because the issue is the
> definition and meaning of a statistial MODE.
What's the relevance of your comment relative to the MODE
definition?
You have a point  that I missed the point  if the
> posters really did not know the definitions, and could
> not give proper examples, of median and mode.
That should have been the end of clearing YOUR misunderstding.
Of course I have a point, and the ONLY point. The declarative
statement (I even used it in the SUBJECT, which I'll do again)
is A MODE is NOT an average.
[snip, insults  beginning to remind me of W. Chambers]
Quid pro quo, Richard. And I haven't called you a Mental Midget
or Idiot yet! :)
BTW, have you read Mosteller and Tukey on that WOES of Regression
> yet?
I mentioned elsewhere that I enjoyed the Tukey texts.
That's just your diversionary tactic. You referred to his first
book which had NOTHING about the WOES of Regression Coefficients
in the two PAGES I cited.
You just swept you own blunder under the rug as you're doing now.
Googling groups shows that I have previously, on various
> occasions, recommended (in sci.stat.*) that book, Tukey's
> EDA, and the volume edited by Hoaglin, Mosteller, and Tukey.
NWITHER of those was the book I recommended for the expected sign
abusers to read. Nor was what I cited taken from either one of
these books!
Let's face it. You never read the Mosteller and Tukey CHAPTER,
and you never understood the SUBSTANCE of that chapter about
the mistakes you've been making.
 Bob.
> 
> Rich Ulrich, wpilib@pitt.edu
> http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: A statistical MODE is NOT an Average
On 20 Apr 2005 14:00:55 0700, Reef Fish
>
[... ]
You have a point  that I missed the point  if the
> posters really did not know the definitions, and could
> not give proper examples, of median and mode.
That should have been the end of clearing YOUR misunderstding.
Of course I have a point, and the ONLY point. The declarative
> statement (I even used it in the SUBJECT, which I'll do again)
> is A MODE is NOT an average.
To borrow your critique of me  That seems to be evasive.
 I promise: I own all three Tukey books mentioned, and I read
them all, and I recommended them all.
Did the posters *not* know the definitions?
*Were* you fussing them for using average where they
should have said mean and that's the whole of it?
[ ... ]

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: A statistical MODE is NOT an Average
<5scd61tmj8dtqrgfge80e19g7gtlqrtdh1@4ax.com>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
This should definitely conclude my exchange with you on these two
topics:
1. The SIGN of a multiple regression coefficient may be positive OR
negative, depending ENTIRELY on what OTHER variables are in the
regression equation. NONE of those who used the expected sign
fallacy cannot argue successfully against Mosteller and Tukey's
declaration of it being one of the WOEs of regression by those
poorly trained in the subject.
2. The MODE is not an Average.
> [... ]
> > You have a point  that I missed the point  if the
> > posters really did not know the definitions, and could
> > not give proper examples, of median and mode.
That should have been the end of clearing YOUR misunderstding.
Of course I have a point, and the ONLY point. The declarative
> statement (I even used it in the SUBJECT, which I'll do again)
> is A MODE is NOT an average.
To borrow your critique of me  That seems to be evasive.
But that was the actual statement of the controversy, archived by
is true.
>  I promise: I own all three Tukey books mentioned, and I read
> them all, and I recommended them all.
Then you should read and reread Chapter 13 of Mosteller and Tukey
on the WOES of Regression. Learn the statistical SUBSTANCE in that
one chapter, and rid yourself of all the blunders you have been
spouting on the expected sign discussion.
Did the posters *not* know the definitions?
Most of them didn't. Many of them argue even after being shown the
correct definition. Just like you arguing about the expected sign
in multiple regression after a lucid and transparent explantion of
why it is untenable, by Mosteller and Tukey.
> *Were* you fussing them for using average where they
> should have said mean and that's the whole of it?
ABSOLUTELY not. That was never the question.
You should learn how to use the archives! (via the advanced search
could easily have seen it for yourself how obtuse and argumentative
discussants in rec.* newsgroups are.
I am beginning to get that feeling on at least one or two of the
discussants in sci.stat.math, amongst those who should know better!
 Bob.
[ ... ]

> Rich Ulrich, wpilib@pitt.edu
> http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: A statistical MODE is NOT an Average
 concerning just the mode and average question.
On 20 Apr 2005 17:53:02 0700, Reef Fish
>
[...]
> Did the posters *not* know the definitions?
Most of them didn't. Many of them argue even after being shown the
> correct definition. Just like you arguing about the expected sign
> in multiple regression after a lucid and transparent explantion of
> why it is untenable, by Mosteller and Tukey.
> *Were* you fussing them for using average where they
> should have said mean and that's the whole of it?
ABSOLUTELY not. That was never the question.
You should learn how to use the archives! (via the advanced search
> could easily have seen it for yourself how obtuse and argumentative
> discussants in rec.* newsgroups are.
I didn't try Google before, because I wasn't eager
to see you incite folks to flame you. My quick
check right now was a bit surprising  you seem to
have reported both major features a bit askew.
For the notes I scanned in a thread around September 5,
2002, the actual definition of Mode was not actively
disputed. Several people did post naive statements
apparently showing that they had Normal distributions
in mind, without making claims that this is the definition.
The argumentative (and insulting) poster was Reef Fish.
Further: the definition from a good dictionary is
usually enough to establish that a usage is moderately
widespread. MW10 says Average can be used for
mean, median, mode. Since there is no languagecourt
for English (there is one for French), that testimony is
worth far more than you credited it  there, or here.
for author:ulrich  mostly, where I recommend using
7 threads for author:large_nassau_grouper@yahoo.com.

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: A statistical MODE is NOT an Average
<5scd61tmj8dtqrgfge80e19g7gtlqrtdh1@4ax.com>
<0edg611lbrc3op8bfn0vesuh0vgp1bh0de@4ax.com>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
>  concerning just the mode and average question.
> I didn't try Google before, because I wasn't eager
> to see you incite folks to flame you.
Like I incited you to flame me because I pointed out
several blunders of yours in the expected sign threads
relating to multiple regression, correlation and causation,
and others?
> For the notes I scanned in a thread around September 5,
> 2002, the actual definition of Mode was not actively
> disputed.
It's not worth my time to point out all your ERRORS here:
Suffices to point out that
The FIRST of my posts on that subject in the rec.games.bridge
thread in which Richard Pavlicek (a wellknown bridge player)
pointed out a trivia concerning the MODE vs mean of certain
bridgehandpatterns, and one Chuck Arthur had already acknowledged
his mistake:
CA> The first thing that I did was to fall into Richard's trap:
responding to
CA> average instead of more likely. Henk pointed out this flaw
before I had
CA> a chance to make a fool of myself, so I returned to the drawing
board.
By then, it had already been unanimously agreed, at least among
Pavlicek, Chuck Arthur, Henk, (and lastly me) that the mode is
NOT an average or mean!
This was my followup to Chuck:
RF> Yup. The mode is a concept that inexplicably alludes many
who
RF> even had some statistical training. Over a period of YEARS, there
RF> are still posters in the rec.scuba group that insists that the
mode is
RF> an average, including a Professor of law at Maryland U who said
RF> he TAUGHT statistics, and he obviously didn't know the first thing
RF> about statistics. :)
I cited the same Professor in sci.stat.math.
It was simply a statement of a lamentable FACT. Did it sound like I
was inciting flames in THAT group?
There were so many in that ng who chose to make a fool of themselve
AFTER my paragraph above that I had to make a catalog of the Village
Idiots in that ng. :) Once my credibility in math, stat, and bridge
are conceded by posters in that group, I haven't been flamed a single
time this year in that group AFAIK. The former flamers are still there.
The same thing happened in other ngs too.
EVERY time you flame me on my posts about STATISTICS, you lose
a bit (or a lot) of your own credibility, because you are batting
100% being WRONG in those subjects.
You're engaging in an activity you CANNOT win. Dozens of others had
tried it since 1988 when I started posting in USENET newsgroups and
LISTSERV lists. None succeeded.
> The argumentative (and insulting) poster was Reef Fish.
And the nonargumentative (and noninsulting) poster was
the allknowing Richard Ulrich no doubt? :)
> for author:ulrich  mostly, where I recommend using
You couldn;t even find your OWN posts. On par with your knowledge
about Multiple Regression theory and methodology.
Rich.Ulrich@comcast.net, and took 0.17 to find 4620 threads
by Richard Ulrich, dating back to August 3 1993, and one
attributed to YOU, on the subject of drivel or not to drivel
on Aug 11, 1993, but apparently posted by Andras Vancsa
in 1994.
How did you manage to miss thousands of your own threads?
> I didn't try Google before,
And it showed in your biased, uninformed, and misguided
ad hominem comments about ME above.
You didn't learn Multiple Regression theory and methods properly
either, but why should THAT deter you from arguing on what you
don't know?
> I find 7 threads for author:large_nassau_grouper@yahoo.com.
LOL! I have to send you the bill for cleaning my monitor for all
that coffe on it CAUSED by your comment.
Google took 0.24 seconds to find 2990 threads by that posting
address which I didn't start using until fairly recently. Had you
asked
for author Reef Fish, you would have found 6320 threads dating
You should have known that.
Don't bother wasting your time to try to excavate DIRT in those
posts of mine. None of my flamers succeeded, and they are
much more skillful than YOU in the art of flaming and searching
archives.
 Bob.
====
Subject: Using Google. Was: Re: A statistical MODE is NOT an Average
On 21 Apr 2005 21:41:15 0700, Reef Fish
>
[snip, other]
for author:ulrich  mostly, where I recommend using
You couldn;t even find your OWN posts. On par with your knowledge
> about Multiple Regression theory and methodology.
People who have been reading my posts for years will
know that I follow a convention of using anglebrackets
I learned that elsewhere. I did not realize it was obscure.
So, I stated, Google finds me in 244 threads where I advocated
Googling, and telling people how to do it. Google finds you in 7,
for the same criteria.
Rich.Ulrich@comcast.net, and took 0.17 to find 4620 threads
> by Richard Ulrich, dating back to August 3 1993, and one
> attributed to YOU, on the subject of drivel or not to drivel in 1994.
How did you manage to miss thousands of your own threads?
As per above  I was explicitly selecting for words.
You should have paused and wondered, after noting
ridiculous discrepancies in numbers. Shouldn't you?
I've figured out before this how to conduct an effective
search for my own posts:
in sci.stat.* and comp.softsys.stat.spss . 17+1 of those
were by someone other than me.
< author:ulrich author:rich author:richard >
I've made relatively few posts anywhere else.
[...]
Don't bother wasting your time to try to excavate DIRT in those
> posts of mine. None of my flamers succeeded, and they are
> much more skillful than YOU in the art of flaming and searching
> archives.
We can see you here, Bob.

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Stepwise regression. Was: A statistical MODE...
On 20 Apr 2005 17:53:02 0700, Reef Fish
This should definitely conclude my exchange with you on these two
> topics:
[snip, rest]
If we are done with that, may I invite you to post on
a special topic that you have hinted at 
How to do stepwise regression that will replicate.
My quick reflex about stepwise algorithms, has been,
Don't bother trying, if you want something with meaning.
I think you agree with that, though with a different twist.
number of successful predictions, as classroom exercises
or otherwise.
I'm asking if you will describe what has worked for you,
at least in brief. There are different numbers of predictors
(5, 15, 100?), or sample Ns (50, 500, 5000?), or Rsquared
expected.
You mentioned, elsewhere, stepdown over stepup.
You also mentioned subsamples and crossvalidation.
When do you use plevels, and How extreme?
How much would you say that users should depend
on holdout samples and replication?
 and so on, as you see fit.

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: A statistical MODE is NOT an Average
<5scd61tmj8dtqrgfge80e19g7gtlqrtdh1@4ax.com>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
This should definitely conclude my exchange with you on these two
> topics:
1. The SIGN of a multiple regression coefficient may be positive OR
> negative, depending ENTIRELY on what OTHER variables are in the
> regression equation.
Sn important correction of a wrongly made statement:
> NONE of those who used the expected sign
> fallacy cannot argue successfully against Mosteller and Tukey's
The cannot should be can of course. NONE CAN.
> declaration of it being one of the WOEs of regression by those
> poorly trained in the subject.
2. The MODE is not an Average.
 Bob.
====
Subject: Re: A statistical MODE is NOT an Average
On 20 Apr 2005 14:00:55 0700, Reef Fish
>
[... ]
Googling groups shows that I have previously, on various
> occasions, recommended (in sci.stat.*) that book, Tukey's
> EDA, and the volume edited by Hoaglin, Mosteller, and Tukey.
NWITHER of those was the book I recommended for the expected sign
> abusers to read. Nor was what I cited taken from either one of
> these books!
(1) that book, being Mosteller and Tukey; (2) Tukey's EDA;
(3) edited volume. Now I know you are reading too fast.
Let's face it. You never read the Mosteller and Tukey CHAPTER,
> and you never understood the SUBSTANCE of that chapter about
> the mistakes you've been making.
there is *information* in the resulting MR  information
which can be explored further. That's a clear message,
if you want to read it, in Tukey's words about the variables
in an equation. Signs depend on which variables are there,
yes, of course. That's the starting place, not the end.
You *seem* willing  no, determined  to elevate an
equation to some mystical plane of knowledge, which
cannot be touched, tampered with, or examined further,
based on information about the variables themselves.
 I'm still trying to find a wedge to open communication.

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: Box PlotsAcceptance?
>
>>It's been at least 15 years since I played with Box plots. I believe
when they
>
>>were introduced some 20 years ago they got something of a mild
acceptance.
Box plots are older than that.
Tukey's boxplot dates back to at least the early 70s, though I think
> his book wasn't published until 1977
> (and I have seen boxplotlike constructs dating back at least to the
> 1940s).
>>Are
>>they now widely use or have any changes been made to the original
approach.
Depends on what you mean by widely. Many people have proposed
> changes.
> I have seen at least 5 different versions of the same basic construct.
>>I used to have the orange ang green books on this subject. I think
Box was one
>
>>author. What were the titles of the books and who, if anyone, was the
other author?
Do you mean Tukey's EDA (Exploratory Data Analysis)? That was
> originally orange IIRC.
Tukey was also an authour on a green book. The book by Mosteller and
> Tukey might have been green, but my memory isn't clear on what books
> were what colour now.
Glen
correct to me. The reason I may have trouble finding them is that by now the
colors may have faded to something entirely different!
On occasion I've seen box plots used in newspapers and government documents
but
certainly not very often.
====
Subject: Statistic class project
I need to collect 100 data entry for my statistic class project. Please
complete my survey. Max 15sec. http://www.epixel.net/statistic.php THANK
YOU!
====
Subject: Help for Delta Method in Correspondence Analysis
I am PhD candidate (Department of Applied Informatics, University of
Macedonia, Thessaloniki, Greece) and I am trying to understand how the delta
method is applied to Correspondence Analysis. My problem is what are the
analytical expressions that relate the multinomial counts or proportions, of
the corresponding contingency table, with the various parameters (singular
values, factorial coordinates etc). Refering to various authors (Gifi,
Marcus, Rao, Israels, Greenacre and others) I have found only a general
description of the method applied to multinomial or binomial counts. None of
the above authors give the mathematical formulae to understand the relation
between the above mentioned parameters (singular values, factorial
coordinates etc) and the multinomial counts or percentages. Is there any way
to help me with this subject? Because my mathematical background is not very
rich I will appreciate to help me by giving not only references but also some
arithmetical examples,
if possible.
Angelos Markos
PhD Candidate,
Department of Applied Informatics,
University of Macedonia, Thessaloniki, Greece
Tel  Fax: 00302310891848
====
Subject: Re: Help for Delta Method in Correspondence Analysis
I believe you'll find that people who pioneered CA under that name or
under the name dual scaling follow the Classification Society discussion
list  classl. There is a strong overlap in membership with the
Psychometric Society and the Math Psych society, so you might Google
those if you don't get help here. Go to
http://www.pitt.edu/~csna/index.html
click on
Art
Art@DrKendall.org
Social Research Consultants
University Park, MD USA
(301) 8645570
I am PhD candidate (Department of Applied Informatics, University of
Macedonia, Thessaloniki, Greece) and I am trying to understand how the delta
method is applied to Correspondence Analysis. My problem is what are the
analytical expressions that relate the multinomial counts or proportions, of
the corresponding contingency table, with the various parameters (singular
values, factorial coordinates etc). Refering to various authors (Gifi,
Marcus, Rao, Israels, Greenacre and others) I have found only a general
description of the method applied to multinomial or binomial counts. None of
the above authors give the mathematical formulae to understand the relation
between the above mentioned parameters (singular values, factorial
coordinates etc) and the multinomial counts or percentages. Is there any way
to help me with this subject? Because my mathematical background is not very
rich I will appreciate to help me by giving not only references but also some
arithmetical examples
,
> if possible.
> Angelos Markos
> PhD Candidate,
> Department of Applied Informatics,
> University of Macedonia, Thessaloniki, Greece
> Tel  Fax: 00302310891848
====
Subject: Convergence of random variables
When talking about almost sure convergence, do we have to clarify the
underlying sample space beforehand?
Say for example, let X_n be iid such that
P(X_n)=1=P(X_n)=0=1/2,
then what's lim X_n?
It looks to me that the answer is X_1. However, by the BorelCantelli lemma
(second), we conclude that X_n=1 io and X_n=0 io. And lim X_n is a tail
function, so P(limsup X_n = 1) is either 0 or 1. But all these two things
are not true if we clarify the probability space, say ([0,1], B[0,1],
Lebesgue measure), then if we set X_n(x) = 1 if 0<=x<1/2, X_n(x) = 0 if
1/2<=x<=1, we have P(x: limsup X_n(x) = 1) = 1/2.
What's wrong there? I'm really confused.
====
Subject: Central Limit Theorem?
I'm having trouble understanding the central limit theorem in the context of
some data I am looking at.
Assume that I have a data set of reasonable size e.g. 100 measurements. Say
I take the standard error of the mean progressively throughout the data
set e.g. after 2 measurements, then again for 3, 4, 5 etc so I end up with 99
values for the standard error (a new value for each sucessive data point). A
plot of these values will of course be most variable for small n, and then
less so for large n (assuming all data points are from the same population).
Can anybody confirm whether this decrease in variability is due to the
CLT, or is there some other way to explain it?
====
Subject: Re: Central Limit Theorem?
Mr. Herman Rubin and Bob
I dare to ask if computers, because work with a finite number of bits,
cannot provide results free of roundingoff.
Specially to Bob
Your is certainly judicious, but let me add some presumptuous
trifle. Can I?
Need not to be remembered that Normality is a Model, a concept that mimics
Nature but not exactly fits it. Or better, fits the set of proprieties that
maters to put in evidence and is the at the epoch. A model is
always growing in complexity in order to include new properties. Normality is
merely the first step. Bla, bla, bla.
Certainly it is rather ridiculous to stress a so basic and uncontroversial
thing. I beg your pardon, I mean.
licas_@hotmail.com
====
Subject: Re: Central Limit Theorem?
In this thread (CLT) I wish to illustrate how the probabilities of the
total of points obtained by throwing 7 (perfect) dice are approximate to
those evaluated by the normal distribution
This is a trivial, only , exercise aiding to assimilate an
extremely useful Theorem.
Concepts
The random experiment (trial) consists in throwing the dice (simultaneously
or not),
The random variable X is the points sum.
X=X_1+X_2+X_3+X_4+X_5+X_6+X_7
The first dice shows X_1 points, the second X_2, etc., the seventh X_7
The trials are independent and the points in each dice are IID, independent
and identically distributed. Cft. LindebergLevy conditions.
Each X has mean miu = 7*(3.5)=24.5
The variance for each dice is
[(13.5)^2+(23.5)^2+...+(63.5)^2]*(1/6) =
=2.875
Then the variance of the total of points(in each trial) is
var=7*2.875=20.125
REM seven
CLS
DEFDBL AZ
miu = 24.5: sigma = SQR(20.125)
DIM x(42), c(42)
FOR i1 = 1 TO 6: FOR i2 = 1 TO 6
FOR i3 = 1 TO 6: FOR i4 = 1 TO 6
FOR i5 = 1 TO 6: FOR i6 = 1 TO 6
FOR i7 = 1 TO 6: j = j + 1
sum = i1 + i2 + i3 + i4 + i5 + i6 + i7
LOCATE 10, 10
PRINT USING ######; 6 ^ 7  j
x(sum) = x(sum) + 1 / (6 ^ 7)
sum = 0
NEXT i7: NEXT i6: NEXT i5
NEXT i4: NEXT i3: NEXT i2: NEXT i1
c(3) = x(3)
FOR k = 3 TO 41
c(k + 1) = c(k) + x(k): z = (k  miu  .5) / sigma
PRINT USING ## ###.#### #.#### ; k; z; c(k);
NEXT k : END
Results:
Score35points, z=2.2291, cumulative prob.=0.9879
Score37points, z=2.6749, cumulative prob.=0.9972
Checking:
Prob(z<=2.2291)=0.9871
Prob(z<=2.6749)=0.9963
Rounding to the third decimal the differences are 0.001.
The Òseven dice strategyÓ could be, in
principle, used to simulate normal data but all the approximate methods are
discarded (I dare to say) in comparison with the BOXMULLER one, exact and
fast.
licas_@hotmail.com
====
Subject: Re: Central Limit Theorem?
>In this thread (CLT) I wish to illustrate how the probabilities of the
total of points obtained by throwing 7 (perfect) dice are approximate to
those evaluated by the normal distribution
>This is a trivial, only , exercise aiding to assimilate an
extremely useful Theorem.
>Concepts
>The random experiment (trial) consists in throwing the dice (simultaneously
or not),
>The random variable X is the points sum.
>X=X_1+X_2+X_3+X_4+X_5+X_6+X_7
>The first dice shows X_1 points, the second X_2, etc., the seventh X_7
>The trials are independent and the points in each dice are IID, independent
and identically distributed. Cft. LindebergLevy conditions.
>Each X has mean miu = 7*(3.5)=24.5
>The variance for each dice is
>[(13.5)^2+(23.5)^2+...+(63.5)^2]*(1/6) =
>=2.875
>Then the variance of the total of points(in each trial) is
var=7*2.875=20.125
>REM seven
>CLS
>DEFDBL AZ
>miu = 24.5: sigma = SQR(20.125)
>DIM x(42), c(42)
>FOR i1 = 1 TO 6: FOR i2 = 1 TO 6
>FOR i3 = 1 TO 6: FOR i4 = 1 TO 6
>FOR i5 = 1 TO 6: FOR i6 = 1 TO 6
>FOR i7 = 1 TO 6: j = j + 1
>sum = i1 + i2 + i3 + i4 + i5 + i6 + i7
>LOCATE 10, 10
>PRINT USING ######; 6 ^ 7  j
>x(sum) = x(sum) + 1 / (6 ^ 7)
>sum = 0
>NEXT i7: NEXT i6: NEXT i5
>NEXT i4: NEXT i3: NEXT i2: NEXT i1
>c(3) = x(3)
>FOR k = 3 TO 41
>c(k + 1) = c(k) + x(k): z = (k  miu  .5) / sigma
>PRINT USING ## ###.#### #.#### ; k; z; c(k);
>NEXT k : END
>Results:
>Score35points, z=2.2291, cumulative prob.=0.9879
>Score37points, z=2.6749, cumulative prob.=0.9972
>Checking:
>Prob(z<=2.2291)=0.9871
>Prob(z<=2.6749)=0.9963
>Rounding to the third decimal the differences are 0.001.
>The seven dice strategy could be, in principle, used to simulate normal
data but all the approximate methods are discarded (I dare to say) in
comparison with the BOXMULLER one, exact and fast.
BoxMuller is exact, modulo computer roundoff, but it is
NOT fast. Also, the computer roundoff can be considerable.
Both the reverse Ziggurat and acceptancereplacement are
as accurate and faster.
If one wants an exact method, assuming the input random
bits are really random, I can provide it. For very high
accuracy, methods of this type will beat anything, but
not for what is wanted now. There is not computer optimal
method, as this would take infinite storage, but one can
come quite close. I have not written up any of the
detailed methods, but they can be deduced from what is
in my technical reports.
If wanted, I can come up with algorithms which will generate
random variables which are normal with mean exactly e and
variance exactly pi, and it is not necessary to know e and
pi to get reasonably efficient ways of doing this. Computer
roundoff is not present in these methods.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
<3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
<3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>,
< snip >
Herman, while I agree with your comments to Afonso, I find your
statement
below very curious and paradoxical, especially the last sentence:
> If wanted, I can come up with algorithms which will generate
> random variables which are normal with mean exactly e and
> variance exactly pi, and it is not necessary to know e and
> pi to get reasonably efficient ways of doing this. Computer
> roundoff is not present in these methods.
I am sure what you mean is that the method of generation will
produce, IN THEORY, data from N(e, pi), but in practice, your
use of exact and computer roundoff is not present is surely
an oxymoron of the unmistable kind.
IN PRACTICE, of course nothing is exactly normal, let alone
knowing the exact value of e or pi. Also, IN PRACTICE, it
doesn't matter because ROUNDOFF (computer or computed to
100,000 digit precision) will not enable one to distinquish
While my comments seem nitpicking in a way, I think it's
important to realize that IN PRACTICE, EVERYTHING is subject
to ROUNDOFF.
To quote Flash Gordon, M.D., who posted these immortal
words in his .sig, in 1993:
FG> in theory, there is no difference between
FG> theory and practice. but in practice, there is.
FG> flash gordon, m.d. f...@well.sf.ca.us
Flash is a PRACTICAL Man (and M.D.) of many interests:
http://www.motosites.com/Detailed/396.html
Not mentioned on that home page is the fact that both he
and his wife Shanna are certified scuba divers. I dived
with both of them in 1993 after they were both newly
certified by an instructor in Cozumel I recommended to
them.
http://www.docflash.com/
We need more PRACTICAL people like Flash in this world,
not to mention INTERESTING people in any field of
endeavor.
The use of the term exactly Normal has its place only
in THEORY, never in PRACTICE.
I have a THEOREM in one chapter of my Data Analysis
Lecture Notes I've used for many years:
Theorem: NOTHING in the Real World is Normally Distributed.
The proof can literally be written on the margin of a
page (re: Fermat :)) that I would not insult this
readership by showing an actual proof.
 Bob.
====
Subject: Re: Central Limit Theorem?
><3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>,
>< snip Herman, while I agree with your comments to Afonso, I find your
>statement
>below very curious and paradoxical, especially the last sentence:
>> If wanted, I can come up with algorithms which will generate
>> random variables which are normal with mean exactly e and
>> variance exactly pi, and it is not necessary to know e and
>> pi to get reasonably efficient ways of doing this. Computer
>> roundoff is not present in these methods.
>I am sure what you mean is that the method of generation will
>produce, IN THEORY, data from N(e, pi), but in practice, your
>use of exact and computer roundoff is not present is surely
>an oxymoron of the unmistable kind.
>IN PRACTICE, of course nothing is exactly normal, let alone
>knowing the exact value of e or pi. Also, IN PRACTICE, it
>doesn't matter because ROUNDOFF (computer or computed to
>100,000 digit precision) will not enable one to distinquish
The procedures produce the some of the bits, all the rest
of the bits being filled in with random bits. What I
stated is correct; if the bits are honest random, the
distribution results are EXACT, and there is no roundoff
introduced by the computer, any computer if programmed
correctly.
>While my comments seem nitpicking in a way, I think it's
>important to realize that IN PRACTICE, EVERYTHING is subject
>to ROUNDOFF.
Read the above. When computers test the primality
of Mersenne numbers, there is NO roundoff. When
factoring large integers, there is NO roundoff.
It is at first surprising that this can be the case
in generating nonuniform random variables, but it
is, and it is easy to prove. I did not state that
the results are often competitive now, but the amount
of computation essentially does not depend on the
number of bits wanted. The most complicated distribution
of interest now for which there is, in my opinion,
a competitive procedure of this type is the density
6x(1x) on (0,1). Here is the entire procedure:
Let N be the distance to the first one in
a random bit stream. Define M to be N/2,
rounded up.
Let K be the distance from that bit to the
next one.
Change, if necessary, the M+Kth bit after the
binary point in a 01 uniform random number to
be the opposite of the Mth bit.
This is the entire procedure; any deviations from the
desired distribution are in the candidates for random
numbers themselves, not coming from computer calculations,
all of which are given here.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
<3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
<3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>,
< snip
>Herman, while I agree with your comments to Afonso, I find your
>statement
>below very curious and paradoxical, especially the last sentence:
> If wanted, I can come up with algorithms which will generate
>> random variables which are normal with mean exactly e and
>> variance exactly pi, and it is not necessary to know e and
>> pi to get reasonably efficient ways of doing this. Computer
>> roundoff is not present in these methods.
Herman, you missed the point of roundoff. See my clarification
below, which you may not have seen when you typed your response
above.
I am sure what you mean is that the method of generation will
>produce, IN THEORY, data from N(e, pi), but in practice, your
>use of exact and computer roundoff is not present is surely
>an oxymoron of the unmistable kind.
IN PRACTICE, of course nothing is exactly normal, let alone
>knowing the exact value of e or pi. Also, IN PRACTICE, it
>doesn't matter because ROUNDOFF (computer or computed to
>100,000 digit precision) will not enable one to distinquish
The procedures produce the some of the bits, all the rest
> of the bits being filled in with random bits. What I
> stated is correct; if the bits are honest random, the
> distribution results are EXACT, and there is no roundoff
> introduced by the computer, any computer if programmed
> correctly.
No, the distribution result CANNOT be exact, when some of the
numbers are INFINITE in precision, if exact!
While my comments seem nitpicking in a way, I think it's
>important to realize that IN PRACTICE, EVERYTHING is subject
>to ROUNDOFF.
Read the above. When computers test the primality
> of Mersenne numbers, there is NO roundoff. When
> factoring large integers, there is NO roundoff.
Mersennes numbers are FINITE! So are the integer FACTORS.
Yes, Mersenne and Sophie Germaine numbers are computed to
thousands of digits with no roundoff.
But the tail ends of a NORMAL distribution are INFINITE!
< procedure snipped because it is not relevant to the roundoff question
This is the entire procedure; any deviations from the
> desired distribution are in the candidates for random
> numbers themselves, not coming from computer calculations,
> all of which are given here.
But as soon as you do anything PRACTICAL with it, whether on a
computer or otherwise, there will be ROUNDOFF, in the sense that
there will be ROUNDOFF on any set of numbers defined on the entire
real line with POSITIVE probability on arbitrarily large, or
irrational numbers, that do NOT lend themselves to EXACT
representation, as in large Mersenne primes or other large INTEGERS.
 Bob.
====
Subject: Re: Central Limit Theorem?
>><3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>,
< snip >Herman, while I agree with your comments to Afonso, I find your
>>statement
>>below very curious and paradoxical, especially the last sentence:
>>> If wanted, I can come up with algorithms which will generate
>>> random variables which are normal with mean exactly e and
>>> variance exactly pi, and it is not necessary to know e and
>>> pi to get reasonably efficient ways of doing this. Computer
>>> roundoff is not present in these methods.
>Herman, you missed the point of roundoff. See my clarification
>below, which you may not have seen when you typed your response
>above.
I did not; you missed what I said. Any trailing bits
which are not stored in the machine are random bits, to
be produced if needed. Randomization allows us not to
have the full description of the number there, as we
can fill in additional bits as needed.
>>IN PRACTICE, of course nothing is exactly normal, let alone
>>knowing the exact value of e or pi. Also, IN PRACTICE, it
>>doesn't matter because ROUNDOFF (computer or computed to
>>100,000 digit precision) will not enable one to distinquish
that the procedure will give a different answer; the
answer from the procedure is filled out to whatever
accuracy is wanted, and if more is needed, and the
number of bits prescribed has already been reached,
additional random bits are brought in.
>> The procedures produce the some of the bits, all the rest
>> of the bits being filled in with random bits. What I
>> stated is correct; if the bits are honest random, the
>> distribution results are EXACT, and there is no roundoff
>> introduced by the computer, any computer if programmed
>> correctly.
>No, the distribution result CANNOT be exact, when some of the
>numbers are INFINITE in precision, if exact!
You fail to realize what CAN be done. The fact that
lower semicontinuity is enough suffices to find a
way to do it. To illustrate, I will show how to
generate a number which is uniform in (0, pi/4).
This procedure is not optimal; getting a fully optimal
procedure is rarely possible. But it is simple.
It is hard to write or read the program, so I will
describe it. Since pi/4 = arctan(1/2) + arctan(1/3),
we let S_n denote the sum of the first n terms of
the usual series. If n is odd, it is too high, and
if n is even, too low. These are rational numbers,
and can be computed to any desired precision.
So we start out with no bits in the output candidate,
and proceed as follows:
start: n=1, q = s_1; x = 0; J=0;
K = distance to the next one in a random bit stream.
if the Kth bit of s_1 = 0, go to start;
else x = s_1 to K bits; J=K;
down: n = n+1; q=s_n;
if(x + 1/(2^J) < q) {return(x, J); exit:};
K = distance to the next one in a random bit stream.
J = J+K;
x = s_1 to K bits; J=K;
if(Jth bit of q ==1) {return(x, J); exit:};
up: n = n+1; q=s_n:
if(x > q) goto start;
K = distance to the next one in a random bit stream.
J = J+K;
if the Kth bit of s_1 = 0, go to start;
else x = s_1 to K bits; J=K;
go to down;
The idea is that at any time, we have an upper or lower
bound for pi/4, and we know x to within an interval from
(a/2^J, (a+1)/2^J). If this entire interval is larger
than an upper bound, we reject. If the entire interval
is smaller than a lower bound, we accept. This is exact.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
>><3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>,
> < snip
>>Herman, while I agree with your comments to Afonso, I find your
>>statement
>>below very curious and paradoxical, especially the last sentence:
>> If wanted, I can come up with algorithms which will generate
>>> random variables which are normal with mean exactly e and
>>> variance exactly pi, and it is not necessary to know e and
>>> pi to get reasonably efficient ways of doing this. Computer
>>> roundoff is not present in these methods.
Herman, you missed the point of roundoff. See my clarification
>below, which you may not have seen when you typed your response
>above.
I did not; you missed what I said. Any trailing bits
> which are not stored in the machine are random bits, to
> be produced if needed. Randomization allows us not to
> have the full description of the number there, as we
> can fill in additional bits as needed.
I heard the same thing you said the FIRST time. But you CANNOT
produce INFINITELY many random bits. Hence, what you drop off
is, technically roundoff.
You mentioned Mersenne numbers and integer factors. These are
FINITE, as I had stated. Not infinite in bits and digits.
>IN PRACTICE, of course nothing is exactly normal, let alone
>>knowing the exact value of e or pi. Also, IN PRACTICE, it
>>doesn't matter because ROUNDOFF (computer or computed to
>>100,000 digit precision) will not enable one to distinquish
that the procedure will give a different answer; the
> answer from the procedure is filled out to whatever
> accuracy is wanted, and if more is needed, and the
> number of bits prescribed has already been reached,
> additional random bits are brought in.
It's still FINITE. I know you know what infinite means. No amount
of arguing will you be able to convince anyone that you, or your
computer program can produce an EXACT number which required INFINITELY
many decimal digits or bits.
> The procedures produce the some of the bits, all the rest
>> of the bits being filled in with random bits. What I
>> stated is correct; if the bits are honest random, the
>> distribution results are EXACT, and there is no roundoff
>> introduced by the computer, any computer if programmed
>> correctly.
No, the distribution result CANNOT be exact, when some of the
>numbers are INFINITE in precision, if exact!
You fail to realize what CAN be done. The fact that
> lower semicontinuity is enough suffices to find a
> way to do it. To illustrate, I will show how to
> generate a number which is uniform in (0, pi/4).
> This procedure is not optimal; getting a fully optimal
> procedure is rarely possible. But it is simple.
But you will NEVER be able to generate any point EXACT equal to
any value that is pi/(integer). You can do so EXACTLY only if
you use some rational number that is arbitrarily CLOSE to pi.
That's ROUNDING pi to a rational approximation.
That's the difference, Herman.
It is hard to write or read the program, so I will
> describe it.
Again, it did NOT address that fact that you will NEVER generate
a value pi/4, pi/5. pi/6 ... or any other irrational number.
> The idea is that at any time, we have an upper or lower
> bound for pi/4, and we know x to within an interval from
> (a/2^J, (a+1)/2^J). If this entire interval is larger
> than an upper bound, we reject. If the entire interval
> is smaller than a lower bound, we accept. This is exact.
That's APPROXIMATE.
Try this Herman, to convince yourself that you have a mental block
regarding what is exact and what is approximate.
Take a discrete distribution with point probability 1/4 on each of
the points pi, pi/2, pi/4, and p/8.
Show us how you would generate that discrete distribution EXACTLY,
without roundoff, with X's having the EXACT values pi/(1 2 4 8).
Your inability to do so EXACTLY is exactly the same reason you can
only approximate a continuous distribution which admit those values.
 Bob.
====
Subject: Re: Central Limit Theorem?
>>><3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>,
< snip > The idea is that at any time, we have an upper or lower
>> bound for pi/4, and we know x to within an interval from
>> (a/2^J, (a+1)/2^J). If this entire interval is larger
>> than an upper bound, we reject. If the entire interval
>> is smaller than a lower bound, we accept. This is exact.
>That's APPROXIMATE.
No; it is not approximate. What happens at any stage
is approximate, but the final result is exact, just
as if one looks at the parity of the first time that
a random bit becomes 1, one gets a probability of
exactly 1/3 that it is even.
>Try this Herman, to convince yourself that you have a mental block
>regarding what is exact and what is approximate.
>Take a discrete distribution with point probability 1/4 on each of
>the points pi, pi/2, pi/4, and p/8.
>Show us how you would generate that discrete distribution EXACTLY,
>without roundoff, with X's having the EXACT values pi/(1 2 4 8).
>Your inability to do so EXACTLY is exactly the same reason you can
>only approximate a continuous distribution which admit those values.
I distinctly stated that to get an infinite precision
procedure as I defined it one needs a lower semicontinuous
DENSITY. This condition is necessary and sufficient for
densities; for discrete or mixed, the condition gets much
more complicated.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
< snip >
Why did you go several rounds back when we were getting down to the
impossibility of your representation of INFINITE precision in FINATE
mathematics?
> The idea is that at any time, we have an upper or lower
>> bound for pi/4, and we know x to within an interval from
>> (a/2^J, (a+1)/2^J). If this entire interval is larger
>> than an upper bound, we reject. If the entire interval
>> is smaller than a lower bound, we accept. This is exact.
That's APPROXIMATE.
And I've gone several rounds explaining why it's not EXACT.
>Try this Herman, to convince yourself that you have a mental block
>regarding what is exact and what is approximate.
Take a discrete distribution with point probability 1/4 on each of
>the points pi, pi/2, pi/4, and p/8.
Show us how you would generate that discrete distribution EXACTLY,
>without roundoff, with X's having the EXACT values pi/(1 2 4 8).
>Your inability to do so EXACTLY is exactly the same reason you can
>only approximate a continuous distribution which admit those values.
> I distinctly stated that to get an infinite precision
> procedure as I defined it one needs a lower semicontinuous
> DENSITY. This condition is necessary and sufficient for
> densities; for discrete or mixed, the condition gets much
> more complicated.
To me, that's just another THEORETICAL mumbojumbo without resolving
the question of the impossibility of INFINITE precision in finite
arithmetic. I think we've both exhausted our reasonedarguments.
I have nothing more to add other than agree to disagree and stand
on whatever I've posted in this tiny nitsubject of EXACT vs
approximate.
 Bob.
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> ><3502330.1115450423900.JavaMail.jakarta@nitrogen.mathforum.org>,
> < snip
> >>Herman, while I agree with your comments to Afonso, I find your
> >>statement
> >>below very curious and paradoxical, especially the last
sentence:
>>> If wanted, I can come up with algorithms which will generate
> >>> random variables which are normal with mean exactly e and
> >>> variance exactly pi, and it is not necessary to know e and
> >>> pi to get reasonably efficient ways of doing this. Computer
> >>> roundoff is not present in these methods.
>Herman, you missed the point of roundoff. See my clarification
> >below, which you may not have seen when you typed your response
> >above.
I did not; you missed what I said. Any trailing bits
> which are not stored in the machine are random bits, to
> be produced if needed. Randomization allows us not to
> have the full description of the number there, as we
> can fill in additional bits as needed.
I heard the same thing you said the FIRST time. But you CANNOT
> produce INFINITELY many random bits. Hence, what you drop off
> is, technically roundoff.
You mentioned Mersenne numbers and integer factors. These are
> FINITE, as I had stated. Not infinite in bits and digits.
>>IN PRACTICE, of course nothing is exactly normal, let alone
> >>knowing the exact value of e or pi. Also, IN PRACTICE, it
> >>doesn't matter because ROUNDOFF (computer or computed to
> >>100,000 digit precision) will not enable one to distinquish
>
The main POINT of this nitpicking argument is that in PRACTICE,
you can only APPROXIMATE any irrational number becaues it takes
INFINITELY many digits to represent it EXACTLY.
Thus, you can only approximate e by e += 10(googol), or
if that's not good enough, e + 10(googolplex), etc.
as I had said several days ago, citing Flash Gordon, M.D.:
FG> in theory, there is no difference between
FG> theory and practice. but in practice, there is.
FG> flash gordon, m.d. f...@well.sf.ca.us
 Bob.
> that the procedure will give a different answer; the
> answer from the procedure is filled out to whatever
> accuracy is wanted, and if more is needed, and the
> number of bits prescribed has already been reached,
> additional random bits are brought in.
It's still FINITE. I know you know what infinite means. No
amount
> of arguing will you be able to convince anyone that you, or your
> computer program can produce an EXACT number which required
INFINITELY
> many decimal digits or bits.
> >> The procedures produce the some of the bits, all the rest
> >> of the bits being filled in with random bits. What I
> >> stated is correct; if the bits are honest random, the
> >> distribution results are EXACT, and there is no roundoff
> >> introduced by the computer, any computer if programmed
> >> correctly.
>No, the distribution result CANNOT be exact, when some of the
> >numbers are INFINITE in precision, if exact!
You fail to realize what CAN be done. The fact that
> lower semicontinuity is enough suffices to find a
> way to do it. To illustrate, I will show how to
> generate a number which is uniform in (0, pi/4).
> This procedure is not optimal; getting a fully optimal
> procedure is rarely possible. But it is simple.
But you will NEVER be able to generate any point EXACT equal to
> any value that is pi/(integer). You can do so EXACTLY only if
> you use some rational number that is arbitrarily CLOSE to pi.
> That's ROUNDING pi to a rational approximation.
That's the difference, Herman.
> It is hard to write or read the program, so I will
> describe it.
Again, it did NOT address that fact that you will NEVER generate
> a value pi/4, pi/5. pi/6 ... or any other irrational number.
> The idea is that at any time, we have an upper or lower
> bound for pi/4, and we know x to within an interval from
> (a/2^J, (a+1)/2^J). If this entire interval is larger
> than an upper bound, we reject. If the entire interval
> is smaller than a lower bound, we accept. This is exact.
That's APPROXIMATE.
Try this Herman, to convince yourself that you have a mental block
> regarding what is exact and what is approximate.
Take a discrete distribution with point probability 1/4 on each of
> the points pi, pi/2, pi/4, and p/8.
Show us how you would generate that discrete distribution EXACTLY,
> without roundoff, with X's having the EXACT values pi/(1 2 4 8).
> Your inability to do so EXACTLY is exactly the same reason you can
> only approximate a continuous distribution which admit those values.
>  Bob.
====
Subject: Re: Central Limit Theorem?
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
It's not due to the CLT.
The CLT is an asymptotic result, while the effect you observe occurs in
small samples as well as large ones. It is simply a consequence of the
fact that the variance of a sum is (absent perfect correlation) less
than the sum of the variances. Consequently, if the individual
variances exist, the standard error of the mean decreases as the sample
size increases.
This is sometimes called the rootn effect. In the situation where
the variables making up your mean are independent, and the common
variance is sigmasquared, this effect in std errors is sometimes
called the sigma on rootn effect.
That's not to say it's totally unrelated to the CLT  the CLT makes use
of such a result, for example (in that simple versions of the CLT look
at the distribution of [xbar  mu]/[sigma/sqrt(n)].
Glen
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> That's not to say it's totally unrelated to the CLT  the CLT makes
use
> of such a result, for example (in that simple versions of the CLT
look
> at the distribution of [xbar  mu]/[sigma/sqrt(n)].
A couple of comments here.
1. The Central Limit Theorem does not always hold! In one extreme
case
of the Cauchy distribution , xbar has exactly the
same
distribution as a single X!
See conditions for the CLT of independent random variables to hold:
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.htm
At the elementary level, iid r.v. with first two moments are
usually
given as the sufficient condition.
2. This is the most important part of the CLT  the sum of X (or
xbar)
converges asymptotally to a NORMAL distribution. This is also the
most amazing part of the CLT. X can come from a Ushaped or
Jshaped
distribution, but xbar will be normally distributed.
3. The convergence of the asymptotic result may be surprisingly fast.
In the early years of computer simulation of standard normal random
variables, this was used: Let Y be the sum of 12 iid U(0,1)
That's not to say it's totally unrelated to the CLT  the CLT makes
> use
> of such a result, for example (in that simple versions of the CLT
> look
> at the distribution of [xbar  mu]/[sigma/sqrt(n)].
A couple of comments here.
1. The Central Limit Theorem does not always hold!
If you look back at my last 13 years of posts to sci.stat.* (and
similar) newsgroups you'll see that I'm well aware of this, and
indeed, have used the Cauchy counterexample myself. Indeed,
distributions where the CLT doesn't apply are quite common in things I
work with (for a recent example, predictive distributions of sums of
future values from lognormal models  which are sums of correlated
logt random variables  don't have moments).
It's not directly relevant to the discussion, though, which is just
whether what I called the rootn effect is due to the CLT. When the
rootn effect doesn't apply at all, the usual CLT doesn't either*;
conversely if none of the more general forms of the CLT apply, you've
got to do some fancy contortions to create a circumstance where you
can claim a rootn effect still comes in (to the extent that the term
rootn becomes effectively unjustifiable). Here we are /discussing/
the rootn effect, so there's little need for the caveat on the CLT.
*there are other nonrootn limit theorems that may apply, of course.
To be more specific, your counterexample is NOT a case where the
variance of the sample mean reduces with samplesize, so it's not
within the bounds of the original question.
While it is possible to set up a situation where a different function
of n is involved for some statistics, I didn't think this point was
worth making to the original poster, who didn't sound like they were
looking for a treatise on counterexamples. **
** If anyone is still reading by this point, and you /are/ looking for
a treatise on counterexamples, the book by Romano and Siegel
(Counterexamples in Probability and Statistics) makes for quite
enjoyable reading.
As far as I can see, neither the original poster nor I gave any reason
to suspect we might have thought the CLT applied in all circumstances.
If every possible caveat is put into every post, I doubt we'll ever
actually get anywhere.
Glen
====
Subject: Re: Central Limit Theorem?
>> That's not to say it's totally unrelated to the CLT  the CLT makes
>use
>> of such a result, for example (in that simple versions of the CLT
>look
>> at the distribution of [xbar  mu]/[sigma/sqrt(n)].
>A couple of comments here.
>1. The Central Limit Theorem does not always hold! In one extreme
>case
> of the Cauchy distribution , xbar has exactly the
>same
> distribution as a single X!
And if you take the reciprocal of the square of a normal
random variable with mean 0, it will be even more spread
out than one observation.
> See conditions for the CLT of independent random variables to hold:
>http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.ht
m
> At the elementary level, iid r.v. with first two moments are
>usually
> given as the sufficient condition.
>2. This is the most important part of the CLT  the sum of X (or
>xbar)
> converges asymptotally to a NORMAL distribution. This is also the
> most amazing part of the CLT. X can come from a Ushaped or
>Jshaped
> distribution, but xbar will be normally distributed.
This statement is incorrect. It is true that the
distribution of xbar CONVERGES to the normal distribution,
but it is NOT the normal distribution unless X is exactly
normally distributed. The approximation is definitely not
great, especially in the tails.
>3. The convergence of the asymptotic result may be surprisingly fast.
> In the early years of computer simulation of standard normal random
> variables, this was used: Let Y be the sum of 12 iid U(0,1)
> Y  6
> will be sufficiently close to N(0,1) that you will not be able to
> judge by eye or most goodness of fit tests!
On small samples, yes; goodness of fit tests do poorly on
those. The KolmogorovSmirnov test, or even better the
Kuiper test, will do much better. A welldrawn graph
will also show the difference in the cdf's.
> For U(0,1), mu = 1, and sigma^2 = 1/12.
> So, for Y = X1 + ... X12, mu(Y) = 12, sigma^2(Y) = 1
> Thus, Z = (Y  mu(Y))/std.dev (y) = Y  6 will tend to N(0,1).
> Bob.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
A couple of comments here.
1. The Central Limit Theorem does not always hold! In one extreme
>case
> of the Cauchy distribution , xbar has exactly the
>same
> distribution as a single X!
And if you take the reciprocal of the square of a normal
> random variable with mean 0, it will be even more spread
> out than one observation.
I was merely citing the WELLKNOWN Cauchy as one extreme case, and
the curiosity that xbar has the same distribution as X.
>2. This is the most important part of the CLT  the sum of X (or
>xbar)
> converges asymptotally to a NORMAL distribution. This is also
the
> most amazing part of the CLT. X can come from a Ushaped or
>Jshaped
> distribution, but xbar will be normally distributed.
This statement is incorrect. It is true that the
> distribution of xbar CONVERGES to the normal distribution,
> but it is NOT the normal distribution unless X is exactly
> normally distributed. The approximation is definitely not
> great, especially in the tails.
You are DEFINITELY wrong about this.
Are you saying The Central Limit Theorem stated in my reference link,
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.htm
is wrong, and you're right?
The convolution of indepdent, exactly normally distributed
random variables, is always exactly normally distributed, for
any finite number of independent normal variates. So, why would
you need the Central Limit Theorem?
My comment 3 shows that the xbar of U(0,1) ocnverges to Normal.
Not only that, but the ocnvergence is so rapid and good that for
years serious scientists had used an IBM Scientific Subroutine
that used the sum of TWELVE uniform random numbers to produce
(approx) standard normal deviates.
>3. The convergence of the asymptotic result may be surprisingly
fast.
> In the early years of computer simulation of standard normal
random
> variables, this was used: Let Y be the sum of 12 iid U(0,1)
> judge by eye or most goodness of fit tests!
On small samples, yes; goodness of fit tests do poorly on
> those. The KolmogorovSmirnov test, or even better the
> Kuiper test, will do much better. A welldrawn graph
> will also show the difference in the cdf's.
While that may be true, the approximation was so good that even in
the 1960s and early 1970s, the IBM Subroutine Library and the IMSL
library had that method of simulation, IIRC, until we now have
algorithms that can simulate pseudorandom numbers from a TRUE
Standard normal distribution.
 Bob.
For U(0,1), mu = 1, and sigma^2 = 1/12.
So, for Y = X1 + ... X12, mu(Y) = 12, sigma^2(Y) = 1
Thus, Z = (Y  mu(Y))/std.dev (y) = Y  6 will tend to N(0,1).
> Bob.

> This address is for information only. I do not claim that these
views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Department of Statistics, Purdue University
> hrubin@stat.purdue.edu Phone: (765)4946054 FAX:
(765)4940558
====
Subject: Re: Central Limit Theorem?
On 21 Apr 2005 19:03:44 0700, Reef Fish
>Are you saying The Central Limit Theorem stated in my reference link,
>http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.ht
m
>is wrong, and you're right?
At least give the proper link:
http://en.wikipedia.org/wiki/Central_limit_theorem
so if people think it is wrong they can change it.
====
Subject: Re: Central Limit Theorem?
<3q1r6112qaa4csm7gat27aqlvl8rngt01b@4ax.com>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> On 21 Apr 2005 19:03:44 0700, Reef Fish
>Are you saying The Central Limit Theorem stated in my reference
link,
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.ht
m
>is wrong, and you're right?
At least give the proper link:
> http://en.wikipedia.org/wiki/Central_limit_theorem
> so if people think it is wrong they can change it.
May be you need a better browser. I clicked my URL and had no trouble
getting the page.
The link I gave IS the correct link.
What you gave may be the alternative URL given by some other source
other than Google. Did you find any SUBSTANCE your link that is
missing in the link I referred to?
 bOB.
====
Subject: Re: Central Limit Theorem?
<3q1r6112qaa4csm7gat27aqlvl8rngt01b@4ax.com>
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.ht
m
> >is wrong, and you're right?
At least give the proper link:
> http://en.wikipedia.org/wiki/Central_limit_theorem
> so if people think it is wrong they can change it.
May be you need a better browser. I clicked my URL and had no
trouble
> getting the page.
The link I gave IS the correct link.
The link you gave is simply taking wikipedia pages. The originals are
from wikipedia. In that sense, they are the correct link. In
addition, by giving the original wikipedia link, there's the advantage
of being able to comment on or suggest (or even make) changes to them.
Glen
====
Subject: Re: Central Limit Theorem?
<3q1r6112qaa4csm7gat27aqlvl8rngt01b@4ax.com>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
>http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.ht
m
> >is wrong, and you're right?
> > At least give the proper link:
> > http://en.wikipedia.org/wiki/Central_limit_theorem
> > so if people think it is wrong they can change it.
May be you need a better browser. I clicked my URL and had no
> trouble
> getting the page.
The link I gave IS the correct link.
The link you gave is simply taking wikipedia pages. The originals are
> from wikipedia. In that sense, they are the correct link. In
> addition, by giving the original wikipedia link, there's the
advantage
> of being able to comment on or suggest (or even make) changes to
them.
Glen
You can nitpick all you want about what's correct and what's not.
I found that link using Google web search. It was an excellent link
for the Central Limit Theorem.
I couldn't less if that link took pages from the winipedia pages
or some other wackiwacki link. I also couldn't care less to
make sugestion for them to make changes. The link I cited was
PLENTY GOOD for me, and IMHSHO plenty good for everyone of the
sci.stat.math readership except a few nitpickers who happened to
their URL is the correct one, when the ONLY thing it mattered
in the cited reference of mine is that it contained what it
contained and is a 100% valid and correct link found by Google.
The AltaVista.com web search engine did pick up your URL. Big deal.
No difference in the SUBSTANCE for the purpose I gave the URL
I found.
 Bob.
====
Subject: Re: Central Limit Theorem?
>>A couple of comments here.
>>1. The Central Limit Theorem does not always hold! In one extreme
>>case
>> of the Cauchy distribution , xbar has exactly the
>>same
>> distribution as a single X!
>> And if you take the reciprocal of the square of a normal
>> random variable with mean 0, it will be even more spread
>> out than one observation.
>I was merely citing the WELLKNOWN Cauchy as one extreme case, and
>the curiosity that xbar has the same distribution as X.
>>2. This is the most important part of the CLT  the sum of X (or
>>xbar)
>> converges asymptotally to a NORMAL distribution. This is also
>the
>> most amazing part of the CLT. X can come from a Ushaped or
>>Jshaped
>> distribution, but xbar will be normally distributed.
>> This statement is incorrect. It is true that the
>> distribution of xbar CONVERGES to the normal distribution,
>> but it is NOT the normal distribution unless X is exactly
>> normally distributed. The approximation is definitely not
>> great, especially in the tails.
>You are DEFINITELY wrong about this.
>Are you saying The Central Limit Theorem stated in my reference link,
>http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.ht
m
>is wrong, and you're right?
I see nothing in that link which disagrees with what I
have stated.
>The convolution of indepdent, exactly normally distributed
>random variables, is always exactly normally distributed, for
>any finite number of independent normal variates. So, why would
>you need the Central Limit Theorem?
What I have said is that the sum of independent random
variables, identical or not, is never normally distributed
unless all of them are.
>My comment 3 shows that the xbar of U(0,1) ocnverges to Normal.
>Not only that, but the ocnvergence is so rapid and good that for
>years serious scientists had used an IBM Scientific Subroutine
>that used the sum of TWELVE uniform random numbers to produce
>(approx) standard normal deviates.
One can do better more cheaply. Using this for simulation
is VERY dangerous, as the pseudorandom numbers usually
used are very definitely NOT independent. I believe that
one of the IBM prng's widely used was about the worst, not
that any of the others back then were that good. I would
not do a serious simulation using prng's only.
Far better prng's have been KNOWN to give wrong results in
the Ising model. In fact, this was the first proof that
one of the ones considered good at the time had serious
drawbacks, and this was a drawback more subtle, but of
somewhat the same type, as the prng's of the 60s and 70s.
Far too many of the users of computers have far too much
faith that the programmers have done a good job; this is
often not so.
>>3. The convergence of the asymptotic result may be surprisingly
>fast.
>> In the early years of computer simulation of standard normal
>random
>> variables, this was used: Let Y be the sum of 12 iid U(0,1)
>> > Y  6
>> will be sufficiently close to N(0,1) that you will not be able
>to
>> judge by eye or most goodness of fit tests!
>> On small samples, yes; goodness of fit tests do poorly on
>> those. The KolmogorovSmirnov test, or even better the
>> Kuiper test, will do much better. A welldrawn graph
>> will also show the difference in the cdf's.
>While that may be true, the approximation was so good that even in
>the 1960s and early 1970s, the IBM Subroutine Library and the IMSL
>library had that method of simulation, IIRC, until we now have
>algorithms that can simulate pseudorandom numbers from a TRUE
>Standard normal distribution.
We had no shortage of such algorithms in those days. The
advantage of this algorithm requires very cheap random
numbers, and the IBM numbers certainly were; none of these
cheap methods is in much use now.
> Bob.
>> For U(0,1), mu = 1, and sigma^2 = 1/12.
>> So, for Y = X1 + ... X12, mu(Y) = 12, sigma^2(Y) = 1
>> Thus, Z = (Y  mu(Y))/std.dev (y) = Y  6 will tend to N(0,1).
No; what will tend to N(0,1) is the sum of K X's, less K/2,
divided by the square root of K/12. Z, as you have given
it above, tends to Z and nothing more. It will have a
distribution which can be easily calculated.
>> Bob.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
>>2. This is the most important part of the CLT  the sum of X
(or
>>xbar)
>> converges asymptotally to a NORMAL distribution. This is
also
>the
>> most amazing part of the CLT. X can come from a Ushaped or
>>Jshaped
>> distribution, but xbar will be normally distributed.
The X's are iid from the same distribution, as stated in the link!
That's why I said you were wrong in saying the statement is incorrect.
> This statement is incorrect. It is true that the
>> distribution of xbar CONVERGES to the normal distribution,
>> but it is NOT the normal distribution unless X is exactly
>> normally distributed. The approximation is definitely not
>> great, especially in the tails.
You are DEFINITELY wrong about this.
Are you saying The Central Limit Theorem stated in my reference
link,
>http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.ht
m
is wrong, and you're right?
I see nothing in that link which disagrees with what I
> have stated.
Then you were quoting me out of context. That was why I asked:
The convolution of indepdent, exactly normally distributed
>random variables, is always exactly normally distributed, for
>any finite number of independent normal variates. So, why would
>you need the Central Limit Theorem?
What I have said is that the sum of independent random
> variables, identical or not, is never normally distributed
> unless all of them are.
I reread your previous statement several times. I don't think you
said what you said now. Besides, if it's iid, your statement is
irrelevant because CLT is an asymptotic result.
>My comment 3 shows that the xbar of U(0,1) ocnverges to Normal.
>Not only that, but the ocnvergence is so rapid and good that for
>years serious scientists had used an IBM Scientific Subroutine
>that used the sum of TWELVE uniform random numbers to produce
>(approx) standard normal deviates.
One can do better more cheaply.
Again, you were commenting out of context. I was merely taking an
example of how the CLT was actually used, IN THE OLD DAYS (which had
been obsolete for decades now). Of course we can do better than
that.
BoxMuller (1958), Marsaglas (1964), and AhrensDieter (1988), are
just some of the more recent methods. BoxMuller is far preferred
because it is exact. I TAUGHT this stuff more than a decade ago in
graduate courses in Monte Carlo Methods.
> Using this for simulation is VERY dangerous,
This was WELLknown even back in the 1960s. But until the Box
Muller made its debut, serious scientists were using the IBM
Scientific Subroutine Library which had the sum of 12 U(0,1)6
for simulating N(0,1) variables.
> as the pseudorandom numbers usually
> used are very definitely NOT independent.
Of course they are not. Most of them are DETERMINISTIC. That's
why they are pseudorandom and not random. But they have very
long cycles within which one CANNOT distinguish the pseudo ones
from the truly random ones.
> Far too many of the users of computers have far too much
> faith that the programmers have done a good job; this is
> often not so.
Very true. It's also another of your strawman! No different from
your strawmen statisticians.
There are PLENTY of these strawmen out there, but there are also
some very knowledgeable ones who would not be subject to your
strawman complaint.
I am one of those. Most of the things I ocmpute do not have canned
or packaged programs written by others. So I programmed them myself.
I MAY be the ONLY statisticaljournal editor and referee who actually
CHECK the accuracy and validity of the numerical results in submitted
papers, and quite often find them wrong.
>3. The convergence of the asymptotic result may be surprisingly
>fast.
>> In the early years of computer simulation of standard normal
>random
>> variables, this was used: Let Y be the sum of 12 iid U(0,1)
>> Y  6
> will be sufficiently close to N(0,1) that you will not be
able
>to
>> judge by eye or most goodness of fit tests!
> On small samples, yes; goodness of fit tests do poorly on
>> those. The KolmogorovSmirnov test, or even better the
>> Kuiper test, will do much better. A welldrawn graph
>> will also show the difference in the cdf's.
While that may be true, the approximation was so good that even in
>the 1960s and early 1970s, the IBM Subroutine Library and the IMSL
>library had that method of simulation, IIRC, until we now have
>algorithms that can simulate pseudorandom numbers from a TRUE
>Standard normal distribution.
>> For U(0,1), mu = 1, and sigma^2 = 1/12.
> So, for Y = X1 + ... X12, mu(Y) = 12, sigma^2(Y) = 1
> Thus, Z = (Y  mu(Y))/std.dev (y) = Y  6 will tend to
N(0,1).
No; what will tend to N(0,1) is the sum of K X's, less K/2,
> divided by the square root of K/12.
Herman, here K IS 12. That is why your sum of K X's less K/2 IS Y  6,
and the square root of K/12 IS 1. Which is why Y  6 tends to N(0,1).
> Z, as you have given
> it above, tends to Z and nothing more. It will have a
> distribution which can be easily calculated.
Did I say otherwise? I said EXACTLY what you said. You were too
careless
to have overlooked that
(Y  mu(Y))/std dev (Y) = (Y  6)/sqrt(1) = Y  6.
 Bob.
====
Subject: Re: Central Limit Theorem?
...............
>>My comment 3 shows that the xbar of U(0,1) ocnverges to Normal.
>>Not only that, but the ocnvergence is so rapid and good that for
>>years serious scientists had used an IBM Scientific Subroutine
>>that used the sum of TWELVE uniform random numbers to produce
>>(approx) standard normal deviates.
>> One can do better more cheaply.
>Again, you were commenting out of context. I was merely taking an
>example of how the CLT was actually used, IN THE OLD DAYS (which had
>been obsolete for decades now). Of course we can do better than
>that.
>BoxMuller (1958), Marsaglas (1964), and AhrensDieter (1988), are
>just some of the more recent methods. BoxMuller is far preferred
>because it is exact. I TAUGHT this stuff more than a decade ago in
>graduate courses in Monte Carlo Methods.
I taught this farther back than that.
I believe the BoxMuller method, or some versions of it,
was know before 1950. Another exact method, also very old,
is to use acceptancerejection starting with the double
exponential. There is no shortage of methods which are
exact except for computer accuracy, and it is even possible
to obtain low computation exact methods not subject to
computer roundoff if one has exact random bits. Unfortunately,
these are difficult to carry out, and slow, with current hardware.
>> Using this for simulation is VERY dangerous,
>This was WELLknown even back in the 1960s. But until the Box
>Muller made its debut, serious scientists were using the IBM
>Scientific Subroutine Library which had the sum of 12 U(0,1)6
>for simulating N(0,1) variables.
>> as the pseudorandom numbers usually
>> used are very definitely NOT independent.
>Of course they are not. Most of them are DETERMINISTIC. That's
>why they are pseudorandom and not random. But they have very
>long cycles within which one CANNOT distinguish the pseudo ones
>from the truly random ones.
Baloney. Long cycles are not the criterion; quasirandom
numbers, carried out to enough precision, have arbitrarily
long cycles, and are more uniformly distributed than
random numbers, but are nowhere near independent. The
pseudorandom generator which gave wrong resuits in the
Ising model had a period of 2^1279  1, which means that
essentially it will never repeat. It was found to have the
random numbers fall mainly in the planes failure in a
complicated form. The real danger is lack of independence,
even in longperiod generators for which there is even
demonstrable shortperiod lack of correlation. There are
some which even have good shortperiod independence.
>> Far too many of the users of computers have far too much
>> faith that the programmers have done a good job; this is
>> often not so.
>Very true. It's also another of your strawman! No different from
>your strawmen statisticians.
But it means they have to understand mathematical statistics,
so they can evaluate the errors.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> ...............
>>My comment 3 shows that the xbar of U(0,1) ocnverges to Normal.
>>Not only that, but the ocnvergence is so rapid and good that for
>>years serious scientists had used an IBM Scientific Subroutine
>>that used the sum of TWELVE uniform random numbers to produce
>>(approx) standard normal deviates.
> One can do better more cheaply.
Again, you were commenting out of context. I was merely taking an
>example of how the CLT was actually used, IN THE OLD DAYS (which had
>been obsolete for decades now). Of course we can do better than
>that.
BoxMuller (1958), Marsaglas (1964), and AhrensDieter (1988), are
>just some of the more recent methods. BoxMuller is far preferred
>because it is exact. I TAUGHT this stuff more than a decade ago in
>graduate courses in Monte Carlo Methods.
I taught this farther back than that.
That's why your ideas are so OUT OF DATE and obsolete, as evidence
by what you said and I refute below.
WHen was the LAST time you taught a course in Monte Carlo methods
(if you ever taught one)?
I believe the BoxMuller method, or some versions of it,
> was know before 1950.
Possibly some Technical Report version that is not as elegant.
1958 is the earliest published record of that method.
> Another exact method, also very old, is to use acceptancerejection
> starting with the double exponential.
Here you are using the term exact incorrectly, at least in the
literature on Simulation and Monte Carlo Methods.
The BoxMuller method is EXACT because it is based on the generation
of two iid U1 and U2 and the transformation of the random variable
is EXACTLY normal.
There are numerous acceptancerejection methods. NONE of the is
exact.
Most of them tend to converge asymptotally to the desired random
variable,
with diffreent rates of convergence (important in Monte Carlo methods).
The naive Monte Carlo method is the most inefficient acceptance
rejection method, probably older than YOU  which would make it
very ancient indeed. :)
> There is no shortage of methods which are
> exact except for computer accuracy, and it is even possible
> to obtain low computation exact methods not subject to
> computer roundoff if one has exact random bits. Unfortunately,
> these are difficult to carry out, and slow, with current hardware.
The exact part is in THEORY. I don't care how many bits you
carry in computation, you cannot represent an irrational number
exactly.
>> Using this for simulation is VERY dangerous,
This was WELLknown even back in the 1960s. But until the Box
>Muller made its debut, serious scientists were using the IBM
>Scientific Subroutine Library which had the sum of 12 U(0,1)6
>for simulating N(0,1) variables.
> as the pseudorandom numbers usually
>> used are very definitely NOT independent.
Of course they are not. Most of them are DETERMINISTIC. That's
>why they are pseudorandom and not random. But they have very
>long cycles within which one CANNOT distinguish the pseudo ones
>from the truly random ones.
Baloney. Long cycles are not the criterion; quasirandom
> numbers, carried out to enough precision, have arbitrarily
> long cycles, and are more uniformly distributed than
> random numbers, but are nowhere near independent.
Since I have given away ALL of my books relating to pseudorandom number
generation and Monte Carlo methods, I don't have a ready reference.
But the BALONEY is YOURS, as can be seen from the links below.
Here's a web link that seems to be quite informative about the subject.
http://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE142.HTM
It talks about the cycle lengths of linear congruential generators, and
some good choices for the selection of the constants. A long cycle is
definitely ONE of the criteria of selecting a pseudorandom number
generator, in addition to dozens of other criteria of randomness.
http://online.physics.uiuc.edu/courses/phys466/fall04/lnotes/random_numbers.
html
*> What are some of the desired properties of random numbers?
*> Uncorrelated, deterministic, longperiods between repeats, uniform
*> converage of range, efficiency of algorithm.
I have read more papers and books about CYCLE LENGTHS than there are
methods of pseudorandom number generation  and I know at least dozens
of them.
> The
> pseudorandom generator which gave wrong resuits in the
> Ising model had a period of 2^1279  1, which means that
> essentially it will never repeat. It was found to have the
> random numbers fall mainly in the planes failure in a
> complicated form.
That's true as proven by Marsaglia (1968) that ktuples from the more
general class of linear congruential generators lie on sets of parallel
hyperplanes. But this known defect is important only when one
simulates
MULTIVARIATE data using the congruential generators. For UNIVARIATE
simulation, that hardly mattered. Plenty of studies have been done
on the CHOICE of constants to minimize the multivariate gap, as in
the gap test (one of the standard criteria of testing pseudorandom
number generators).
There are also modern methods (post1968) that assures that the
generated
ktuples do not line on hyperplanes.
Which one to use depends very much on the dimensionality of the
application,
which randomness criteria are more important than others, etc., etc.,
etc. There is NO single pseudorandom number generator that's best for
all.
> The real danger is lack of independence,
There are MANY dangers. They are ALL real. See my preceding paragraph
and the paragraph below.
> even in longperiod generators for which there is even
> demonstrable shortperiod lack of correlation. There are
> some which even have good shortperiod independence.
Herman. That's really ANCIENT stuff. Take a look at the 1964 Handbook
of Mathematical Functions (NBS). It discussed many such tests there.
> Far too many of the users of computers have far too much
>> faith that the programmers have done a good job; this is
>> often not so.
Very true. It's also another of your strawman! No different from
>your strawmen statisticians.
But it means they have to understand mathematical statistics,
> so they can evaluate the errors.
Those who do, DO know much more than you do, as evidence by your
discussion
above. You are still living in the simulation world of the 1960s, and
before.
 Bob.
====
Subject: Re: Central Limit Theorem?
...............
>>>My comment 3 shows that the xbar of U(0,1) ocnverges to Normal.
>>>Not only that, but the ocnvergence is so rapid and good that for
>>>years serious scientists had used an IBM Scientific Subroutine
>>>that used the sum of TWELVE uniform random numbers to produce
>>>(approx) standard normal deviates.
>>> One can do better more cheaply.
>>Again, you were commenting out of context. I was merely taking an
>>example of how the CLT was actually used, IN THE OLD DAYS (which had
>>been obsolete for decades now). Of course we can do better than
>>that.
>>BoxMuller (1958), Marsaglas (1964), and AhrensDieter (1988), are
>>just some of the more recent methods. BoxMuller is far preferred
>>because it is exact. I TAUGHT this stuff more than a decade ago in
>>graduate courses in Monte Carlo Methods.
>> I taught this farther back than that.
>That's why your ideas are so OUT OF DATE and obsolete, as evidence
>by what you said and I refute below.
>WHen was the LAST time you taught a course in Monte Carlo methods
>(if you ever taught one)?
I have taught a course in numerical methods in probability
and statistics quite a few times, roughly every other year,
and I certainly include simulation in the course, including
methods you probably have never heard of.
Bradford Johnson and I have a paper coming out soon on
the use of acceptancecomplement methods in generating
exponential and normal random variables. I also have
methods for generating Gamma and Zeta random variables
which will compare favorably, if not beat, anything in
the literature. Jeesen Chen and I have published a
paper on simulating from a distribution which is itself
random, and doing it reasonably well. The method of
generating stable random variables, if you trace the
references, will be found in a footnote to be due to me.
>> I believe the BoxMuller method, or some versions of it,
>> was know before 1950.
>Possibly some Technical Report version that is not as elegant.
>1958 is the earliest published record of that method.
So?
>> Another exact method, also very old, is to use acceptancerejection
>> starting with the double exponential.
>Here you are using the term exact incorrectly, at least in the
>literature on Simulation and Monte Carlo Methods.
No, acceptance rejection methods can be exact.
>The BoxMuller method is EXACT because it is based on the generation
>of two iid U1 and U2 and the transformation of the random variable
>is EXACTLY normal.
One version of the BoxMuller method is to take a random
point in a semicircle and transform it.
>There are numerous acceptancerejection methods. NONE of the is
>exact.
>Most of them tend to converge asymptotally to the desired random
>variable,
>with diffreent rates of convergence (important in Monte Carlo methods).
Unless you mean that there is a small probability that a
large number of trials will be needed to get an answer,
there is nothing nonexact about acceptancerejection
methods. One could equally say that the BoxMuller method
is inexact due to computer rounding, and it can give
substantial errors because of that.
>The naive Monte Carlo method is the most inefficient acceptance
>rejection method, probably older than YOU  which would make it
>very ancient indeed. :)
This is correct. However, there is the problem of
coming up with efficient ones.
>> There is no shortage of methods which are
>> exact except for computer accuracy, and it is even possible
>> to obtain low computation exact methods not subject to
>> computer roundoff if one has exact random bits. Unfortunately,
>> these are difficult to carry out, and slow, with current hardware.
>The exact part is in THEORY. I don't care how many bits you
>carry in computation, you cannot represent an irrational number
>exactly.
No, but you can get the representation to a given accuracy,
with all subsequent bits being independent uniform random
bits. These methods do not involve carrying many bits in
the computational process.
>>> Using this for simulation is VERY dangerous,
>>This was WELLknown even back in the 1960s. But until the Box
>>Muller made its debut, serious scientists were using the IBM
>>Scientific Subroutine Library which had the sum of 12 U(0,1)6
>>for simulating N(0,1) variables.
>>> as the pseudorandom numbers usually
>>> used are very definitely NOT independent.
>>Of course they are not. Most of them are DETERMINISTIC. That's
>>why they are pseudorandom and not random. But they have very
>>long cycles within which one CANNOT distinguish the pseudo ones
>>from the truly random ones.
>> Baloney. Long cycles are not the criterion; quasirandom
>> numbers, carried out to enough precision, have arbitrarily
>> long cycles, and are more uniformly distributed than
>> random numbers, but are nowhere near independent.
>Since I have given away ALL of my books relating to pseudorandom number
>generation and Monte Carlo methods, I don't have a ready reference.
>But the BALONEY is YOURS, as can be seen from the links below.
Why have you given them away?
>Here's a web link that seems to be quite informative about the subject.
>http://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE142.HTM
>http://online.physics.uiuc.edu/courses/phys466/fall04/lnotes/random_numbers
.html
>*> What are some of the desired properties of random numbers?
>*> Uncorrelated, deterministic, longperiods between repeats, uniform
>*> converage of range, efficiency of algorithm.
>I have read more papers and books about CYCLE LENGTHS than there are
>methods of pseudorandom number generation  and I know at least dozens
>of them.
>It talks about the cycle lengths of linear congruential generators, and
>some good choices for the selection of the constants. A long cycle is
>definitely ONE of the criteria of selecting a pseudorandom number
>generator, in addition to dozens of other criteria of randomness.
As I said, long cycles are easy.
I would never use a pseudorandom generator for production work.
There are ways of using physical random numbers, which need not
be perfect, to greatly lessen the problems of independence.
>> The
>> pseudorandom generator which gave wrong resuits in the
>> Ising model had a period of 2^1279  1, which means that
>> essentially it will never repeat. It was found to have the
>> random numbers fall mainly in the planes failure in a
>> complicated form.
>That's true as proven by Marsaglia (1968) that ktuples from the more
>general class of linear congruential generators lie on sets of parallel
>hyperplanes. But this known defect is important only when one
>simulates
>MULTIVARIATE data using the congruential generators. For UNIVARIATE
>simulation, that hardly mattered. Plenty of studies have been done
>on the CHOICE of constants to minimize the multivariate gap, as in
>the gap test (one of the standard criteria of testing pseudorandom
>number generators).
For univariate simulation, the use of quasirandom numbers
and inverting the cdf is likely to be better. This is even
the case for good multivariate problems, where the multi
is not too large. Remember that quasirandom numbers are
uniformly distributed, not random.
>There are also modern methods (post1968) that assures that the
>generated
>ktuples do not line on hyperplanes.
There are?
>Which one to use depends very much on the dimensionality of the
>application,
>which randomness criteria are more important than others, etc., etc.,
>etc. There is NO single pseudorandom number generator that's best for
>all.
>> The real danger is lack of independence,
>There are MANY dangers. They are ALL real. See my preceding paragraph
>and the paragraph below.
>> even in longperiod generators for which there is even
>> demonstrable shortperiod lack of correlation. There are
>> some which even have good shortperiod independence.
>Herman. That's really ANCIENT stuff. Take a look at the 1964 Handbook
>of Mathematical Functions (NBS). It discussed many such tests there.
Weak tests. I would not use such, and would not have then.
Most of what I have done is after that time. But none of
the pseudorandom generators available then was good enough
to be useful for the simulation which I did in 1970. I
mixed random and pseudorandom to get reasonable results.
>>> Far too many of the users of computers have far too much
>>> faith that the programmers have done a good job; this is
>>> often not so.
>>Very true. It's also another of your strawman! No different from
>>your strawmen statisticians.
>> But it means they have to understand mathematical statistics,
>> so they can evaluate the errors.
>Those who do, DO know much more than you do, as evidence by your
>discussion
>above. You are still living in the simulation world of the 1960s, and
>before.
I do not remember when the failure of the longperiod
shiftregister method was noted, but it was certainly not
before 1980. And the failure was shown to be of the
planes type, but just more complicated. Even the
Mersenne twister has been found to have weaknesses.
All of the intelligent discussion of pseudorandom numbers
relies heavily on mathematics.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
...............
>>>My comment 3 shows that the xbar of U(0,1) ocnverges to
Normal.
>>>Not only that, but the ocnvergence is so rapid and good that
for
>>>years serious scientists had used an IBM Scientific Subroutine
>>>that used the sum of TWELVE uniform random numbers to produce
>>>(approx) standard normal deviates.
>> One can do better more cheaply.
>Again, you were commenting out of context. I was merely taking
an
>>example of how the CLT was actually used, IN THE OLD DAYS (which
had
>>been obsolete for decades now). Of course we can do better than
>>that.
>BoxMuller (1958), Marsaglas (1964), and AhrensDieter (1988),
are
>>just some of the more recent methods. BoxMuller is far
preferred
>>because it is exact. I TAUGHT this stuff more than a decade ago
in
>>graduate courses in Monte Carlo Methods.
> I taught this farther back than that.
That's why your ideas are so OUT OF DATE and obsolete, as evidence
>by what you said and I refute below.
WHen was the LAST time you taught a course in Monte Carlo methods
>(if you ever taught one)?
I have taught a course in numerical methods in probability
> and statistics quite a few times, roughly every other year,
> and I certainly include simulation in the course,
Like I included some simulation in EVERY probability and statistics
course I ever taught? :) But I was talking about Graduate courses
in Monte Carlo methods with advanced probability and statistics
courses as prerequisites. These are much more SPECIALIZED on the
subject of Monte Carlo methods.
> including methods you probably have never heard of.
That I don't doubt a bit.
>> I believe the BoxMuller method, or some versions of it,
>> was know before 1950.
Possibly some Technical Report version that is not as elegant.
>1958 is the earliest published record of that method.
So?
> Another exact method, also very old, is to use
acceptancerejection
>> starting with the double exponential.
Here you are using the term exact incorrectly, at least in the
>literature on Simulation and Monte Carlo Methods.
No, acceptance rejection methods can be exact.
Shortly before your post (about 3 minutes, so you probably hadn't seen
s...@sherwood.csv.warwick.ac.u[CapitalEth]k, explaining where my
acceptance
rejection notion came from.
The BoxMuller method is EXACT because it is based on the generation
>of two iid U1 and U2 and the transformation of the random variable
>is EXACTLY normal.
One version of the BoxMuller method is to take a random
> point in a semicircle and transform it.
That sounds like the same one, the one and only BoxMuller I know,
and widely referenced in the literature.
There are numerous acceptancerejection methods. NONE of the is
>exact.
>Most of them tend to converge asymptotally to the desired random
>variable,
>with diffreent rates of convergence (important in Monte Carlo
methods).
Unless you mean that there is a small probability that a
> large number of trials will be needed to get an answer,
> there is nothing nonexact about acceptancerejection
> methods. One could equally say that the BoxMuller method
> is inexact due to computer rounding, and it can give
> substantial errors because of that.
No that's not what I meant. See my reply to
s...@sherwood.csv.warwick.ac.u[CapitalEth]k
The naive Monte Carlo method is the most inefficient acceptance
>rejection method, probably older than YOU  which would make it
>very ancient indeed. :)
This is correct. However, there is the problem of
> coming up with efficient ones.
That's where we spent half a SEMESTER studying various more efficient
Monte Carlo methods of integral evaluation, quite separate and
distinct from the problem of pseudorandom number generation.
>>> Using this for simulation is VERY dangerous,
>This was WELLknown even back in the 1960s. But until the Box
>>Muller made its debut, serious scientists were using the IBM
>>Scientific Subroutine Library which had the sum of 12 U(0,1)6
>>for simulating N(0,1) variables.
>> as the pseudorandom numbers usually
>>> used are very definitely NOT independent.
>Of course they are not. Most of them are DETERMINISTIC. That's
>>why they are pseudorandom and not random. But they have very
>>long cycles within which one CANNOT distinguish the pseudo ones
>>from the truly random ones.
> Baloney. Long cycles are not the criterion; quasirandom
>> numbers, carried out to enough precision, have arbitrarily
>> long cycles, and are more uniformly distributed than
>> random numbers, but are nowhere near independent.
Since I have given away ALL of my books relating to pseudorandom
number
>generation and Monte Carlo methods, I don't have a ready reference.
>But the BALONEY is YOURS, as can be seen from the links below.
Why have you given them away?
Because I had already quit coldturkey from our/your silly profession
by taking an early retirement in 1999. :) I had given nearly all of
my journals/books to those who need them more than I do  my former
grad students and 10 different university libraries in China.
I can recall most of the results from memory, such as all the theory
and methods about Linear Models, and all the partial correlation
theory and methods I've been telling Richard Ulrich on his abuse of
Multiple Regression expected signs; and even the computational
details
of using SWEEP and how every single entry of a swept matrix relate to
a DIFFERENT bit of information in a multiple regression problem,
without having to refer to any books or notes. :)
The webpages now have quite a bit of references, especially the
expository kind, that are as good or better than those in books and
journals, and are quite uptodate.
Here's a web link that seems to be quite informative about the
subject.
http://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE142.HTM
>http://online.physics.uiuc.edu/courses/phys466/fall04/lnotes/random
numbers.html
*> What are some of the desired properties of random numbers?
>*> Uncorrelated, deterministic, longperiods between repeats,
uniform
>*> converage of range, efficiency of algorithm.
I have read more papers and books about CYCLE LENGTHS than there are
>methods of pseudorandom number generation  and I know at least
dozens
>of them.
It talks about the cycle lengths of linear congruential generators,
and
>some good choices for the selection of the constants. A long cycle
is
>definitely ONE of the criteria of selecting a pseudorandom number
>generator, in addition to dozens of other criteria of randomness.
As I said, long cycles are easy.
Nevertheless, it IS an important criterion. Certainly not the only
criterion.
I would never use a pseudorandom generator for production work.
> There are ways of using physical random numbers, which need not
> be perfect, to greatly lessen the problems of independence.
Well that's a hoss of a different color there.
>> The
>> pseudorandom generator which gave wrong resuits in the
>> Ising model had a period of 2^1279  1, which means that
>> essentially it will never repeat. It was found to have the
>> random numbers fall mainly in the planes failure in a
>> complicated form.
That's true as proven by Marsaglia (1968) that ktuples from the
more
>general class of linear congruential generators lie on sets of
parallel
>hyperplanes. But this known defect is important only when one
>simulates
>MULTIVARIATE data using the congruential generators. For UNIVARIATE
>simulation, that hardly mattered. Plenty of studies have been done
>on the CHOICE of constants to minimize the multivariate gap, as in
>the gap test (one of the standard criteria of testing pseudorandom
>number generators).
For univariate simulation, the use of quasirandom numbers
> and inverting the cdf is likely to be better. This is even
> the case for good multivariate problems, where the multi
> is not too large. Remember that quasirandom numbers are
> uniformly distributed, not random.
The inverting the cdf method is INDEPENDENT of the uniform random
number
generation method. The problem there is that many of the common pdfs
don't have cdf's in closed form, let alone invertible.
That's why in a typical Monte Carlo course, we study at least half a
dozen different simulation methods for each common distribution.
That's
where the BoxMuller, AhrensDieter, and other methods come into play.
There are also modern methods (post1968) that assures that the
>generated
>ktuples do not line on hyperplanes.
There are?
Yes, unless you take the nitpick position that a ktuple always lies
on a hyperplane of (k+1) dimentions.
Which one to use depends very much on the dimensionality of the
>application,
>which randomness criteria are more important than others, etc.,
etc.,
>etc. There is NO single pseudorandom number generator that's best
for
>all.
> The real danger is lack of independence,
There are MANY dangers. They are ALL real. See my preceding
paragraph
>and the paragraph below.
> even in longperiod generators for which there is even
>> demonstrable shortperiod lack of correlation. There are
>> some which even have good shortperiod independence.
Herman. That's really ANCIENT stuff. Take a look at the 1964
Handbook
>of Mathematical Functions (NBS). It discussed many such tests
there.
Weak tests. I would not use such, and would not have then.
Never said they were strong tests. The POINT was that all the
ISSUES about independence, serial correlation, etc. were known and
tested LONG ago, which is considered standard today. We just have
better testing tools that's all.
Most of what I have done is after that time. But none of
> the pseudorandom generators available then was good enough
> to be useful for the simulation which I did in 1970. I
> mixed random and pseudorandom to get reasonable results.
That would be rather tedious if your simulation required billionz
and billionz (ala Carl sagen) of random or pseudorandom deviates.
>> Far too many of the users of computers have far too much
>>> faith that the programmers have done a good job; this is
>>> often not so.
>Very true. It's also another of your strawman! No different
from
>>your strawmen statisticians.
> But it means they have to understand mathematical statistics,
>> so they can evaluate the errors.
Those who do, DO know much more than you do, as evidence by your
>discussion
>above. You are still living in the simulation world of the 1960s,
and
>before.
I do not remember when the failure of the longperiod
> shiftregister method was noted, but it was certainly not
> before 1980. And the failure was shown to be of the
> planes type, but just more complicated. Even the
> Mersenne twister has been found to have weaknesses.
All of the intelligent discussion of pseudorandom numbers
> relies heavily on mathematics.
AND statistics, numerical analysis, and compuation.
 Bob.

> This address is for information only. I do not claim that these
views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Department of Statistics, Purdue University
> hrubin@stat.purdue.edu Phone: (765)4946054 FAX:
(765)4940558
====
Subject: Re: Central Limit Theorem?
...............
>>>>My comment 3 shows that the xbar of U(0,1) ocnverges to
>Normal.
>>>>Not only that, but the ocnvergence is so rapid and good that
>for
>>>>years serious scientists had used an IBM Scientific Subroutine
>>>>that used the sum of TWELVE uniform random numbers to produce
>>>>(approx) standard normal deviates.
>>>> One can do better more cheaply.
>>>Again, you were commenting out of context. I was merely taking
>an
>>>example of how the CLT was actually used, IN THE OLD DAYS (which
>had
>>>been obsolete for decades now). Of course we can do better than
>>>that.
>>>BoxMuller (1958), Marsaglas (1964), and AhrensDieter (1988),
>are
>>>just some of the more recent methods. BoxMuller is far
>preferred
>>>because it is exact. I TAUGHT this stuff more than a decade ago
>in
>>>graduate courses in Monte Carlo Methods.
>>> I taught this farther back than that.
>>That's why your ideas are so OUT OF DATE and obsolete, as evidence
>>by what you said and I refute below.
>>WHen was the LAST time you taught a course in Monte Carlo methods
>>(if you ever taught one)?
>> I have taught a course in numerical methods in probability
>> and statistics quite a few times, roughly every other year,
>> and I certainly include simulation in the course,
>Like I included some simulation in EVERY probability and statistics
>course I ever taught? :) But I was talking about Graduate courses
>in Monte Carlo methods with advanced probability and statistics
>courses as prerequisites. These are much more SPECIALIZED on the
>subject of Monte Carlo methods.
Who needs a full course on Monte Carlo methods? And what
do you mean by advanced probability? Other than the use of
characteristic functions and their representations, and
occasionally using stochastic processes, the lowest course
in probability we accept for the PhD program is all I have
ever seen used in generating random variables with
preassigned distributions. This includes the central limit
theorem with the Lindeberg proof, or at least its idea.
As far as statistics, I do point out that one can do better
by using synthetic variables, and where to use expectations
and where to use sample moments. Monte Carlo methods are
not statistical procedures, but are used to compute integrals,
and are some of a large collection of such.
If one teaches in a conceptual manner, not a collection of
techniques, it goes much faster, and the student is in a
position to fill in the details.
>> including methods you probably have never heard of.
>That I don't doubt a bit.
>>> I believe the BoxMuller method, or some versions of it,
>>> was know before 1950.
>>Possibly some Technical Report version that is not as elegant.
>>1958 is the earliest published record of that method.
>> So?
>>> Another exact method, also very old, is to use
>acceptancerejection
>>> starting with the double exponential.
>>Here you are using the term exact incorrectly, at least in the
>>literature on Simulation and Monte Carlo Methods.
>> No, acceptance rejection methods can be exact.
>Shortly before your post (about 3 minutes, so you probably hadn't seen
>s=2E..@sherwood.csv.warwick.ac.u=ADk, explaining where my acceptance
>rejection notion came from.
>>The BoxMuller method is EXACT because it is based on the generation
>>of two iid U1 and U2 and the transformation of the random variable
>>is EXACTLY normal.
>> One version of the BoxMuller method is to take a random
>> point in a semicircle and transform it.
>That sounds like the same one, the one and only BoxMuller I know,
>and widely referenced in the literature.
There are other versions which compute trigonometric
functions. Taking a random point in a semicircle is
usually done by acceptancerejection. A method which is
equally efficient and computationally more robust is to
get the angle by acceptancerejection.
>>There are numerous acceptancerejection methods. NONE of the is
>>exact.
>>Most of them tend to converge asymptotally to the desired random
>>variable,
>>with diffreent rates of convergence (important in Monte Carlo
>methods).
>> Unless you mean that there is a small probability that a
>> large number of trials will be needed to get an answer,
>> there is nothing nonexact about acceptancerejection
>> methods. One could equally say that the BoxMuller method
>> is inexact due to computer rounding, and it can give
>> substantial errors because of that.
>No that's not what I meant. See my reply to
>s=2E..@sherwood.csv.warwick.ac.u=ADk
>>The naive Monte Carlo method is the most inefficient acceptance
>>rejection method, probably older than YOU  which would make it
>>very ancient indeed. :)
>> This is correct. However, there is the problem of
>> coming up with efficient ones.
>That's where we spent half a SEMESTER studying various more efficient
>Monte Carlo methods of integral evaluation, quite separate and
>distinct from the problem of pseudorandom number generation.
>>>> Using this for simulation is VERY dangerous,
>>>This was WELLknown even back in the 1960s. But until the Box
>>>Muller made its debut, serious scientists were using the IBM
>>>Scientific Subroutine Library which had the sum of 12 U(0,1)6
>>>for simulating N(0,1) variables.
>>>> as the pseudorandom numbers usually
>>>> used are very definitely NOT independent.
>>>Of course they are not. Most of them are DETERMINISTIC. That's
>>>why they are pseudorandom and not random. But they have
very
>>>long cycles within which one CANNOT distinguish the pseudo ones
>>>from the truly random ones.
>>> Baloney. Long cycles are not the criterion; quasirandom
>>> numbers, carried out to enough precision, have arbitrarily
>>> long cycles, and are more uniformly distributed than
>>> random numbers, but are nowhere near independent.
>>Since I have given away ALL of my books relating to pseudorandom
>number
>>generation and Monte Carlo methods, I don't have a ready reference.
>>But the BALONEY is YOURS, as can be seen from the links below.
>> Why have you given them away?
>Because I had already quit coldturkey from our/your silly profession
>by taking an early retirement in 1999. :) I had given nearly all of
>my journals/books to those who need them more than I do  my former
>grad students and 10 different university libraries in China.
At that time, I was already past retirement age. I am still
doing research, and will continue to do so as long as I can.
>I can recall most of the results from memory, such as all the theory
>and methods about Linear Models, and all the partial correlation
>theory and methods I've been telling Richard Ulrich on his abuse of
>Multiple Regression expected signs; and even the computational
>details
>of using SWEEP and how every single entry of a swept matrix relate to
>a DIFFERENT bit of information in a multiple regression problem,
>without having to refer to any books or notes. :)
Heck, I knew that 60 years ago. I considered it obvious then.
I even supervised people using desk calculators.
>The webpages now have quite a bit of references, especially the
>expository kind, that are as good or better than those in books and
>journals, and are quite uptodate.
>>Here's a web link that seems to be quite informative about the
>subject.
>>http://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE142.HTM
>>http://online.physics.uiuc.edu/courses/phys466/fall04/lnotes/random_number
=
>s=2Ehtml
>>*> What are some of the desired properties of random numbers?
>>*> Uncorrelated, deterministic, longperiods between repeats,
>uniform
>>*> converage of range, efficiency of algorithm.
I consider independence, not merely lack of correlation,
to be desirable. There are many purposes for which this
is the case. In fact, I want to look at the process as
generating a string of random bits, which can be so used
if desirable.
As far as deterministic, if this is desired, make a copy
of what is needed to get them, which may be the whole
set. Storage facilities are good.
>>I have read more papers and books about CYCLE LENGTHS than there are
>>methods of pseudorandom number generation  and I know at least
>dozens
>>of them.
>>It talks about the cycle lengths of linear congruential generators,
>and
>>some good choices for the selection of the constants. A long cycle
>is
>>definitely ONE of the criteria of selecting a pseudorandom number
>>generator, in addition to dozens of other criteria of randomness.
>> As I said, long cycles are easy.
>Nevertheless, it IS an important criterion. Certainly not the only
>criterion.
>> I would never use a pseudorandom generator for production work.
>> There are ways of using physical random numbers, which need not
>> be perfect, to greatly lessen the problems of independence.
>Well that's a hoss of a different color there.
>>> The
>>> pseudorandom generator which gave wrong resuits in the
>>> Ising model had a period of 2^1279  1, which means that
>>> essentially it will never repeat. It was found to have the
>>> random numbers fall mainly in the planes failure in a
>>> complicated form.
>>That's true as proven by Marsaglia (1968) that ktuples from the
>more
>>general class of linear congruential generators lie on sets of
>parallel
>>hyperplanes. But this known defect is important only when one
>>simulates
>>MULTIVARIATE data using the congruential generators. For UNIVARIATE
>>simulation, that hardly mattered. Plenty of studies have been done
>>on the CHOICE of constants to minimize the multivariate gap, as in
>>the gap test (one of the standard criteria of testing pseudorandom
>>number generators).
>> For univariate simulation, the use of quasirandom numbers
>> and inverting the cdf is likely to be better. This is even
>> the case for good multivariate problems, where the multi
>> is not too large. Remember that quasirandom numbers are
>> uniformly distributed, not random.
>The inverting the cdf method is INDEPENDENT of the uniform random
>number
>generation method. The problem there is that many of the common pdfs
>don't have cdf's in closed form, let alone invertible.
Invertibility is easier than you think, and fixed processes,
not using too many, can be used with multidimensional types
of quasirandom numbers.
>That's why in a typical Monte Carlo course, we study at least half a
>dozen different simulation methods for each common distribution.
>That's
>where the BoxMuller, AhrensDieter, and other methods come into play.
BoxMuller, with its logarithm, is already too slow.
The fastest ones I know are acceptancereplacement and
the new type of ziggurat. They are comparable in speed.
>>There are also modern methods (post1968) that assures that the
>>generated
>>ktuples do not line on hyperplanes.
>> There are?
>Yes, unless you take the nitpick position that a ktuple always lies
>on a hyperplane of (k+1) dimentions.
The shiftregister procedures have a different type of
plane behavior. The base field is not the reals, but
the lack of independence is just as great.
>>Which one to use depends very much on the dimensionality of the
>>application,
>>which randomness criteria are more important than others, etc.,
>etc.,
>>etc. There is NO single pseudorandom number generator that's best
>for
>>all.
>>> The real danger is lack of independence,
>>There are MANY dangers. They are ALL real. See my preceding
>paragraph
>>and the paragraph below.
>>> even in longperiod generators for which there is even
>>> demonstrable shortperiod lack of correlation. There are
>>> some which even have good shortperiod independence.
>>Herman. That's really ANCIENT stuff. Take a look at the 1964
>Handbook
>>of Mathematical Functions (NBS). It discussed many such tests
>there.
>> Weak tests. I would not use such, and would not have then.
>Never said they were strong tests. The POINT was that all the
>ISSUES about independence, serial correlation, etc. were known and
>tested LONG ago, which is considered standard today. We just have
>better testing tools that's all.
For any pseudorandom generator, there is at least one test
it will fail, namely, the test that that generator produced
the outcome. As von Neumann said, even thinking of using
systematic numbers for random puts one in a state of sin.
>> Most of what I have done is after that time. But none of
>> the pseudorandom generators available then was good enough
>> to be useful for the simulation which I did in 1970. I
>> mixed random and pseudorandom to get reasonable results.
>That would be rather tedious if your simulation required billionz
>and billionz (ala Carl sagen) of random or pseudorandom deviates.
The one I did in 1970 used more than 5 million. Yet the
uniform, exponential, and normal random variables used took
a little more than 1% of the computing time. The computations
took roughly 2.5 hours.
>>>> Far too many of the users of computers have far too much
>>>> faith that the programmers have done a good job; this is
>>>> often not so.
>>>Very true. It's also another of your strawman! No different
>from
>>>your strawmen statisticians.
>>> But it means they have to understand mathematical statistics,
>>> so they can evaluate the errors.
>>Those who do, DO know much more than you do, as evidence by your
>>discussion
>>above. You are still living in the simulation world of the 1960s,
>and
>>before.
Considering I am using methods not even thought of in that
time, this is a rather odd statement.
>> I do not remember when the failure of the longperiod
>> shiftregister method was noted, but it was certainly not
>> before 1980. And the failure was shown to be of the
>> planes type, but just more complicated. Even the
>> Mersenne twister has been found to have weaknesses.
>> All of the intelligent discussion of pseudorandom numbers
>> relies heavily on mathematics.
>AND statistics, numerical analysis, and compuation.
NOT on statistics. It does rely on numerical analysis,
of which computation is a part. But numerical analysis
is really part of analysis. I have no problems in
applying any part of theory which I have seen to real
problems of any complexity, which is why I am still
able to do reasonable research.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
>
< much snippage for brevity and getting to some real ISSUES >WHen was the LAST time you taught a course in Monte Carlo methods
>>(if you ever taught one)?
> I have taught a course in numerical methods in probability
>> and statistics quite a few times, roughly every other year,
>> and I certainly include simulation in the course,
Like I included some simulation in EVERY probability and statistics
>course I ever taught? :) But I was talking about Graduate courses
>in Monte Carlo methods with advanced probability and statistics
>courses as prerequisites. These are much more SPECIALIZED on the
>subject of Monte Carlo methods.
Who needs a full course on Monte Carlo methods?
LOL! This coming from a man who thought a 4quarter sequance in
Measure Theory and Probability Theory is necessary for an APPLIED
statistician!
Please excuse me while I clean off the coffee on my monitor
caused by your question.
That one sentence says it all about your prejudice and ignorance
about the subject.
The simple answer is: My doctoral students and some doctoral
students from Engineering and Computer Science have taken my
Monte Carlo methods course because they NEEDED the material
for their doctoral dissertation work.
Your doctoral students in mathematical statistics doesn't
even need to know how to compute anything.
C'est la difference, monsieur Rubin.
In fact, there's enough technical material there to make it a
TWO SEMESTER course, as you make your Measure TheoryProbability
Theory a 4quarter sequence.
In MY applied statistical environment we offer ZERO course of
YOUR kind in Measure Theory OR Probability Theory, because
for most of the doctoral students there is absolutely NO USE
for it, as we had argued in a separtely thread about my view
of the uselessness of Measure Theory in Applied Statistics.
The rest of your points are really largely pointless, given
the difference in our statistical/computational orientation
in Statistics and Statistical Education.
> Monte Carlo methods are
> not statistical procedures, but are used to compute integrals,
> and are some of a large collection of such.
So what's your point? Why did you use Monte Carlo methods then?
> If one teaches in a conceptual manner, not a collection of
> techniques,
It's my turn to say, balony!
>>Since I have given away ALL of my books relating to pseudorandom
>number
>>generation and Monte Carlo methods, I don't have a ready
reference.
>>But the BALONEY is YOURS, as can be seen from the links below.
> Why have you given them away?
Because I had already quit coldturkey from our/your silly
profession
>by taking an early retirement in 1999. :) I had given nearly all
of
>my journals/books to those who need them more than I do  my former
>grad students and 10 different university libraries in China.
At that time, I was already past retirement age. I am still
> doing research, and will continue to do so as long as I can.
I have no problem about that. The question for history to judge is
whether your publication has any impact on statistics, or from my
point of view, more importantly any impact on the APPLICATION of
Statistics.
I chose to retire because I had made a few meager contributions
to Applicd Statistics, and I was bored with much of what's going
on in ASA and IMS, especially the IMS and mathematical statsticians.
If you don't pretend to be an applied statistician, and be honest
like Hardy, Littlewood, and Erdos, then I wouldn't even have any
problem with THEIR warped view of application of mathematics, as
you have about statistics.
Hardy's rated mathematicians on a scale of 1 to 100, in which
he ranked himself 20, Littlewood 25, and David Hilbert 60. I
would say you are about a 2 on that scale. :) Erdos was
publishing useful MATHEMATICS till the day he died. But he didn't
pretend that his research was useful or intended to have any use
in the application of mathematics or statistics.
I foiled Erdos by actually using some of his asymptotic results
(with Renyi) on Random Graphs.
So, if you can't find things more useful or interesting to do in
your life, it's your business. Just don't PRETEND to be an
applied statistician on your worthless publications for
STATISTICAL APPLICATIONS.
I can recall most of the results from memory, such as all the theory
>and methods about Linear Models, and all the partial correlation
>theory and methods I've been telling Richard Ulrich on his abuse of
>Multiple Regression expected signs; and even the computational
>details
>of using SWEEP and how every single entry of a swept matrix relate
to
>a DIFFERENT bit of information in a multiple regression problem,
>without having to refer to any books or notes. :)
Heck, I knew that 60 years ago.
Why am I not surprised at a statement like that from you?
What you knew 60 years ago was the Gaussian Seeep, which dated
over a hundred years ago. What revolutionized MODERN regression
computation was Al Beaton's SWP which was his Harvard doctoral
dissertation in 1964. That was only 40 years ago.
It's a commutative and reversible operator that is not possessed
by any Gaussian (or other elmination) methods up till 1964.
It was the reversibility of Beaton's SWEEP operator that made
multiple regression, stepwise regression, and all kinds of MODERN
computer software packages adcpt that approach. Jim Goodnight
of SAS is one of the ones who used it well.
Do you know how to do the absolutely most efficient (you cannot
so it with less number of arithmetic operations any other way)
way of getting ALL possible regressions of Y on k independent
variables via Beaton's SWP in the order of the Hamiltonian path?
I implementated that in a software package 33 years ago,
BEFORE any of the known stat packages today did it, efficiently.
Some of them probably still use the brute force inefficient
method than the Hamiltonian path.
> I considered it obvious then.
> I even supervised people using desk calculators.
That's about your speed. :)Che
For some reason  the desk calculator I guess  about Chester
Bliss. He was still insisting his students to use the desk
calculator (in hte mid 1960s) because that was the only thing
he knew.
The classic line Jimmie Savage made about Chester Bliss was,
Ignorance is Bliss. :)
That's called the inverse=transform method. Those that cannot be
done explicitly are called something else. Too bad I am no longer
teaching my Monte Carlo course, else you could learn a few things
from it, from the Rubinstein and Fishman books I've used as TEXTBOOKS
and chapters from books by Applied Statisticians the likes of
Bill kennedy (ASA Fellow 1979) and Jim Gentle (ASA Fellow 1982)
and other APPLIED statisticians on Monte Carlo and Simulation
methods.
>> All of the intelligent discussion of pseudorandom numbers
>> relies heavily on mathematics.
AND statistics, numerical analysis, and compuation.
NOT on statistics. It does rely on numerical analysis,
> of which computation is a part. But numerical analysis
> is really part of analysis.
You're entitled to YOUR opinion, as I am entitled to mine.
Again, we have to agree to disagree here.
 Bob.
====
Subject: Re: Central Limit Theorem?
< much snippage for brevity and getting to some real ISSUES >>WHen was the LAST time you taught a course in Monte Carlo methods
>>>(if you ever taught one)?
>>> I have taught a course in numerical methods in probability
>>> and statistics quite a few times, roughly every other year,
>>> and I certainly include simulation in the course,
>>Like I included some simulation in EVERY probability and statistics
>>course I ever taught? :) But I was talking about Graduate courses
>>in Monte Carlo methods with advanced probability and statistics
>>courses as prerequisites. These are much more SPECIALIZED on the
>>subject of Monte Carlo methods.
>> Who needs a full course on Monte Carlo methods?
>LOL! This coming from a man who thought a 4quarter sequance in
>Measure Theory and Probability Theory is necessary for an APPLIED
>statistician!
I would settle for three, but 4 would be better.
>Please excuse me while I clean off the coffee on my monitor
>caused by your question.
>That one sentence says it all about your prejudice and ignorance
>about the subject.
>The simple answer is: My doctoral students and some doctoral
>students from Engineering and Computer Science have taken my
>Monte Carlo methods course because they NEEDED the material
>for their doctoral dissertation work.
>Your doctoral students in mathematical statistics doesn't
>even need to know how to compute anything.
I will admit that some of them did not. My current PhD
student is working on a procedure which will, with
reasonable assumptions, produce robust prior Bayes
estimates of spectral densities under squared error loss.
These estimates are asymptotically good, and should match
any of the nonparametric methods in use. He has carried
out both precise and simulation computations.
One of the receding ones computed numerical solutions of
partial differential equations. This gave some surprises,
which were verified theoretically.
>C'est la difference, monsieur Rubin.
>In fact, there's enough technical material there to make it a
>TWO SEMESTER course, as you make your Measure TheoryProbability
>Theory a 4quarter sequence.
Learn the basics, and apply them. Your students do
not learn the basics, as measuretheoretic probability
is needed for that.
>In MY applied statistical environment we offer ZERO course of
>YOUR kind in Measure Theory OR Probability Theory, because
>for most of the doctoral students there is absolutely NO USE
>for it, as we had argued in a separtely thread about my view
>of the uselessness of Measure Theory in Applied Statistics.
You seem to advocate teaching of ritual. I have no problems
with using numerical calculations, and none in using theory
to carry them out. Forty years ago, I received a request to
compute the significance level WAY out in the tails for the
sum of a large number of absolute normal random variables.
This turned out to be rather easy; simulation would have
been useless.
>The rest of your points are really largely pointless, given
>the difference in our statistical/computational orientation
>in Statistics and Statistical Education.
>> Monte Carlo methods are
>> not statistical procedures, but are used to compute integrals,
>> and are some of a large collection of such.
>So what's your point? Why did you use Monte Carlo methods then?
Because there are no other available methods to carry
out high dimensional integration. This is well known
in numerical analysis circles. For smooth problems,
quasirandom procedures are generally better, but not
always, and they are somewhat harder to use.
>> If one teaches in a conceptual manner, not a collection of
>> techniques,
>It's my turn to say, balony!
It takes half as long to learn twice as much.
...................
>> At that time, I was already past retirement age. I am still
>> doing research, and will continue to do so as long as I can.
>I have no problem about that. The question for history to judge is
>whether your publication has any impact on statistics, or from my
>point of view, more importantly any impact on the APPLICATION of
>Statistics.
>I chose to retire because I had made a few meager contributions
>to Applicd Statistics, and I was bored with much of what's going
>on in ASA and IMS, especially the IMS and mathematical statsticians.
I am not a member of ASA because I consider IMS not to
be sufficiently mathematical.
>If you don't pretend to be an applied statistician, and be honest
>like Hardy, Littlewood, and Erdos, then I wouldn't even have any
>problem with THEIR warped view of application of mathematics, as
>you have about statistics.
For all x, to apply x, one needs to understand the theory
of x. My first job resulted in methods, based on theory,
which are still being used today. The appliers with whom
I worked soon realized that they needed to formulate the
problems in terms of probability models. Simultaneous
equation people are still using them. And people will be
using the methods of generating random variables with
nonuniform distributions as well, as they now are in a
few situations.
How should significance levels vary with sample size?
This question was answered by Sethuraman and me 40
years ago; theory can and should be applied.
>Hardy's rated mathematicians on a scale of 1 to 100, in which
>he ranked himself 20, Littlewood 25, and David Hilbert 60. I
>would say you are about a 2 on that scale. :) Erdos was
>publishing useful MATHEMATICS till the day he died. But he didn't
>pretend that his research was useful or intended to have any use
>in the application of mathematics or statistics.
>I foiled Erdos by actually using some of his asymptotic results
>(with Renyi) on Random Graphs.
>So, if you can't find things more useful or interesting to do in
>your life, it's your business. Just don't PRETEND to be an
>applied statistician on your worthless publications for
>STATISTICAL APPLICATIONS.
I have given you some examples of applications of my
methods based on theoretical arguments. Do you know
the theory well enough to read them?
>>I can recall most of the results from memory, such as all the theory
>>and methods about Linear Models, and all the partial correlation
>>theory and methods I've been telling Richard Ulrich on his abuse of
>>Multiple Regression expected signs; and even the computational
>>details
>>of using SWEEP and how every single entry of a swept matrix relate
>to
>>a DIFFERENT bit of information in a multiple regression problem,
>>without having to refer to any books or notes. :)
>> Heck, I knew that 60 years ago.
>Why am I not surprised at a statement like that from you?
>What you knew 60 years ago was the Gaussian Seeep, which dated
>over a hundred years ago. What revolutionized MODERN regression
>computation was Al Beaton's SWP which was his Harvard doctoral
>dissertation in 1964. That was only 40 years ago.
THAT is a PhD dissertation? My standards are far higher. And
in no way would it be even a statistics result, but one in
numerical analysis.
>It's a commutative and reversible operator that is not possessed
>by any Gaussian (or other elmination) methods up till 1964.
>It was the reversibility of Beaton's SWEEP operator that made
>multiple regression, stepwise regression, and all kinds of MODERN
>computer software packages adcpt that approach. Jim Goodnight
>of SAS is one of the ones who used it well.
>Do you know how to do the absolutely most efficient (you cannot
>so it with less number of arithmetic operations any other way)
>way of getting ALL possible regressions of Y on k independent
>variables via Beaton's SWP in the order of the Hamiltonian path?
I suggest you read my paper in _Multivariate Analysis II_, in
which I showed that one could get the sums of squares of the
residuals in time O(2^k), which is clearly best possible. But
this would not justify a thesis.
>I implementated that in a software package 33 years ago,
>BEFORE any of the known stat packages today did it, efficiently.
>Some of them probably still use the brute force inefficient
>method than the Hamiltonian path.
I do not think the lexicographic approach is that much less
efficient, and it is easier to keep track of.
>> I considered it obvious then.
>> I even supervised people using desk calculators.
>That's about your speed. :)Che
>For some reason  the desk calculator I guess  about Chester
>Bliss. He was still insisting his students to use the desk
>calculator (in hte mid 1960s) because that was the only thing
>he knew.
>The classic line Jimmie Savage made about Chester Bliss was,
>Ignorance is Bliss. :)
>That's called the inverse=transform method. Those that cannot be
>done explicitly are called something else. Too bad I am no longer
>teaching my Monte Carlo course, else you could learn a few things
>from it, from the Rubinstein and Fishman books I've used as TEXTBOOKS
>and chapters from books by Applied Statisticians the likes of
>Bill kennedy (ASA Fellow 1979) and Jim Gentle (ASA Fellow 1982)
>and other APPLIED statisticians on Monte Carlo and Simulation
>methods.
Kennedy and Gentle was very weak when it came out.
I reluctantly used it as a text once.
>>> All of the intelligent discussion of pseudorandom numbers
>>> relies heavily on mathematics.
>>AND statistics, numerical analysis, and compuation.
>> NOT on statistics. It does rely on numerical analysis,
>> of which computation is a part. But numerical analysis
>> is really part of analysis.
>You're entitled to YOUR opinion, as I am entitled to mine.
>Again, we have to agree to disagree here.
> Bob.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
< much snippage for brevity and getting to some real ISSUES
>> Who needs a full course on Monte Carlo methods?
LOL! This coming from a man who thought a 4quarter sequance in
>Measure Theory and Probability Theory is necessary for an APPLIED
>statistician!
I would settle for three, but 4 would be better.
That one sentence says it all about your prejudice and ignorance
>about the subject.
The simple answer is: My doctoral students and some doctoral
>students from Engineering and Computer Science have taken my
>Monte Carlo methods course because they NEEDED the material
>for their doctoral dissertation work.
Your doctoral students in mathematical statistics doesn't
>even need to know how to compute anything.
I will admit that some of them did not.
That says a lot about your notion of applicable statistics.
>C'est la difference, monsieur Rubin.
In MY applied statistical environment we offer ZERO course of
>YOUR kind in Measure Theory OR Probability Theory, because
>for most of the doctoral students there is absolutely NO USE
>for it, as we had argued in a separtely thread about my view
>of the uselessness of Measure Theory in Applied Statistics.
You seem to advocate teaching of ritual.
I don't expect a statistical mathematician like yourself to under
what APPLIED statistics and Data Analysis are all about.
> Forty years ago, I received a request to
> compute the significance level WAY out in the tails for the
> sum of a large number of absolute normal random variables.
> This turned out to be rather easy; simulation would have
> been useless.
One thing a good applied statistician learn is WHEN to apply certain
methods and when NOT. pvalue and tail probability calculations
generally generally do not call for Monte Carlo methods. Another
one of Herman Rubin's strawman.
> ...................
> At that time, I was already past retirement age. I am still
>> doing research, and will continue to do so as long as I can.
I have no problem about that. The question for history to judge is
>whether your publication has any impact on statistics, or from my
>point of view, more importantly any impact on the APPLICATION of
>Statistics.
I chose to retire because I had made a few meager contributions
>to Applicd Statistics, and I was bored with much of what's going
>on in ASA and IMS, especially the IMS and mathematical statsticians.
I am not a member of ASA because I consider IMS not to
> be sufficiently mathematical.
That figures! And ASA is considered TOO mathematical by those foot
soldiers in the field DOING statistical application. Even the
Application of JASA and the American Statistician (which is REALLY
low level in mathematical prerequisites) are beyond their mathematical
comprehension level.
Yet many of them CAN and ARE producing creditable applied statistical
work, by following the correct methodologies and avoiding all the
pitfalls in applying those methodologies.
And YOU, in your fantasy world, is arguing that they need to know
Measure Theory and Loeve level Probability Theory before they can
apply statistics well.
The absurdity of your stance should be clear to EVERYONE in this
sci.stat.math group except yourself.
> How should significance levels vary with sample size?
> This question was answered by Sethuraman and me 40
> years ago; theory can and should be applied.
This would be a completely USELESS result in MY book:
30 years ago, an important chapter in my Data Analysis Lecture Notes
is statistical significance and practical significance are
COMPLETELY unrelated! I didn't need any MATHEMATICAL proof to
prove that. All I had to do was to exhibit many statistically
significant results that were completely USELESS in PRACTICE.
That articulates our different worlds, Herman.
>>I can recall most of the results from memory, such as all the
theory
>>and methods about Linear Models, and all the partial correlation
>>theory and methods I've been telling Richard Ulrich on his abuse
of
>>Multiple Regression expected signs; and even the computational
>>details
>>of using SWEEP and how every single entry of a swept matrix
relate
>to
>>a DIFFERENT bit of information in a multiple regression problem,
>>without having to refer to any books or notes. :)
> Heck, I knew that 60 years ago.
Why am I not surprised at a statement like that from you?
What you knew 60 years ago was the Gaussian Seeep, which dated
>over a hundred years ago. What revolutionized MODERN regression
>computation was Al Beaton's SWP which was his Harvard doctoral
>dissertation in 1964. That was only 40 years ago.
THAT is a PhD dissertation? My standards are far higher. And
> in no way would it be even a statistics result, but one in
> numerical analysis.
Your remark merely shows that you're completely ignorant about Al
Beaton's SWP, and the OTHER Operators for ANOVA and other statistical
computations in his 1964 Ed.D. dissertation at Harvard.
I mentioned SWP because it was one of the CLEVEREST results ever came
out of applied statistics, for Linear Regression computation. It is
ALL statistics.
>It's a commutative and reversible operator that is not possessed
>by any Gaussian (or other elmination) methods up till 1964.
It was the reversibility of Beaton's SWEEP operator that made
>multiple regression, stepwise regression, and all kinds of MODERN
>computer software packages adcpt that approach. Jim Goodnight
>of SAS is one of the ones who used it well.
Do you know how to do the absolutely most efficient (you cannot
>so it with less number of arithmetic operations any other way)
>way of getting ALL possible regressions of Y on k independent
>variables via Beaton's SWP in the order of the Hamiltonian path?
> I suggest you read my paper in _Multivariate Analysis II_, in
> which I showed that one could get the sums of squares of the
> residuals in time O(2^k), which is clearly best possible. But
> this would not justify a thesis.
Please excuse me for LOL. When you talk about big O, you're already
into another realm of ASYMPTOTIC MATHEMATICS.
Let's say I am using the SWP operator for my Multiple regression
computation on 100,000 observations.. After I have the results for
Y regressed on X1, ...X10, say, with the SSE being ONE element of
a 20 x 20 matrix being sweeped (because X11, X12, ... X18 are not
yet in the multiple regression), I can get the SSE of the regression
of Y on X1, ..., X10, together with any one of the remaining Xj, in
THREE arithmetic operations!
ONE multiplcation, ONE division, and ONE subtraction.
Mull on that a bit to let it sink in.
>I implementated that in a software package 33 years ago,
>BEFORE any of the known stat packages today did it, efficiently.
>Some of them probably still use the brute force inefficient
>method than the Hamiltonian path.
I do not think the lexicographic approach is that much less
> efficient, and it is easier to keep track of.
It is MUCH less efficient. It doesn't matter what you think in this
case because you don't KNOW Beaton's operator SWP and you don't know
how much more efficient it is (A FACT) than any lexicographical
approach!
The order of computing ALL possible regressions on X1, ... Xk is
by applying Beaton's SWP in the order of the Hamiltonian path
121312141213121... etc to produce the order of different combinations
of X in this order:
X1, (X1, X2), X2, (X2, X3), (X1, X2, X3), (X2, X3), ...
because Beaton's SWP brings an X in if it's not already in the
Multiple Regression, and take it out, if it is (because of the
REVERSIBLE property of SWP), thus resulting in the most efficient
method of computation, because EACH of the 2^k 1 possible
regressions takes exactly ONE SWP, no matter how many independent
variables there are in the combination! (One SWP is the equivalent
of pivotal step in a Gaussian elmination method .
You snipped the fact that I used Rubinstein and Fishman's books
for MY courses in Monte Carlo methods ...
>and chapters from books by Applied Statisticians the likes of
>Bill kennedy (ASA Fellow 1979) and Jim Gentle (ASA Fellow 1982)
>and other APPLIED statisticians on Monte Carlo and Simulation
>methods.
Kennedy and Gentle was very weak when it came out.
> I reluctantly used it as a text once.
Here what's weak and what's strong is not only subjective, but
context and subject matter dependent isn't it?
I would say for statistical computing, the Kennedy and Gentle
book was stronger than the TOTALITY of all of the papers ever
published in the Annals of Mathematical Statistics, and I would
mean it seriously!
 Bob.
>>> All of the intelligent discussion of pseudorandom numbers
>>> relies heavily on mathematics.
>AND statistics, numerical analysis, and compuation.
> NOT on statistics. It does rely on numerical analysis,
>> of which computation is a part. But numerical analysis
>> is really part of analysis.
You're entitled to YOUR opinion, as I am entitled to mine.
Again, we have to agree to disagree here.
 Bob.

> This address is for information only. I do not claim that these
views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Department of Statistics, Purdue University
> hrubin@stat.purdue.edu Phone: (765)4946054 FAX:
(765)4940558
====
Subject: Re: Central Limit Theorem?
>...
>There are numerous acceptancerejection methods. NONE of the is
>exact.
>Most of them tend to converge asymptotally to the desired random
>variable,
>with diffreent rates of convergence (important in Monte Carlo methods).
Please can you clarify what you mean by exact, or give a reference.
I don't know what you mean by saying that (e.g.) AhrensDieter is not
exact, or only tends to converge asymptotically...
>The naive Monte Carlo method is the most inefficient acceptance
>rejection method, probably older than YOU  which would make it
>very ancient indeed. :)
There's no need for that.
>...
>That's true as proven by Marsaglia (1968) that ktuples from the more
>general class of linear congruential generators lie on sets of parallel
>hyperplanes. But this known defect is important only when one
>simulates
>MULTIVARIATE data using the congruential generators. For UNIVARIATE
>simulation, that hardly mattered.
Googling for: Neave Box Muller
will give references to the problems with Box Muller & not only
linear congruential generators, but also (e.g.) with Tausworthe
generators.

J.E.H.Shaw [Ewart Shaw] strgh@uk.ac.warwick TEL: +44 2476 523069
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
http://www.warwick.ac.uk/statsdept http://www.ewartshaw.co.uk
3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@:2^:2))&.>@]^:(i.@[) <#:3 6 2
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
>...
>There are numerous acceptancerejection methods. NONE of the is
>exact.
>Most of them tend to converge asymptotally to the desired random
>variable,
>with diffreent rates of convergence (important in Monte Carlo
methods).
Please can you clarify what you mean by exact, or give a reference.
> I don't know what you mean by saying that (e.g.) AhrensDieter is not
> exact, or only tends to converge asymptotically...
My bad! That was my brain flatulence (but to our 'Merkin readers,
it was my brain fart).
I stand corrected.
I was thinking of the acceptancerejection methods in the use Monte
Carlo methods for integral evaluation, hence my mention of convergence
and inexactness.
AhrensDieter is an acceptancerejection method of pseudorandom number
GENERSTION, independent of any acceptancerejection method in Monte
Carlo evaluations.
Thsnks for your question to draw attention to my carelessness.
The naive Monte Carlo method is the most inefficient acceptance
>rejection method, probably older than YOU  which would make it
>very ancient indeed. :)
There's no need for that.
That was for Herman calling me balony. :)
I wasn't at all offended, the statement you cited was merely my
quid pro quo for his ideas being ancient. I did have a smiley there.
You Brits don't seem to have much sense of humor of this kind. The
naive Monte Carlo is of course the integralevaluation kind.
But I stand on my statement that Herman's OTHER comments (which I
refuted, about various criteria of pseudorandom number generation)
are outofdate as well as ancient.
...
>That's true as proven by Marsaglia (1968) that ktuples from the
more
>general class of linear congruential generators lie on sets of
parallel
>hyperplanes. But this known defect is important only when one
>simulates
>MULTIVARIATE data using the congruential generators. For UNIVARIATE
>simulation, that hardly mattered.
Googling for: Neave Box Muller
> will give references to the problems with Box Muller & not only
> linear congruential generators, but also (e.g.) with Tausworthe
> generators.
Statistics. Again, because all of these are PSDUDORANDOM generators,
some defects are more important than others, depending on the
actual application itself.
As Box pointed out in his Science and Statistics paper in JASA,
since all models are wrong,
it is important to worry about the tigers and not the mice.
IMHO, both Margalis's and Neaves's results are little mice, in many
if not most Monte Carlo simulation and applications.
 Bob.
> 
> J.E.H.Shaw [Ewart Shaw] strgh@uk.ac.warwick TEL: +44 2476
523069
> Department of Statistics, University of Warwick, Coventry CV4
7AL, UK
> http://www.warwick.ac.uk/statsdept
http://www.ewartshaw.co.uk
> 3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@:2^:2))&.>@]^:(i.@[) <#:3
6 2
====
Subject: Re: Central Limit Theorem?
> You are DEFINITELY wrong about this.
Are you saying The Central Limit Theorem stated in my reference link,
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.htm
is wrong, and you're right?
>
As I can see it, it is not the central limit theorem, but a
sample distribution of the sum (goes to normal when n goes up.
I do have a small Flash demo where the exact distrubution of the sum for
some diskrete distributions (uniform, bernoulli, geometric, Uform
distribution, ...) is calculated.
http://noppa5.pc.helsinki.fi/koe/flash/clt/clt2.html
Juha
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> You are DEFINITELY wrong about this.
Are you saying The Central Limit Theorem stated in my reference
link,
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.htm
is wrong, and you're right?
> As I can see it, it is not the central limit theorem, but a
> sample distribution of the sum (goes to normal when n goes up.
What is explained and proved in the link cited is what is generally
known
as The Centeral Limit Theorem, of the CLT expressed in its simplest
form.
The web link is also gives the historical reference to more general
extensions by Liapanov, and the Lindeberg's condition by Feller.
See e.g. Theorem 1 (the central limit theorem, which states in its
simplest form), Encyclopedia of Statistical Sciences, Vol 6, p.350,
under Normal Distribution.
 Bob.
====
Subject: Re: Central Limit Theorem?
>
>> You are DEFINITELY wrong about this.
>> Are you saying The Central Limit Theorem stated in my reference
> link,
>
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.htm
>> is wrong, and you're right?
>> As I can see it, it is not the central limit theorem, but a
>> sample distribution of the sum (goes to normal when n goes up.
What is explained and proved in the link cited is what is generally
> known
> as The Centeral Limit Theorem, of the CLT expressed in its simplest
> form.
The web link is also gives the historical reference to more general
> extensions by Liapanov, and the Lindeberg's condition by Feller.
See e.g. Theorem 1 (the central limit theorem, which states in its
> simplest form), Encyclopedia of Statistical Sciences, Vol 6, p.350,
> under Normal Distribution.
 Bob.
I am so sorry.
My idea was to critisize the external link:
Central Limit Theorem Java
http://www.math.csusb.edu/faculty/stanton/probstat/clt.html
not the page
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.htm
Juha
====
Subject: Re: Central Limit Theorem?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
>> You are DEFINITELY wrong about this.
>> Are you saying The Central Limit Theorem stated in my
reference
> link,
>
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.htm
>> is wrong, and you're right?
That was actually my comment to Herman Rubin's comment! :)
>> As I can see it, it is not the central limit theorem, but a
>> sample distribution of the sum (goes to normal when n goes up.
What is explained and proved in the link cited is what is generally
> known
> as The Centeral Limit Theorem, of the CLT expressed in its
simplest
> form.
The web link is also gives the historical reference to more general
> extensions by Liapanov, and the Lindeberg's condition by Feller.
See e.g. Theorem 1 (the central limit theorem, which states in its
> simplest form), Encyclopedia of Statistical Sciences, Vol 6,
p.350,
> under Normal Distribution.
 Bob.
> I am so sorry.
No problem! I thought EVERYONE knows the simple version of the CLT
anyway.
My idea was to critisize the external link:
> Central Limit Theorem Java
> http://www.math.csusb.edu/faculty/stanton/probstat/clt.html
This link does make the statement example of the CLT unnecessarily
obscure.
not the page
>
http://www.absoluteastronomy.com/encyclopedia/C/Ce/Central_limit_theorem.htm
I still think that's an excellent expository page, covering all aspects
of the CLT without getting tangled by any deep mathematics, but only
pointing to those results.
> Juha
 Bob.
====
Subject: Please help... I am SO confused right now about statistics
EdU3Zw0AAAC1UObQGTj_fW8apNdfPK7S
I need to find the autocovariances gamma(j), j = 0,1,2,..., of the
AR(3) process
(1  0:5B)(1  0.4B)(1  0.1B)Xt = Zt, {Zt} ~ WN(0,1)
However, I'm not sure exactly where to start...can anyone give me tips
as to how to approach this problem?
====
Subject: Re: Please help... I am SO confused right now about statistics
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
> I need to find the autocovariances gamma(j), j = 0,1,2,..., of the
> AR(3) process
> (1  0:5B)(1  0.4B)(1  0.1B)Xt = Zt, {Zt} ~ WN(0,1)
However, I'm not sure exactly where to start...can anyone give me
tips
> as to how to approach this problem?
Depends on what you know.
Could you do it for an AR(1)?
(1  0.1B)Xt = Zt, {Zt} ~ WN(0,1)
or not?
Glen
====
Subject: Is Quantum Mechanics A Limit Cycle Theory
Hello
May You help me to understand the meaning of the limit Cycle in the
Following paper
Is Quantum mechanics a limit cycle theoryCetto and de la penna 1995 in
Fundamental problems in Quantum Physics Editor Van den Marve
In fact I Am intersted in the Hilbert 16th problem which main object is
Limit cycle
I had presented the simillar question
//mathforum.org/kb/thread.jspa?forumID=253&threadID=1092416&messageID=345685
9#3456859
in sci.math.research but I think this forum is more appropriate for such
Conversation
Your comments will be very appreciated
Ali Taghavi
====
Subject: Conditional probabilities
Trying to sort a (for me) tricky combinational situation.
L is a process with 3 subprocesses, F, A and T. F, A and T are sequential
and independent other than each process must be successful before the next
can be considered ie if F fails, the process terminates and L has failed.
What is the overall probability that L will fail for failure probabilities
P(F), P(A) and P(T) and why?
pete
====
Subject: Re: Conditional probabilities
Here are my Solution for it..
the subprocess F, A and T has a probability of 0.001 to be failed. then we
use geometric probability that is finding the probability of the 1st failure:
P(Failure) = probability that subprocess F failed +
probability that subprocess A failed +
probability that subprocess T failed
P(Failure) = (0.001)(0.999^0) + (0.001)(0.999^1) +
(0.001)*0.999^2)
It is my idea.. but this problem is quite tricky..
====
Subject: Re: Conditional probabilities
Here are my thoughts (2) which produce significantly different results 
significant in that one breaks the target and one doesn't!
1.
P(Success) = 1  P(Fail)
P(success_L) = P(success_F) x P(success_A) x p(success_T)
P(Fail) for F, A and T has a target of 1 x103
So P(Success) for each part is 1  1 x103 = 0.999
Therefore P(success_L) = 0.999 x 3 = 0.997
Therefore P(fail_L) = 1  P(success_L) = 0.002997
2. However, using combinational probability:
Taking P(AF) and then using this in P(T(AF)) gives P(AF) as 0.999 (ie
0.999 x 2/0.999) and so P(T(AF)) = 0.999 as well.
Therefore, P(success_L) = P(T(AF)) = 0.999 and P(fail_L) = 0.001
So what's right, or is there a 3rd way?
Hurts my head
pete
====
Subject: Re: Conditional probabilities
What is 5+5?
====
Subject: Re: Conditional probabilities
you said it is sequential...ie F is the first, A second and T is the Last.
Am I correct?
P(LF) = Probability that the First process failed. Since it is the first
subprocess. if it fails then there will be no process A and T.
P(LA) = Probability that 2nd process failed... that is probability that
process failed given that Process F succeed.
P(LT) = probability that 3rd process failed given that the two succeed.
make use of the bayes theorem or go back to basic counting priciples
(general multiplication rule)
====
Subject: determining sample size for infinite population with unknown mean
I am trying to determine a good sample size for 90+% confidence measurements
of an infinite population.
Unfortunately, all equations I've found for determining ideal sample size of
an infinite population rely on the total population's standard deviation.
Because the population is infinite, I don't know the total population's
standard deviation (and it is impossible to know, right?)
Any suggestions? I would like to avoid Bayesian methods, just because I
find them confusing, but if someone can clearly explain a Bayesian method for
solving this problem, I will give it a shot. We do have previous results for
a slightly different infinite population, based on a sample size of 80.
Chris.
====
Subject: Re: determining sample size for infinite population with unknown
mean
On Thu, 21 Apr 2005 13:11:26 EDT, Chris Chatham measurements of an infinite population.
Unfortunately, all equations I've found for determining ideal
> sample size of an infinite population rely on the total population's
> standard deviation. Because the population is infinite, I don't know
> the total population's standard deviation (and it is impossible to
> know, right?)
And, you will *never* know what the infinite population
is, will you? You don't say what you are estimating, how
often, for what purpose. Is the variance a function of the
mean, as with polls on candidates?
Most folks take the variance estimate that they happen to
have on hand  from a random sample  as true. A more
conservative approach will use a slightly larger value;
or provide several estimates using various realistic estimates.
Political polls use the maximum estimate of variance, var(50%).
More complicated methods exist. Look for tolerance
intervals instead of confidence intervals.
[snip, Q about Bayesian. I wouldn't know if that could help.]

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Fuzzy Clustering and Data Analysis Toolbox
Fuzzy Clustering and Data Analysis Toolbox
The first release of the toolbox is now available from
http://www.fmt.vein.hu/softcomp/fclusttoolbox/
The purpose of the development of this toolbox was to compile a
continuously extensible, standard tool, which is useful for any
Matlab user for one's aim. In Chapter 1 of the downloadable related
documentation one can find a theoretical introduction containing the
theory of the algorithms, the definition of the validity measures
and the tools of visualization, which help to understand the
programmed Matlab files. Chapter 2 deals with the exposition of the
files and the description of the particular algorithms, and they are
illustrated with simple examples, while in Chapter 3 the whole
Toolbox is tested on real data sets during the solution of three
clustering problems: comparison and selection of algorithms;
estimating the optimal number of clusters; and examining
multidimensional data sets.
About the Toolbox
The Fuzzy Clustering and Data Analysis Toolbox is a collection of
Matlab functions. The toolbox provides five categories of functions:
 Clustering algorithms. These functions group the given data set
into clusters by different approaches: functions Kmeans and Kmedoid
are hard partitioning methods, FCMclust, GKclust, GGclust are fuzzy
partitioning methods with different distance norms.
 Evaluation with cluster prototypes. On the score of the clustering
results of a data set there is a possibility to calculate membership
for unseen data sets with these set of functions. In 2dimensional
case the functions draw a contourmap in the data space to visualize
the results.
 Validation. The validity function provides cluster validity
measures for each partition. It is useful when the number of cluster
is unknown a priori. The optimal partition can be determined by the
point of the extrema of the validation indexes in dependence of the
number of clusters. The indexes calculated are: Partition
Coefficient (PC), Classification Entropy (CE), Partition Index (SC),
Separation Index (S), Xie and Beni's Index (XB), Dunn's Index (DI)
and Alternative Dunn Index (DII).
 Visualization. The Visualization part of this toolbox provides the
modified Sammon mapping of the data. This mapping method is a
multidimensional scaling method described by Sammon.
 Examples. An example based on industrial data set to present the
usefulness of these toolbox and algorithms.

Janos Abonyi, Ph.D
Head of the Department of Process Engineering
University of Veszprem
P.O.Box 158 H8200, Veszprem, Hungary
Tel: +3688624209 or 3688622793
Fax: +3688421709
www.fmt.vein.hu/softcomp
You can order our new book (Fuzzy Model Identification for Control)
from Birkhauser Boston (Springer  NY)
http://www.springerny.com/detail.tpl?cart=1048164347947749&ISBN=0817642382
or from Amazon.com
http://www.amazon.com/exec/obidos/ASIN/0817642382/
====
Subject: Looking for example Logistic Regression problems
I am developing a program to perform Logistic Regression analysis, and I
need test cases to run through it. I need data sets with descriptions of
the variables. Ideally, I would like to have results generated by other
established programs like SAS, SPSS, LogXact, etc. to use for comparison,
but I will be happy to take any reasonable data.
I have managed to find about a halfdozen worked examples for which I have
results from other programs, and my results match the published results.
But I need another 20 or so problems of varying complexity to use for
testing.

Phil Sherrod
(phil.sherrod 'at' sandh.com)
http://www.dtreg.com (decision tree modeling)
http://www.nlreg.com (nonlinear regression)
http://www.NewsRover.com (Usenet newsreader)
http://www.LogRover.com (Web statistics analysis)
====
Subject: GianCarlo Rota's Twelve problems in probability no one likes to
bring up.
ZHxqtQ0AAABsLpd9eambR4kDlN15V8h
One day, quite by accident, I ran across Algebraic Combinatorics and
Computer Science: A tribute to GianCarlo Rota Rota is a wellknown
algebraist recently passed away.
On p57 is a reprint of his 1998 Fubini Lecture titled Twelve
problems in probability no one likes to bring up. Among those
tweleve problems are:
(4) Work on entropy and algebra
(5) Maximum entropy principle
(6) Conditional probability, Bayes' Law
(10) Multivariate Normal Distribution and the Clifford Distribution
And, perhaps, most controversial:
(12) Free Probability Theory which aims to refute the generally
accepted platitude that to observables in quantum probability do not
have a joint distribution.
All of this work falls under the general category of a revision of
the notion of a sample space as his ultimate aim.
For a number of reasons, I would like to consider one of these subjects
as a potential thesis subject. I do not know  but I suspect  that
thesis advisors sometimes shy away from controversial subjects or
classical outstanding problems (ex. Riemann Hypothesis). Moreover,
despite the fact that Rota was a worldclass algebraist, the
mathematicalstatistical community may see anyone of these problems as
silly, wrong, or wrongly motivated and therefore dismiss them out of
hand.
My hope was to get some feed back on how this might play and,
generally, what the statistics people think.
====
Subject: Re: GianCarlo Rota's Twelve problems in probability no one likes
to bring up.
0lU0bA0AAAAg3C2mxP6zREVnYH2XhiV
Hello clearthink@cavtel.net,
There are several groups of people who think about these problems...
Cambridge Inference Group: http://www.inference.phy.cam.ac.uk/is/
Probability Theory as Extended Logic: http://bayes.wustl.edu/
MaxEnt regulars: http://www.maxent2005.org
I myself have just published a paper that I feel clarifies #4:
Lattice Duality: The Origin of Probability and Entropy
Kevin H. Knuth
Neurocomputing 2005
http://www.huginn.com/knuth/publications.html
The sample space is literally the Boolean space of assertions.
How this relates to the space of questions leads to the concept of
entropy.
How this relates to to Quantum Mechanics is still unclear.
Philip Goyal at Cambridge (Steve Gull's student) just finished a thesis
on the topic.
Ariel Caticha has a fine paper on Quantum Amplitudes
http://www.arxiv.org/abs/quantph/9804012
He has many other nice papers too.
Yoel Tikochinsky developed some threads along Caticha's line about a
decade earlier...
http://www.arxiv.org/abs/quantph/9903031
And I discuss the basic methodology in my paper Deriving Laws from
Ordering Relations...
http://www.arxiv.org/abs/physics/0403031
Hope this helps,
Kevin H. Knuth
> One day, quite by accident, I ran across Algebraic Combinatorics and
> Computer Science: A tribute to GianCarlo Rota Rota is a wellknown
> algebraist recently passed away.
On p57 is a reprint of his 1998 Fubini Lecture titled Twelve
> problems in probability no one likes to bring up. Among those
> tweleve problems are:
(4) Work on entropy and algebra
> (5) Maximum entropy principle
> (6) Conditional probability, Bayes' Law
> (10) Multivariate Normal Distribution and the Clifford Distribution
And, perhaps, most controversial:
(12) Free Probability Theory which aims to refute the generally
> accepted platitude that to observables in quantum probability do not
> have a joint distribution.
All of this work falls under the general category of a revision of
> the notion of a sample space as his ultimate aim.
For a number of reasons, I would like to consider one of these
subjects
> as a potential thesis subject. I do not know  but I suspect 
that
> thesis advisors sometimes shy away from controversial subjects or
> classical outstanding problems (ex. Riemann Hypothesis). Moreover,
> despite the fact that Rota was a worldclass algebraist, the
> mathematicalstatistical community may see anyone of these problems
as
> silly, wrong, or wrongly motivated and therefore dismiss them out of
> hand.
My hope was to get some feed back on how this might play and,
> generally, what the statistics people think.
====
Subject: Re: GianCarlo Rota's Twelve problems in probability no one likes
to bring up.
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
And, perhaps, most controversial:
(12) Free Probability Theory which aims to refute the generally
> accepted platitude that to observables in quantum probability do not
> have a joint distribution.
I don't think that's controversial anymore, after Godel pulled the
rug under the Foundation of Mathemtics by demonstrating that no
complex mathematical system was complete. In other words, no
matter what axioms are chosen, meaningful mathematical statements
can be made whose truth or falseness can be demonstrated within
the system!
Bertrand Russell, who toiled for 20 years with Whitehead in writing
their Principia Mathematica, which was inpenetrable even to
mathematicians, was crushed by Godel's revelation.
Russell said, ... I came to the conclusion that there was nothing
more I could do to make mathematical knowledge indubitable.
> but I suspect  that
> thesis advisors sometimes shy away from controversial subjects or
> classical outstanding problems (ex. Riemann Hypothesis).
I am reading a book about Paul Erdos, the SECOND most prolific
writer of mathematics in the history of mathematics, and arguably
the greatest mathematician of the 20th century. Erdos had this
story to tell about Hardy (of Hardy and Littlewood fame) and
Riemann's Hypothesis.
On a turbulent boat trip from Scandinavian to England, Hardy dashed
off a postcard to a colleague announcing that he had proved the
Riemann Hypothesis.
According to Erdos, Hardy did that because he believed Erdos'
SF (God) would not let him die with the potential
of people thinking he had proved Riemann's Hypothesis.
It was in that era that Godel (whom Paul Hoffman, author of
The Man Who Loved Only Numbers described as not a poster boy
for mathematical sanity) emerged to rock the foundation of
Mathematics.
Not exactly a good doctoral dissertation topic, IMHO. But a well
researched account of the History of Mathematics would make an
interesting book fof everyone to read.
 Bob.
====
Subject: Re: GianCarlo Rota's Twelve problems in probability no one likes
to bring up.
zuiTXwwAAADHDQA2vQPjoyoWimvkgeWk
In part, if there is a tendency for advisors to shy away from
controversial
topics it is out of concern for the student. IMO (and the opinion of
others I've talked to) a graduate student should worry about finding
a doable thesis topic, that is something that can be reasonably
expected to yield an acceptable thesis in the time frame that one
expects for the degree. After a person has his credentials (perhaps
even after one is established, whatever that means), and has
aquired the necessary mastery of the field, is the time to make
one's mark on the field by tackling contoversial topics. Some may
disagree with this approach, perhaps arguing that I'm stifling
creativity and promoting mediocracy. They are not the ones
gambling with their future, and the reality is that very few grad
students make really significant contributions to their field with
their thesis, and you probably are not the next Riemann or Liapunov.
If you think you are, then go for it. Good luck.
Russell
====
Subject: Re: GianCarlo Rota's Twelve problems in probability no one likes
to bring up.
ZHxqtQ0AAABsLpd9eambR4kDlN15V8h
> topics it is out of concern for the student. IMO (and the opinion of
> others I've talked to) a graduate student should worry about finding
> a doable thesis topic, that is something that can be reasonably
> expected to yield an acceptable thesis in the time frame that one
> expects for the degree.
I get this. And it is very reasonable. And probably best in the
short run for the reasons you explain.
> gambling with their future, and the reality is that very few grad
> students make really significant contributions to their field with
> their thesis, and you probably are not the next Riemann or Liapunov.
> If you think you are, then go for it. Good luck.
But this, if I may be so bold, is an example of the concerns I have;
that to even brush into subjects out of the ordinary leads one off in
the
wrong direction. Even though my math GPA was 3.9+ I know/think I am
just
of average ability  almost certainly lower than what passes for
normal at UCB, Stanford etc.. Hell, I am 35 and only got back into math
because, besides loving it, I got sick and tired of software.
I used the example of Riemann Hypoth (with some success I might add)
as an example to illustrate that there touchpoints that students
ought to stay away from because they are prone to being misunderstood
i.e when you write you probably are not the next Riemann. By that
point in time, the jibe go for it risks nothing on your part and adds
nothing to the conversation.
Again, your advice earlier is rather reasonable and reasonably argued.
I, like you, want to stay away from crazy claims, unreasonable subject
areas, and taking on tasks that are crazy. All these sorts of things
consume resources and return little if anything for either the
University,
the prof, or the student. Folks, time is short ... so let's forget
about
being the Riemann and return to the bigger picture.
To get into a PhD program means typing up a statement of work. But that
can lead to the catch22: how can I really know if is tough unless
and until I attempt it? So perhaps it best to say I like probability
and I did a, b, and c in probability. This way one does not have to
pigeon hole himself in any one thesis with its attendant risks above.
Further, one can delay the decision until a relationship has developed
between the profs and the student.
====
Subject: Re: GianCarlo Rota's Twelve problems in probability no one likes
to bring up.
zuiTXwwAAADHDQA2vQPjoyoWimvkgeWk
> topics it is out of concern for the student. IMO (and the opinion
of
> others I've talked to) a graduate student should worry about
finding
> a doable thesis topic, that is something that can be reasonably
> expected to yield an acceptable thesis in the time frame that one
> expects for the degree.
> I get this. And it is very reasonable. And probably best in the
> short run for the reasons you explain.
gambling with their future, and the reality is that very few grad
> students make really significant contributions to their field with
> their thesis, and you probably are not the next Riemann or
Liapunov.
> If you think you are, then go for it. Good luck.
> But this, if I may be so bold, is an example of the concerns I have;
> that to even brush into subjects out of the ordinary leads one off in
> the
> wrong direction. Even though my math GPA was 3.9+ I know/think I am
> just
> of average ability  almost certainly lower than what passes for
> normal at UCB, Stanford etc.. Hell, I am 35 and only got back into
math
> because, besides loving it, I got sick and tired of software.
I used the example of Riemann Hypoth (with some success I might
add)
> as an example to illustrate that there touchpoints that students
> ought to stay away from because they are prone to being misunderstood
> i.e when you write you probably are not the next Riemann. By that
> point in time, the jibe go for it risks nothing on your part and
adds
> nothing to the conversation.
Perhaps you mistook me. My point was that I wouldn't categorically
tell anyone how to live their life, and if someone really thinks
he/she has what it takes to attack some problem that has resisted
the best minds for decades, then they should follow their bliss, as
Joseph Campbell used say. I just want them to make an informed
decision.
Again, your advice earlier is rather reasonable and reasonably
argued.
> I, like you, want to stay away from crazy claims, unreasonable
subject
> areas, and taking on tasks that are crazy. All these sorts of things
> consume resources and return little if anything for either the
> University,
> the prof, or the student. Folks, time is short ... so let's forget
> about
> being the Riemann and return to the bigger picture.
To get into a PhD program means typing up a statement of work. But
that
> can lead to the catch22: how can I really know if is tough
unless
> and until I attempt it? So perhaps it best to say I like
probability
> and I did a, b, and c in probability. This way one does not have to
> pigeon hole himself in any one thesis with its attendant risks
above.
> Further, one can delay the decision until a relationship has
developed
> between the profs and the student.
Ahh, I didn't understand from your original post that your query
assumed you were already in the program, that's my fault. So am I
correct that you are writing something in response to a question on
an grad school application like What research topic would you like
to pursue if you are admitted to our program?, or are you in the
graduate program and looking for a research topic? If the former
is the case, unless you know that a topic that really interests
you is one that is of interest to one or more faculty (preferably
faculty who have money to support you ;) ) then I'd suggest the
generic approach is preferable. For instance, if you rave about
how wonderful Bayesian statistics is and there are no Bayesians
on the staff, you might be at a disadvantage because the profs
(on the whole, IMO) want a mutually satisfying experience for
the students and themselves. Of course, it may not be good to
be too generic, either. Perhaps mention that you've read about
X and you could see yourself pursuing it if the opportunity
arose. I personally found such questions to be annoying when I
was faced with them. As you say, potential catch22. Sorry I
don't have more concrete advice.
Russell
====
Subject: Re: GianCarlo Rota's Twelve problems in probability no one likes
to bring up.
Mzt37gwAAACjYRm6XIoKF1hrhw8NW9aW
> On p57 is a reprint of his 1998 Fubini Lecture titled Twelve
> problems in probability no one likes to bring up. Among those
> tweleve problems are:
(4) Work on entropy and algebra
> (5) Maximum entropy principle
> (6) Conditional probability, Bayes' Law
> (10) Multivariate Normal Distribution and the Clifford Distribution
And, perhaps, most controversial:
(12) Free Probability Theory which aims to refute the generally
> accepted platitude that to observables in quantum probability do not
> have a joint distribution.
All of this work falls under the general category of a revision of
> the notion of a sample space as his ultimate aim.
I'm no expert statistician, so I may have missed something here. But,
choosing Bayes law as an example, this is an extremely frequently
brought up topic. Searching on all the other topics reveals lots of
web links, conferences, etc. I know that this doesn't prove anything as
there are still cold fusion conferences, web pages, etc. But, reading
the start of your posting I expected to find a whole lot of rare and
unexplored topics.
I'm not criticising your potential choice of topic. But, I think that
the langauge .... no one likes to bring up ... may be a bit of an
exaggeration.
Rossc
====
Subject: Re: GianCarlo Rota's Twelve problems in probability no one likes
to bring up.
ZHxqtQ0AAABsLpd9eambR4kDlN15V8h
> I'm no expert statistician, so I may have missed something here. But,
> choosing Bayes law as an example, this is an extremely frequently
> brought up topic.
To judge, first read what Rota. He was not pandering to generalities...
>But, I think that the langauge .... no one likes to bring up ... may
be a bit of an
>exaggeration.
This was not my title. It was the title of Rota's Fubini lecture in
Italy (a very, very well received lecture). As far as I know, Rota was
so good in mathematics he didn't sweat
these small issues ... he had far bigger fish to fry.
Shane
====
Subject: ignorance quote
Looking for the complete text of a quote. It is something like
Before, our ignorance was of a meager sort. Now it is profound and
satisfying.
But it has lots more words. As I recall, it was supposedly posted to a
door of a (lab? classroom?) at the University of (Tromsko? Somewhere in
Finland? Norway?)
I thought I remembered it from the forward of Kloeden & Platen's
Numerical Solution of Stochastic Differential Equations but it isn't
in the 1999 edition. Google didn't help.
Sound familiar to anyone?
====
Subject: Re: ignorance quote
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> Looking for the complete text of a quote. It is something like
Before, our ignorance was of a meager sort. Now it is profound and
> satisfying.
>
I have used this (or variations of it) in newsgroups about some
posters:
As the saying goes, before you opened your mouth, there is doubt about
the depth of your ignorance; but as soon as you opened your mouth,
you removed all doubts.
SOURCE UNKNOWN.
Now THAT characterizes profound ignorance. :)
 Bob.
====
Subject: Re: ignorance quote
> Looking for the complete text of a quote. It is something like
Before, our ignorance was of a meager sort. Now it is profound and
> satisfying.
But it has lots more words. As I recall, it was supposedly posted to a
> door of a (lab? classroom?) at the University of (Tromsko? Somewhere in
> Finland? Norway?)
I thought I remembered it from the forward of Kloeden & Platen's
> Numerical Solution of Stochastic Differential Equations but it isn't
> in the 1999 edition. Google didn't help.
Sound familiar to anyone?
Yes, it sounds kind of familiar, but I can't say more than that. I'd
love to know the source.
Glen
====
Subject: Re: ignorance quote
>> Looking for the complete text of a quote. It is something like
>>
>> Before, our ignorance was of a meager sort. Now it is profound and
>> satisfying.
>>
>> But it has lots more words. As I recall, it was supposedly posted to a
>> door of a (lab? classroom?) at the University of (Tromsko? Somewhere in
>> Finland? Norway?)
>>
>> I thought I remembered it from the forward of Kloeden & Platen's
>> Numerical Solution of Stochastic Differential Equations but it isn't
>> in the 1999 edition. Google didn't help.
>>
>> Sound familiar to anyone?
> Yes, it sounds kind of familiar, but I can't say more than that. I'd
> love to know the source.
> Glen
This sound vaguely like the quote from Lord Kelvin concerning
the role of measurement in knowledge.
When you measure what you are speaking about and express it in numbers,
you know something about it, but when you cannot (or do not) measure it,
when you cannot (or do not) express it in numbers, then your knowledge
is of a meagre and unsatisfactory kind.
See, e.g., http://sres.anu.edu.au/associated/mensuration/measure.htm

==============
Mike Lacy, Ft Collins CO 80523
Clean out the 'junk' to email me.
====
Subject: Re: ignorance quote
>
>>>Looking for the complete text of a quote. It is something like
>>>>Before, our ignorance was of a meager sort. Now it is profound and
>>>satisfying.
>>>>But it has lots more words. As I recall, it was supposedly posted to a
>>>door of a (lab? classroom?) at the University of (Tromsko? Somewhere in
>>>Finland? Norway?)
>>>>I thought I remembered it from the forward of Kloeden & Platen's
>>>Numerical Solution of Stochastic Differential Equations but it isn't
>>>in the 1999 edition. Google didn't help.
>>>>Sound familiar to anyone?
>>Yes, it sounds kind of familiar, but I can't say more than that. I'd
>>love to know the source.
>>Glen
> This sound vaguely like the quote from Lord Kelvin concerning
> the role of measurement in knowledge.
When you measure what you are speaking about and express it in numbers,
> you know something about it, but when you cannot (or do not) measure it,
> when you cannot (or do not) express it in numbers, then your knowledge
> is of a meagre and unsatisfactory kind.
See, e.g., http://sres.anu.edu.au/associated/mensuration/measure.htm
must have conflated it with the target quote in my memory.
I found what I was looking for, and the key word is confused:
We have not succeeded in answering all our problems. The answers we
have found only serve to raise a whole set of new questions. In some
ways we feel we are as confused as ever, but we believe we are confused
on a higher level and about more important things.
Quoted in Stochastic Differential Equations: An Introduction with
Applications by Bernt ¯ksendal, 2nd ed., SpringerVerlag, 1989.
Google this, and you will see it has propagated to 165 pages! Most put
no attribution or anonymous. The only attributions I've found are
¯ksendal. There's no telling who said it first.
M*Z
====
Subject: Re: ignorance quote
>
>>Looking for the complete text of a quote. It is something like
>>>>Before, our ignorance was of a meager sort. Now it is profound and
>>>satisfying.
>>>>But it has lots more words. As I recall, it was supposedly posted to
a
>>>door of a (lab? classroom?) at the University of (Tromsko? Somewhere
in
>>>Finland? Norway?)
>>>>I thought I remembered it from the forward of Kloeden & Platen's
>>>Numerical Solution of Stochastic Differential Equations but it
isn't
>>>in the 1999 edition. Google didn't help.
>>>>Sound familiar to anyone?
>>Yes, it sounds kind of familiar, but I can't say more than that. I'd
>>love to know the source.
>>Glen
> This sound vaguely like the quote from Lord Kelvin concerning
> the role of measurement in knowledge.
When you measure what you are speaking about and express it in
numbers,
> you know something about it, but when you cannot (or do not) measure
it,
> when you cannot (or do not) express it in numbers, then your knowledge
> is of a meagre and unsatisfactory kind.
See, e.g., http://sres.anu.edu.au/associated/mensuration/measure.htm
must have conflated it with the target quote in my memory.
I found what I was looking for, and the key word is confused:
We have not succeeded in answering all our problems. The answers we
> have found only serve to raise a whole set of new questions. In some
> ways we feel we are as confused as ever, but we believe we are confused
> on a higher level and about more important things.
Quoted in Stochastic Differential Equations: An Introduction with
> Applications by Bernt ¯ksendal, 2nd ed., SpringerVerlag, 1989.
Yes, I remember that! I'd heard it years ago (undergraduate school,
so perhaps I should say decades ago ;) ), and ran across it in the
5th edition of that book recently, so your original post sounded
> Google this, and you will see it has propagated to 165 pages! Most put
> no attribution or anonymous. The only attributions I've found are
> ¯ksendal. There's no telling who said it first.
M*Z
Russell

All too often the study of data requires care.
====
Subject: Re: ignorance quote
>>> Looking for the complete text of a quote. It is something like
>>>
>>> Before, our ignorance was of a meager sort. Now it is profound and
>>> satisfying.
...
>This sound vaguely like the quote from Lord Kelvin concerning
>the role of measurement in knowledge.
>When you measure what you are speaking about and express it in numbers,
>you know something about it, but when you cannot (or do not) measure it,
>when you cannot (or do not) express it in numbers, then your knowledge
>is of a meagre and unsatisfactory kind.
Being a contrary sort, one of the great men in the business of
measuring metabolism of subjects did, I believe, three runs of
his experiment in his lifetime, and spent a decade of preparation
and enhancement of technique before each run. There is a a great
quote from him in a book describing his results and the field in
general, something like:
The more precisely you measure this the less it has to do with anything.
I wish I could provide a better reference to this.
====
Subject: Re: ignorance quote
On Thu, 21 Apr 2005 17:01:09 0400, Major Zed
> Looking for the complete text of a quote. It is something like
Before, our ignorance was of a meager sort. Now it is profound and
> satisfying.
But it has lots more words. As I recall, it was supposedly posted to a
> door of a (lab? classroom?) at the University of (Tromsko? Somewhere in
> Finland? Norway?)
I thought I remembered it from the forward of Kloeden & Platen's
> Numerical Solution of Stochastic Differential Equations but it isn't
> in the 1999 edition. Google didn't help.
Sound familiar to anyone?
I don't find anything at all from Google, either.
I tried the words, and I read a bunch of nice proverbs
about ignorance at several different sites.
might be a private translation. It does feel somewhat
familiar.
Alt.usage.english has a lot of readers who are
widely read, and I suggest posting there.

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: CYCLING: INTER QUARTILE RANGES
CYCLING: INTER QUARTILE RANGES
This is not exactly a question but an example I found that at a time varying
process the dispersion tends to increase. In fact this is not at all
surprising however I think that it worth pedagogically because is dealing
with sport an activity popular to everybody.
The dispersion is evaluated by IQ. Think the volume of work if it was by
the standard deviation of the times the runners spent in each stage! Teachers
does fail to emphasize this fact I«m sure.
Bike races are common all over the Europe, the ÒTour de
FranceÓ being the most famous. Lance Armstrong that wined from
1999 onwards.(Italian, ÒGiroÓ, Spanish,
ÒVueltaÓ, Portuguese
ÒVoltaÓ) is the most popular runner nowadays.
They are is performed by Ò.8etapesÓ, which
are partial races (or stages) day by day at the end of which one the time
spent by each racer is added to the previous times in order to evaluate the
time spent until then. According to these times, at the end each
Ò.8etapeÓ, the position is recorded (rank)
[CapitalEth] first, second, third, fourth, and so on.
A ÒselfdispersiveÓ (say) process is developed
as race goes by: the difference of times among runners grow progressively as
its number decreases (some desist by different reasons).
At the end the winner (three weeks or so) is who spent the least time.
DATA
If t_1 is the time spent by the runner with the rank INT(N/4)+1
and t_2 that of INT(3*N/4)+1 then IQR= t_2 [CapitalEth] t_1
This table shows what is the relation
N (Number of Runners) vs. IQR
stage 4, number of cyclists, 138
t_1=0.14.40 t_2=0.51.37 IQR=2517s.
stage 6, number of cyclists, 131
t_1=0.14.37 t_2=1.07.39 IQR=3182s
stage 7, number of cyclists, 123
t_1=0.14.32 t_2=1.13.06 IQR=3514s
stage 8, number of cyclists, 121
t_1=0.25.19 t_2=1.41.22 IQR=4563s
licas_@hotmail.com
====
Subject: Uniform sum distribtuion
cWQPQ0AAAAjwPsxmggW0_fhjlXzWit
X uniform distributed on the interval [0,1]
Y uniform distributed on the interval [0,2]
Z uniform distributed on the interval [0,3]
What is the probability density function of X+Y+Z
on the interval[0,6]
====
Subject: Re: Uniform sum distribtuion
> X uniform distributed on the interval [0,1]
> Y uniform distributed on the interval [0,2]
> Z uniform distributed on the interval [0,3]
What is the probability density function of X+Y+Z
> on the interval[0,6]
Hmm. Let me guess  homework.
What did you get for the density of X+Y?
Glen
====
Subject: Re: Uniform sum distribtuion
>X uniform distributed on the interval [0,1]
>Y uniform distributed on the interval [0,2]
>Z uniform distributed on the interval [0,3]
>What is the probability density function of X+Y+Z
>on the interval[0,6]
Here is a general method for doing problems like this,
going back to the 18th century.
The Laplace transform of the distribution of a uniform
random variable on (u, v), u < v, is
[exp(ut)  exp(vt)]/[(vu)t],
and the Laplace transform of the density x^k on
(0, infinity) is 1/[k!*t^{k+1}].
So the Laplace transform here is
(1exp(t))*(1exp(2t))* (1exp(3t))/(6*t^3).
The product of the exponential factors is
1  u  u^2 + u^4 + u^5  u^6,
where u = exp(t)).
So the density is 1/3 times
x_^2  (x1)_^2  (x2)_^2 + (x4)_^2 + (x5)_^2  (x6)_^2,
where a_ is the maximum of a and 0. As we have symmetry,
it is only necessary to compute the density up to 3, for
which we get
x^2/3 0 < x < 1
(2x1)/3 1 < x < 2
(x^2+6x5)/3 2 < x < 4,
and complete it by symmetry.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Uniform sum distribtuion
cWQPQ0AAAAjwPsxmggW0_fhjlXzWit
How beautiful! Could you please give a reference to where this discuss
is
proved!
>X uniform distributed on the interval [0,1]
>Y uniform distributed on the interval [0,2]
>Z uniform distributed on the interval [0,3]
What is the probability density function of X+Y+Z
>on the interval[0,6]
Here is a general method for doing problems like this,
> going back to the 18th century.
The Laplace transform of the distribution of a uniform
> random variable on (u, v), u < v, is
[exp(ut)  exp(vt)]/[(vu)t],
and the Laplace transform of the density x^k on
> (0, infinity) is 1/[k!*t^{k+1}].
So the Laplace transform here is
(1exp(t))*(1exp(2t))* (1exp(3t))/(6*t^3).
The product of the exponential factors is
1  u  u^2 + u^4 + u^5  u^6,
where u = exp(t)).
So the density is 1/3 times
x_^2  (x1)_^2  (x2)_^2 + (x4)_^2 + (x5)_^2  (x6)_^2,
where a_ is the maximum of a and 0. As we have symmetry,
> it is only necessary to compute the density up to 3, for
> which we get
x^2/3 0 < x < 1
(2x1)/3 1 < x < 2
(x^2+6x5)/3 2 < x < 4,
and complete it by symmetry.

> This address is for information only. I do not claim that these
views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Department of Statistics, Purdue University
> hrubin@stat.purdue.edu Phone: (765)4946054 FAX:
(765)4940558
====
Subject: =?ISO88591?Q?Chi=B2Test_automatic_grouping=3F=60?=
I have to write a function that makes an estimation for some
frequencydistributions and tells me which distribution fits best to my
data. The decision will be based on a Chisquaretest.
The problem now is that I have some frequencies that haven't been
observed but are very likely to happen. So I think of a datagrouping
for the Chisqtest (e.g. cluster1 = 1..10 observations cluster2 = ...)
Could somebody propose an automatism that could do this grouping?
Carsten
====
Subject: =?iso88591?q?Re:_Chi=B2Test_automatic_grouping=3F`?=
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
All I can say is Why on earth are you doing these things?
1) Why choose between some collection of distributions based on
goodness of fit? What are you trying to achieve by it?
2) Why the ones in your list and not others?
3) Why on /earth/ use chisquare?
4) Why worry about an observed of zero, as long as your expected are
reasonable?
Glen
====
Subject: Re: =?ISO88591?Q?Chi=B2Test_automatic_grouping=3F=60?=
> All I can say is Why on earth are you doing these things?
1) Why choose between some collection of distributions based on
> goodness of fit? What are you trying to achieve by it?
I have to implement an insurance model. The approach is well known in
theory and there are only a few distr's proposed to fit.
> 2) Why the ones in your list and not others?
because it's only a model and others have tested that some will fit
better than others
> 3) Why on /earth/ use chisquare?
because it's easy to implement. Better for the date would be a graphical
test but there's less objectivity
Carsten
====
Subject: =?iso88591?q?Re:_Chi=B2Test_automatic_grouping=3F`?=
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
>> 1) Why choose between some collection of distributions based on
>> goodness of fit? What are you trying to achieve by it?
> I have to implement an insurance model. The approach is well
> known in theory and there are only a few distr's proposed to fit.
I must have missed this particular theory. Which theory says that this
is a good way to select between distributions?
>> 2) Why the ones in your list and not others?
> because it's only a model and others have tested that some will fit
> better than others
Frankly, I don't believe this is why you'd exclude candidates they
mightn't have even been aware of, but I'll let this go.
>> 3) Why on /earth/ use chisquare?
> because it's easy to implement. Better for the date would be a
> graphical test but there's less objectivity
Plainly, it's not all that easy to implement in practice, or your
question wouldn't have been necessary.
If goodnessoffit was your only interest, something better able to
distinguish between your candidates might be better (I would guess, for
example, that all of your proposed distribution are unimodal, and
rightskew). Goodness of fit via chisquare makes poor use of the
information. Some other choices aren't really any harder to implement
and totally avoid the problems created by binning in the first place.
If you're fixated on using a goodness of fit criterion, perhaps a
cdfdiscrepancy like the AndersonDarling statistic would make a better
measure, though one better suited still could be designed with more
information.
However, I think that's missing the point. Why not choose by, say
maximum likelihood, or in the case where some of your proposed
distributions have different numbers of parameters, some statistic that
takes account of that. Perhaps something like BIC or AIC? (Which one
I'd use would depend on what I was using the fits for.)
But there's a second big However here.
Since you're using the fitted distribution for something else,
presumably you want to /achieve/ something in that application. *That*,
rather than fit using chisquare (or anything else) ought to drive your
choice.
What is it you actually want to be best? If you used two different
distributions in your application, what would it be about the answers
they provide that would make one answer better than another?
I have some actuarial background, if that helps.
If you're using those distributions in some predictive way (fit an
insurance model is uninformative), you should probably take account of
the difference between fitted and predictive distributions (any
parameter estimates have associated uncertainty  you can take that
into account when forecasting).
[Indeed, you can even take account of the model selection uncertainty
in your choice between distributions.]
Glen
====
Subject: =?iso88591?q?Re:_Chi=B2Test_automatic_grouping=3F`?=
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
>> 1) Why choose between some collection of distributions based on
>> goodness of fit? What are you trying to achieve by it?
> I have to implement an insurance model. The approach is well
> known in theory and there are only a few distr's proposed to fit.
I must have missed this particular theory. Which theory says that this
is a good way to select between distributions?
>> 2) Why the ones in your list and not others?
> because it's only a model and others have tested that some will fit
> better than others
Frankly, I don't believe this is why you'd exclude candidates they
mightn't have even been aware of, but I'll let this go.
>> 3) Why on /earth/ use chisquare?
> because it's easy to implement. Better for the date would be a
> graphical test but there's less objectivity
Plainly, it's not all that easy to implement in practice, or your
question wouldn't have been necessary.
If goodnessoffit was your only interest, something better able to
distinguish between your candidates might be better (I would guess, for
example, that all of your proposed distribution are unimodal, and
rightskew). Goodness of fit via chisquare makes poor use of the
information. Some other choices aren't really any harder to implement
and totally avoid the problems created by binning in the first place.
If you're fixated on using a goodness of fit criterion, perhaps a
cdfdiscrepancy like the AndersonDarling statistic would make a better
measure, though one better suited still could be designed with more
information.
However, I think that's missing the point. Why not choose by, say
maximum likelihood, or in the case where some of your proposed
distributions have different numbers of parameters, some statistic that
takes account of that. Perhaps something like BIC or AIC? (Which one
I'd use would depend on what I was using the fits for.)
But there's a second big However here.
Since you're using the fitted distribution for something else,
presumably you want to /achieve/ something in that application. *That*,
rather than fit using chisquare (or anything else) ought to drive your
choice.
What is it you actually want to be best? If you used two different
distributions in your application, what would it be about the answers
they provide that would make one answer better than another?
I have some actuarial background, if that helps.
If you're using those distributions in some predictive way (fit an
insurance model is uninformative), you should probably take account of
the difference between fitted and predictive distributions (any
parameter estimates have associated uncertainty  you can take that
into account when forecasting).
[Indeed, you can even take account of the model selection uncertainty
in your choice between distributions.]
Glen
====
Subject: Generating a PDF for data set using IQR, mean and median
Hopefully this is quite a straightforward stats question . . . I'm doing a
MonteCarlo analysis and need to generate a probability distribution function
to sample from.
The PDF needs to reflect as accurately as possible the distribution of a set
of data which represents the price of some goods.
I have the mean price, the median price, the 25th, 75th ntiles and the
maximum and minimum price (i.e. the range and interquartile range) but no
more detail than this.
What is my best approximation for this PDF? My current best try is to use
the 0.5*IQR/0.674 as an approximation for the standard deviation use a Normal
distribution for the PDF. Any comments or suggestions most welcome!
====
Subject: Re: Generating a PDF for data set using IQR, mean and median
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
You'd need to provide more information about what best means, because
in general an infinite number of PDFs will match your sample values
exactly.
You need to provide information that will restrict the solution space a
little.
Glen
====
Subject: Re: Generating a PDF for data set using IQR, mean and median
You'd need to provide more information about what
> best means, because
> in general an infinite number of PDFs will match your
> sample values
> exactly.
You need to provide information that will restrict
> the solution space a
> little.
Glen
>
As the consensus seems to be that an infinite number of distributions I
suppose by 'best' I am looking for something fairly simple & will run quickly
in the MonteCarlo simulation.
Jake
====
Subject: Re: Generating a PDF for data set using IQR, mean and median
<22021833.1114525220802.JavaMail.jakarta@nitrogen.mathforum.org>
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
You may want to consider a family or several families of distributions
that can be skewed left or right, and perhaps with varying amounts of
light or heavytailedness. There are a variety of well known families
that are amenable to simulation
Maybe the Johnson families would help.
http://www.qualityamerica.com/knowledgecente/knowctrBest_Fit_Johnson.htm
johnson distributiondistributions sbsus_bs_u
familiesfamilysystem to turn up lots of relevant links).
There are many other possible choices.
Glen
====
Subject: Re: Generating a PDF for data set using IQR, mean and median
j1mTRwwAAADzgndA_zkUptpIw3BECfQi
> Hopefully this is quite a straightforward stats question . . . I'm
doing a MonteCarlo analysis and need to generate a probability
distribution function to sample from.
The PDF needs to reflect as accurately as possible the distribution
of a set of data which represents the price of some goods.
I have the mean price, the median price, the 25th, 75th ntiles and
the maximum and minimum price (i.e. the range and interquartile range)
but no more detail than this.
> What is my best approximation for this PDF? My current best try is to
use the 0.5*IQR/0.674 as an approximation for the standard deviation
use a Normal distribution for the PDF. Any comments or suggestions most
welcome!
For a given IQR, I think the expected range is larger for a fattailed
distribution such as the Student t than for the Normal. Maybe the ratio
range/IQR could be used to estimate the degreesoffreedom parameter,
but I don't know of an analytical formula. You could do a simulation to
derive an empirical formula.
(Meanmedian) / IQR is a measure of skewness, so you could consider the
skew normal or skew t distributions http://azzalini.stat.unipd.it/SN/ .
Again, I don't know of specific estimators given the data you have.
====
Subject: Re: Generating a PDF for data set using IQR, mean and median
zuiTXwwAAADHDQA2vQPjoyoWimvkgeWk
Prices, strictly speaking, can not be normally distributed (unless you
have negative prices). Assuming they are may be good enough for
what you're doing, but then again it may not. Are the 25th and 75th
percentiles about equally distant from the median? How about the
distances from the max and min to the median. How much do the
mean and median differ by? How many values went in to determining
these parameters? How much will it cost if your simulation turns out
to
be significantly in error compared to the real world? Maybe you've
already thought about these questions and determined that the normal
distribution is good enough. I'll take your word on the formula
relating
the IQR and SD, since that is basically mechanics and may be the
least of your problems.
Russell
====
Subject: Simple Statistical Packages on the Web (Free)?
Are there any simple statistical packages on the web that are either
implemented
as part of a web page or downloadable? I plan to teach a pretty simple short
introductory class on data analysis and would like some of the students get
their hands wet. Excel might be ideal for some of this, particularly the
graphics and analysis package; however, I don't think these students are
going
to run out and buy a copy of Excel to try it out. I'd prefer not to use
student
demo packages. that is, not a student version of MatLab. I'd like something
available with a minimum of fuss to the student. Something with simple data
entry and some reasonable graphics and analyses. For example, something that
produces a few types of histograms, produces summary data [average, mean,
median
(Q1, Q2, Q3)], fits a straight line, scatter plot, possibly a simple ANOVA,
calculates residual for a linear fit, maybe a rank test, etc.). I would
expect
data entry from a txt file produce by notepad or something like it.

Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
Obz Site: 39¡ 15' 7 N,
121¡ 2' 32 W, 2700 feet
Academic disputes are vicious because so little
is at stake.  Anonymous
Web Page:
====
Subject: Re: Simple Statistical Packages on the Web (Free)?
j1mTRwwAAADzgndA_zkUptpIw3BECfQi
> Are there any simple statistical packages on the web that are either
implemented
> as part of a web page or downloadable? I plan to teach a pretty
simple short
> introductory class on data analysis and would like some of the
students get
> their hands wet.
R http://www.rproject.org/ is a free and powerful statistical package,
available for several operating systems, including Windows.
Introductory Statistics with R by Dalgaard could serve as a textbook.
You can get an almost instant answer to any R question by asking it on
the active mailing list, although you should read the documentation
first :).
====
Subject: Re: Simple Statistical Packages on the Web (Free)?
Mzt37gwAAACjYRm6XIoKF1hrhw8NW9aW
R would be my first suggestion too.
An alternative if the OP wants something more similar to Excell would
be to use the OpenOffice free office suite. It includes OpenOffice
calc, a spreadsheet program.
http://www.openoffice.org
Rossc
====
Subject: Re: Simple Statistical Packages on the Web (Free)?
om6X7Q0AAAACiLemITlTL_hSSX2zvtG1
> R would be my first suggestion too.
An alternative if the OP wants something more similar to Excell would
> be to use the OpenOffice free office suite. It includes OpenOffice
> calc, a spreadsheet program.
http://www.openoffice.org
> Rossc
Another option, if you want something like a spreadsheet, is KyPlot. I
seem to remember hearing that it had pretty good statistical
capabilities.
http://www.woundedmoon.org/win32/kyplot.html

Bruce Weaver
bweaver@lakeheadu.ca
www.angelfire.com/wv/bwhomedir
====
Subject: Re: Simple Statistical Packages on the Web (Free)?
Am 23.04.05 00:02 schrieb Bruce Weaver:
>
>>R would be my first suggestion too.
>>An alternative if the OP wants something more similar to Excell would
>>be to use the OpenOffice free office suite. It includes OpenOffice
>>calc, a spreadsheet program.
>>http://www.openoffice.org
>>Rossc
Another option, if you want something like a spreadsheet, is KyPlot. I
> seem to remember hearing that it had pretty good statistical
> capabilities.
http://www.woundedmoon.org/win32/kyplot.html
>
It seems, that is no more for free (but I may be in error about that).
Gottfried Helms
====
Subject: Re: Simple Statistical Packages on the Web (Free)?
j1mTRwwAAADzgndA_zkUptpIw3BECfQi
> Another option, if you want something like a spreadsheet, is
KyPlot. I
> seem to remember hearing that it had pretty good statistical
> capabilities.
http://www.woundedmoon.org/win32/kyplot.html
It seems, that is no more for free (but I may be in error about
that).
I just downloaded and installed it without being asked for payment. As
Bruce Weaver said, it has good statistics functionality. In the area of
time series analysis, for example, it can fit both ARMA and
====
Subject: Re: Simple Statistical Packages on the Web (Free)?
R has already been mentioned and Peter Dalgaard's book would be an
excellent and about as gentle an introduction to both R and statistics
as one might find.
If there is a concern that using R requires students to learn a
programming language and that there might be resistance to this, there
are some GUI frontends for R that are available that can insulate the
students from this aspect:
Two that I would point out specifically are:
1. R Commander (http://socserv.mcmaster.ca/jfox/Misc/Rcmdr/), which is a
tcl/tk based GUI available for multiple platforms. It provides menu
based access to many common R functions in the base installation and
common addon packages.
2. JGR (http://stats.math.uniaugsburg.de/JGR/) which is a Java based
GUI for R and recently won the 2005 John Chambers Statistical Software
Award, which is sponsored by the Statistical Computing Section of the ASA.
Also, with respect to the mentions of spreadsheets, I would only point
out the usual cautionary words regarding the accuracy of certain
functions, especially the continuous distributions. These have been well
Specifically with respect to OO.org's Calc, be aware that in their zeal
to be a dropin replacement for Excel, they have unfortunately
replicated most of Excel's problems when it comes to math/stats
functions, including the modifications to the IEEE 754 floating point
standard, resulting in the rounding of numbers that are close to zero
to zero.
If the OP wants more of a spreadsheet approach and is in a position of
using a Linux based platform, I would point out Gnumeric
(http://www.gnome.org/projects/gnumeric/index.shtml), where the
developers have gone to lengths to validate the math/stats functions,
including working with some members of the R development team. There is
a version available for Windows, but from what I can tell, it is still
effectively a beta release with the associated issues.
HTH,
Marc Schwartz
====
Subject: Re: Simple Statistical Packages on the Web (Free)?
om6X7Q0AAAACiLemITlTL_hSSX2zvtG1
> Are there any simple statistical packages on the web that are either
implemented
> as part of a web page or downloadable? I plan to teach a pretty
simple short
 snip 
You might find something suitable (and better than Excel) in John
Pezzullo's list of free programs:
http://members.aol.com/johnp71/javasta2.html

Bruce Weaver
bweaver@lakeheadu.ca
www.angelfire.com/wv/bwhomedir
====
Subject: CFP: QSIC 2005
grGBPg0AAAAmUQZ5yGRkpdLi2PB8G7Dy
CALL FOR PAPERS
QSIC 2005 solicits research papers, experience reports, and workshop
papers on various aspects of quality software. See the topics of
interests, paper submission guidelines, and workshops. Submissions must
not have been published or be concurrently considered for publication
elsewhere. All submissions will be fully reviewed by at least two
reviewers and will be judged on the basis of originality, contribution,
technical and presentation quality, and relevance to the conference.
The proceedings will be published by IEEE Computer Society Press.
Authors of selected papers will be invited to submit an extended
International Journal of Software Engineering and Knowledge Engineering
.
We have decided to extend the deadline for two weeks to Friday,
May 6, 2005. Please refer to
http://www.ict.swin.edu.au/conferences/qsic2005
for submission details of the main conference as well as its related
workshops.
SUBMISSION GUIDELINES
Manuscripts should be typeset in English, and can be submitted as
either long papers (within 30005000 words, but not exceeding 8 pagess,
typeset in fonts no smaller than 10pt with singleline spacing) or
short papers (less than 3000 words and no more than 5 pages). The cover
page of the manuscript should include:
*the type of submission (research paper or experience report),
*the title of the paper with 150word abstract and 3 to 6 keywords,
*three most relevant topics, preferably chosen from the above list of
topics of interests,
*the affiliation, correspondence address, email address, phone and fax
numbers of each author, indicating the contact author if different from
the first author.
http://www.ict.swin.edu.au/conferences/qsic2005
====
Subject: seeking help for linearity measure
I am seeking help on linearity measurement. I have two groups of data,
shown in this web page (http://mason.gmu.edu/~xli6/index.html). My
measured data started in the case B (stricltly linear) and gradually
changed its linearity due to changing parameter and finnaly ended up
like the case A. So cases B and A are the extremes, and other groups of
data(not shown in plot) are intermediate between the two.
I hope to find out a way for measuring the linearity, so for case B,
this linearity measure=1, and for case A, this linearity measure=0, and
for other data, linear measure is between 0 and 1. I don't know how to
do it. Could you please kindly help me?
====
Subject: Re: seeking help for linearity measure
I am seeking help on linearity measurement. I have two groups of data,
> shown in this web page (http://mason.gmu.edu/~xli6/index.html). My
> measured data started in the case B (stricltly linear) and gradually
> changed its linearity due to changing parameter and finnaly ended up
> like the case A. So cases B and A are the extremes, and other groups of
> data(not shown in plot) are intermediate between the two.
I hope to find out a way for measuring the linearity, so for case B,
> this linearity measure=1, and for case A, this linearity measure=0, and
> for other data, linear measure is between 0 and 1. I don't know how to
> do it. Could you please kindly help me?
How about mean square error? You could normalize that case B is one.
Case A is zero by definition.
OUP
====
Subject: Re: seeking help for linearity measure
On Fri, 22 Apr 2005 16:08:43 0500, One Usenet Poster
I am seeking help on linearity measurement. I have two groups of data,
> shown in this web page (http://mason.gmu.edu/~xli6/index.html). My
> measured data started in the case B (stricltly linear) and gradually
> changed its linearity due to changing parameter and finnaly ended up
> like the case A. So cases B and A are the extremes, and other groups of
> data(not shown in plot) are intermediate between the two.
I hope to find out a way for measuring the linearity, so for case B,
> this linearity measure=1, and for case A, this linearity measure=0, and
> for other data, linear measure is between 0 and 1. I don't know how to
> do it. Could you please kindly help me?
How about mean square error? You could normalize that case B is one.
> Case A is zero by definition.
>
Case B looks like the perfect line which will intersect at (0,0)
if extended. But there are just those few points from X= 1 to 2.
Case A looks *pretty* straight, after it starts upwards.
It looks Linear but with a cutoff. Would it be considered
a far worse fit, if it was nearer to B but was *decreasing*?
(Are you positive about what you are calling extremes?
and about the possible range of *future* data where you
might want to apply the same algorithm?)
If the straight line, intersection at (0,0) is the ideal, then
the sum of squares around B (if that is perfect) gives one
measure. Or the sum of absolute deviations, or whatever.
I think I would leave it as an openended measure, but
normalizing to a range of 01 or 10 is straightforward.
A crude correlation with B is better, if a constant output
is bad, or an example like mine above is bad.

Rich Ulrich, wpilib@Pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: C code for weighted regression.
XRFC2646: Format=Flowed; Original
Can anyone recommend some (free) C source code for fitting Weighted Least
Sqaures Regression models? As well as the parameter values I would like to
know the standrad errors of the parameters and the R^2adj value for the
model.
====
Subject: please give me some pointers on conditional
probabilities/expectations and Brownian Motion?
XRFC2646: Format=Flowed; Original
Hi all,
I am studying Brownian motion and other stochastic processes.
However I am having trouble in those conditional
probabilities/densities/expectations which frequently appear everywhere in
the textbook. But strangely enough, I have already had some classes in basic
probabilities, so theoratically I should have no problem understanding those
probabilities/densities/expectations... So I really don't want to read
those introductory text book about basic definitions again...
I guess this was due to the fact that I did not have enough training in
working out exercises when I was taking those introductory classes...
I found there is a missing link between the introductory classes I have had
and the current stochastical processes... ie. missing exercises training at
the intermediate level...
I specifically found the mixedtype of conditional
probabilities/densities/expectations confusing. For example,
P(continuous X=x  some discrete events)
or
P(X_1 < x  min(Xs, for 0<=s<=T, T>1)>=0) where Xt is Brownian Motion, etc.
This kind of conditional probabilities/densities/expectations occur
everywhere...
Could anybody please point me to some lecture notes/exercises with
solutions, specifically on conditional
probabilities/densities/expectations?
Also, could anybody please point me to some good lecture notes/exercises
with solutions, specifically on Brownian Motion?
Currently I am doing Google search... I'd like to hear from you about your
recommendations... thank you very much!
====
Subject: Re: please give me some pointers on conditional
probabilities/expectations and Brownian Motion?
tyq2IQ0AAAAuNErVkOWXc866QgLV9Cn9
> I am studying Brownian motion and other stochastic processes.
However I am having trouble in those conditional
> probabilities/densities/expectations which frequently appear
everywhere in
> the textbook. But strangely enough, I have already had some classes
in basic
> probabilities, so theoratically I should have no problem
understanding those
> probabilities/densities/expectations... So I really don't want to
read
> those introductory text book about basic definitions again...
You may have to.
I guess this was due to the fact that I did not have enough training
in
> working out exercises when I was taking those introductory classes...
I found there is a missing link between the introductory classes I
have had
> and the current stochastical processes... ie. missing exercises
training at
> the intermediate level...
doubtful
I specifically found the mixedtype of conditional
> probabilities/densities/expectations confusing. For example,
P(continuous X=x  some discrete events)
I assume you refer to a conditional density. Simply take the
derivative of the conditional CDF. P(X<=x  A) = P(X<=x and A) / PA,
as always.
> or
P(X_1 < x  min(Xs, for 0<=s<=T, T>1)>=0) where Xt is Brownian
Motion, etc.
What is the problem? X1 and min(Xs: 0<=s<=T) are jointly
continuous random variables. Use the usual definition of conditional
probability or distribution.
This kind of conditional probabilities/densities/expectations occur
> everywhere...
Could anybody please point me to some lecture notes/exercises with
> solutions, specifically on conditional
probabilities/densities/expectations?
Also, could anybody please point me to some good lecture
notes/exercises
> with solutions, specifically on Brownian Motion?
Ross's books are always good for such things.
====
Subject: Re: please give me some pointers on conditional
probabilities/expectations
and Brownian Motion?
> Hi all,
I am studying Brownian motion and other stochastic processes.
[...]
expect much better from Encyclopaedia Britannica.
The second section, on Description of the mathematical model,
has links to relevant math. or statistics ideas.
http://en.wikipedia.org/wiki/Brownian_motion
David Bernier
====
Subject: rank of covariance matrix
xW2uuQ0AAAAphJJjeFiArsOWDHbThyY
Is there a rigirous way to show that the covariance matrix cannot be
full rank? It's easy to see that by low dimensional examples, but a
general proof would be interesting.
====
Subject: Re: rank of covariance matrix
kRo0gwAAABaMKrfkiXQeaA3HWrrWqWk
There are a variety of ways of determining the rank directly, and a
variety of ways you might be able to tell one is not of full rank even
before you see it (if you have information like variables being linear
combinations of other variables), but it's very difficult to tell what
it is you're trying to ask.
Glen
====
Subject: Re: rank of covariance matrix
On 23 Apr 2005 12:27:23 0700, b83503104@yahoo.com
> Is there a rigirous way to show that the covariance matrix cannot be
> full rank? It's easy to see that by low dimensional examples, but a
> general proof would be interesting.
Starting from where?
It's not full rank if the determinant is zero,
and that will happen whenever there are fewer
cases going into it, than variables....

Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
====
Subject: Re: rank of covariance matrix
Am 24.04.05 21:33 schrieb Richard Ulrich:
> On 23 Apr 2005 12:27:23 0700, b83503104@yahoo.com
>>Is there a rigirous way to show that the covariance matrix cannot be
>>full rank? It's easy to see that by low dimensional examples, but a
>>general proof would be interesting.
Starting from where?
It's not full rank if the determinant is zero,
> and that will happen whenever there are fewer
> cases going into it, than variables....
>
... and/or if one or more variables are linear combinations
of others...
====
Subject: Re: rank of covariance matrix
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> Am 24.04.05 21:33 schrieb Richard Ulrich:
> On 23 Apr 2005 12:27:23 0700, b83503104@yahoo.com
>>Is there a rigirous way to show that the covariance matrix cannot
be
>>full rank? It's easy to see that by low dimensional examples, but
a
>>general proof would be interesting.
Starting from where?
It's not full rank if the determinant is zero,
> and that will happen whenever there are fewer
> cases going into it, than variables....
... and/or if one or more variables are linear combinations
> of others...
It's not clear at all what the OP was asking, or if OP knew what
a covariance matrix is.
Both the criterion (DET = 0) and the reason given by Ulrich are
rather poor answers for the question of a rank of a COV matrix.
You are correct in pointing out the most COMMON reason for rank
deficiency in a covariance matrix.
But the most definitive tool would be an eigenvalueeigenvector
analysis of the covariance.
The number of POSITIE eigenvalues would be the actual rank of the
matrix. The eigenvectors of the 0 eigenvalues indicate the linear
dependence and HOW MANY such linear dependences there are in the
set of variables.
 Bob.
====
Subject: Re: rank of covariance matrix
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> Is there a rigirous way to show that the covariance matrix cannot be
> full rank?
What do you mean when you say the covariance matrix?
Is a 2x2 identity matrix a covariance matrix? If not, why not?
If so, explain this:
> It's easy to see that by low dimensional examples, but a
> general proof would be interesting.
 Bob.
====
Subject: Copyright your own material
gjvgVg0AAACycq0xOrgw6ZQfnozytszk
www.electroniccopyright.com invites anyone interested in protecting
the copyright to their own material to visit our website. We assist you
in verifying your copyright ownership by documenting the recorded date
and content of your submitted files, and by maintaining secure,
encrypted copies of your intellectual property to support your claim of
copyright ownership in future disputes. Our services and prices are
described on our website, as well as other relevant information to help
you protect your copyright.
www.electroniccopyright.com
====
Subject: Re: Copyright your own material
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> www.electroniccopyright.com invites anyone interested in protecting
> the copyright to their own material to visit our website. We assist
you
> in verifying your copyright ownership by documenting the recorded
date
> and content of your submitted files, and by maintaining secure,
> encrypted copies of your intellectual property to support your claim
of
> copyright ownership in future disputes. Our services and prices are
> described on our website, as well as other relevant information to
help
> you protect your copyright.
> www.electroniccopyright.com
to at least 14 other newsgroups today.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
If you want to copyright anything, all you have to do is to put
your own copy right statement on your intellecutal property, such as
copyright @2005 Your Name
What protection does that give you? Ah, THAT's the can of worm that
even most twolegged sharks don't exactly know.
Dictionaries are copyrighted. But anyone can cite a dictionary
definition anytime.
Textbooks are copyrighted. I've (legally) used pages from
copyrighted textbooks in the courses I taught.
something not worth teh paper it's written on!
because one of my perennial flamer accused me of misquoting him.
(That was probably a settrap by him, and indeed it turned
out to be  for me to quote my friend VERBATIM, to show that
I represented what he said correctly).
As soon as I posted that paragraph, showing I paraphrased what
he said was exactly right, this stalker of me immediately hinted
that he would write the publisher and the author about my
copyright violation. :)
====
Subject: Re: Lecture on copyright and copyright violation
< I initiated that thread, and gave a layman's version, in
7 lines cited below, explaining some legal copying and
distribution of copyrighted material What can you expect from a lowlevel Army employee (Hugh) and
> lowlevel US Goverment empolyees (Lee) who spend 24/7 on rec.scuba
> to know ANYTHING about copyright laws and how they apply?
< those were the two stalkers in question :) Professors are LEGALLY allowed to copy ANY copyrighted material
> (Xeroz from Libraries, e.g.) for personal use. Professors are
> LEGALLY allowed to copy pages, or a chapter from a copyright book
> for DIESTRIBUTION to students in an entire CLASS, without
> requiring the students to purchase the copyrighted book, just for
> the selected page(s) or a small portion of it, such as a single
> chapter.
There happened to be a lawyer who was among my stalkers too, who was
too happy to show that I was TECHNICALLY not exactly right,
by citing some codes.
So, he produced the actual lawmumbojumble below. I am reproducing
it because once he has done the nitpick, I might as well let YOU
know what the can of worm looks like. :)
He sez> Not exactly.
BEGIN EXCERPT of LAW
The U.S. Copyright Office publishes Circular 21, entitled Reproduction
of
Copyrighted Works by Educators and Librarians. I suggest you read it.
http://www.copyright.gov/circs[CapitalEth]/circ21.pdf
In Circular 21, the USCO sets forth guidelines of the safe harbor in
which
educators and librarians can take advantage of the fair use exception
to the
copyright laws. Exceeding the guidelines isn't automatically violating
the
copyright laws as it always depends on casebycase analysis.
Educators are permitted to copy a chapter from a copyrighted book, but
not
for DIESTRIBUTION [sic] to students in an entire CLASS as you so
wrongly
suggest:
I. Single Copying for Teachers
A single copy may be made of any of the following by or for a teacher
at his
or her individual request for his or her scholarly research or use in
teaching or preparation to teach a class:
A. A chapter from a book;
C. A short story, short essay or short poem, whether or not from a
collective work;
D. A chart, graph, diagram, drawing, cartoon or picture from a book,
periodical, or newspaper;
To reiterate, the copying of an entire chapter is only allowed for his
or
her scholarly research or use in teaching or preparation to teach a
class.
As for distribution to an entire class:
II. Multiple Copies for Classroom Use
Multiple copies (not to exceed in any event more than one copy per
pupil in
a course) may be made by or for the teacher giving the course for
classroom
use
or discussion; provided that:
A. The copying meets the tests of brevity and spontaneity as defined
below;
and,
B. Meets the cumulative effect test as defined below; and,
C. Each copy includes a notice of copyright
Definitions
Brevity
(ii) Prose:
or
(b) an excerpt from any prose work of not more than 1,000 words or 10%
of
the work, whichever is less, but in any event a minimum of 500 words.
END EXCERPT of LAW.
sez he >Perhaps you should stick to lecturing on statistics.
LOL, I should have invited him to sci.stat.math! Nitpickers are
dime a dozen. At least he cited some FACTS, though hardly
appropriate for his nitpick in a SCUBA forum.
> The notion of personal use (for REFERENCE) as citing items in
> dictionaries or me citing paragraphs from Bjorn's copyrighted
EXCERPT OF MORE NITPIT 
Well, again not exactly.
First of all, it's the notion of fair use not personal use.
Second,
it's not for REFERENCE, it's for purposes of criticism, comment,
news
reporting, teaching, scholarship, and research. Finally, it's not
necessarily PERFECTLY LEGAL for ANYONE and EVERYONE to do since:
The distinction between 'fair use' and infringement may be unclear and
not
easily defined. There is no specific number of words, lines, or notes
that
may safely be taken without permission. Acknowledging the source of the
copyrighted material does not substitute for obtaining permission.
Section 107 also sets out four factors to be considered in determining
whether or not a particular use is fair:
1 the purpose and character of the use, including whether such use is
of
commercial nature
or is for nonprofit educational purposes;
2 the nature of the copyrighted work;
3 the amount and substantiality of the portion used in relation to the
copyrighted work as a
whole; and
4 the effect of the use upon the potential market for or value of the
copyrighted work.
END EXCERPT OF NITPICK 
To complete the story, this was my friend (the author of the
This was the unedited post, by Bjorn, in its entirety:
> What Hugh actually SAID was:
> hh> If I get a chance, I'll write an email to Strike and Bjorn to
> hh> mention to them how you've gotten cropping, downsamping and
> hh> lossy file formats all confused   I'm sure that they'll get
> hh> a good laugh out of it.
> What Hugh acctually DID was sending Bjorn the email goading Bjorn
> to act against my copyright violoation.
He did send me a mail, and because it was private, I will not quote it

some of us have ethics :)
I replied along exactly the same lines as I have done in this forum,
which
be
used, abused, misunderstood or misquoted by anyone, and that is the
price I
pay for my 15 minutes of fame. I don't know whether it WAS in fact
abused,
misunderstood or misquoted, but I have Bob's word (100% backed up by
Hugh's
email) that he quoted me verbatim and with credit to me and the site
that
posted it. That's plenty good enough for me. With any luck, some people
because
they would perhaps have learned something, and they would have become
acquainted with Nekton.
When challenged, Hugh replied that he was NOT trying to entice me to go
on
rec.scuba and refute anything, and that's good enough for me, too.
Bjorn
Aren't newsgroups wonderful places to meet some nonstatistical
deviates (deviants?) and learn some of the most unexpected things
at the unexpected forums?
 Bob.
====
Subject: Help comparing the tails of 2 prob. mass functions
hIyrGg0AAADZ1CIV6lGbRDiZ2_vdwabF
I have two probability mass functions defined over the domain of
nonnegative intergers.
The first is Binomial(n,1/M) where n < M1:
P1(k) = (n)C(k) (1/M)^k (11/M)^(nk)
and the other is a binomial convolved with a Bernoulli (r/M) trial
(r <=n < M1):
P2(k) = (nr)C(k1) (1/M)^(k1) (11/M)^((nr)(k1)) * r/M +
(nr)C(k) (1/M)^(k) (11/M)^((nr)k) (1r/M)
where (n)C(k) denotes the binomial coefficient.
I need help proving P1(K>k) >= P2(K>k) for all k>0.
In particular P1(K>1) > P2(K>1).
Mahmoud
====
Subject: Skewness
Skewness of normal standard samples
Here are the sizedependent confidence intervals I found: .(the program
listing relative to these results was posted in the thread Kurtosis, skewness
and bootstrapping, Tim De Meyer, my Re:)
size=10 p[1.162 , 1.162]=95%
p[1.580 , 1.580]=99%
size=20 p[0.942 , 0.942]=95%
p[1.312 , 1.312]=99%
size=25 p[0.866 , 0.866]=95%
p[1.207 , 1.207]=99%
size=30 p[0.805 , 0.805]=95%
p[1.814 , 1.814]=99%
There is a post from James Dean Brown (University of Haway at Manoa
www.jalt.org/test/bro_1.htm) where the following formula provides the
confidence interval (95%) ( Barbara Tabachnick & Linda Fidell):
[1.960*Sqrt(k/size), 1.960*sqrt(k/size)]
being k=6.
This formula is approximate (as it is well known): this Table shows how
accurate for small sizes:
Size=10, k=3.515
Size=20, k=4.620
Size=25, k=4.880
Size=30, k=5.061
The T&F formula should be used for mediumlarge sizes, I presume.
Licas_@hotmail.com
====
Subject: Re: Skewness
It is well [CapitalEth] known that the CHIsquared probability density
(degree of freedom, df, equal to 3 or more) have a long (and thin ) right
tail. Therefore the SKEWNESS is positive E[(XE(X))^3]>0. (positively
skewed).
This THIRD moment about the mean value divided by the variance raised to
1.5 provides a dimensionless quantity called the Pearson«s
Coefficient of Skewness.
O
OOOO
OOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOO
OOOO
OOO
OO
O
O
This diagram (rotated 90 degrees as usual, X axis vertically) intend to
represent roughly a positively skewed histogram).
I performed a M.C. simulation as follows.
:
1.415, 1.405, 1.416, 1.432, 1.412
mean value and its standard error: 1.416 +/ 0.004.
The theoretical formula is b=2^(1.5) / sqrt (n) being n the number of df.
The result sqrt(2)= 1.414....
Licas_@hotmail.com
====
Subject: Re: Skewness
Mr. David Heiser
In a more Òin deptÓ consult I found that
SKEWNESS is evaluated by different formulas.(MATHWORLD).
If you agree and have time to spend we can made a short
ÒtourÓ in this particular (same research) in
order to find the CONFIDENCE INTERVALS of skewness (K. Pearson)
As I am not an expert in this particular I would be very pleased if you post
what are the currently used estimators of the CENTRAL MOMENTS (I think that
part of the difficulty is here).
As you notice I am able to simulate (Monte Carlo) all this
ÒstuffÓ. I will not spend too much time, 12
month, I think.
It would be ÒgreatÓ if you could check my
results on a ÒgrownÓ (faster) computer, or even
on a PC. Have you access to one?
If I could check the literature results I do it, is my
ÒphilosophyÓ. I detest to be a Museum curator
(a keeper of the Holy Texts). I do not think that to confirm myself is a
lost of time.
It would be said that your comment ÒThe formula
is way offÓ
summarised a Ònol me tangereÓ attitude.
I expect to hear you soon.
Luis Afonso
====
Subject: Re: Skewness
XRFC2646: Format=Flowed; Original
> Skewness of normal standard samples
> Here are the sizedependent confidence intervals I found: .(the program
> listing relative to these results was posted in the thread Kurtosis,
> skewness and bootstrapping, Tim De Meyer, my Re:)
size=10 p[1.162 , 1.162]=95%
> p[1.580 , 1.580]=99%
size=20 p[0.942 , 0.942]=95%
> p[1.312 , 1.312]=99%
size=25 p[0.866 , 0.866]=95%
> p[1.207 , 1.207]=99%
size=30 p[0.805 , 0.805]=95%
> p[1.814 , 1.814]=99%
There is a post from James Dean Brown (University of Haway at Manoa
> www.jalt.org/test/bro_1.htm) where the following formula provides the
> confidence interval (95%) ( Barbara Tabachnick & Linda Fidell):
[1.960*Sqrt(k/size), 1.960*sqrt(k/size)]
> being k=6.
This formula is approximate (as it is well known): this Table shows how
> accurate for small sizes:
Size=10, k=3.515
> Size=20, k=4.620
> Size=25, k=4.880
> Size=30, k=5.061
The T&F formula should be used for mediumlarge sizes, I presume.
Licas_@hotmail.com
+++++++++++++++++++++++++++++++++++++
The formula is way off. Somebody never did a literature search here. Look up
the works by D'Agostino.
David Heiser
http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+
Newsgroups
= East and WestCoast Server Farms  Total Privacy via Encryption =
====
Subject: Re: Skewness
Considering the problem (normal distribution Tabachnick) I proposed in this
thread I preferred to list the 95% semiamplitudes of the central C.I
(confidence intervals) instead of to modify the Tabachnick &
Linda«s formula.
After ÒsmoothingÓ by a fitting equation
(empirical) the results were:
Size=10, 1.152
Size=15, 1.035
Size=20, 0.941
Size=25, 0.866
Size=30, 0.806
Size=35, 0.757
Size=40, 0.715
Size=45, 0.680
Size=50, 0.649
Size=55, 0.622
Size=60, 0.599
Size=65, 0.577
Size=70, 0.558
Size=75, 0.541
Size=80, 0.525
Size=85, 0.510
Size=90, 0.497
Size=95, 0.485 Size=100, 0.473
An ÒempiricalÓ isolated (not smoothed) value
for size 200 gave 0.335. Even for this large size k=6 is not attained in the
Tabachnick & Linda«s formula but only k=5.84.
As a general remark nobody disagree that to test normality through the value
of skewness (as I notice) is not advisable, absolutely. The
KolmogorovSmirnovLilliefors or any other depending on the cumulative
frequencies are likely to be better, I think.
Licas_@hotmail.com
====
Subject: Measuring Spread of Combinations
XRFC2646: Format=Flowed; Original
This problem arose from losing the Mega Millions lottery drawing last
Friday. The game is played by picking a set of five numbers from 1 to 52,
plus the Mega Ball number, also from 1 to 52. This problem ignores the Mega
Ball number and concentrates on the nonMega combination.
I noticed that the winning five nonMega numbers (23,25,43,46,49) were
bunched up in the higher range of possibilities and wondered if there
were
some way to measure the spread of fivenumber picks. I tried two approaches,
statistical and geometric, which gave conflicting results.
STATISTICAL
I used three combinations for this test, took the mean and standard
deviation of each combination, then divided standard deviation by mean to
get a measure of spread around the mean. The first combination was chosen so
that the results would be evenly spread across the possible values; its
ratio is taken as the standard. The second is the winning combination and
the third is a purposely distorted combination. Results were:
(1,14,26,39,52) m=26.40, sd=20.08, ratio= 0.76
(23,25,43,46,49) m=37.20, sd=12.26, ratio=0.33, to standard =43%
(1,15,50,51,52) m=33.80, sd=24.08, ratio=0.71, to standard 94%
This seems to indicate that the spread on the winning numbers was 43% of the
spread of the standard, fairly bunched up, while the third, purposely
distorted combination had 94% of the spread of the standard, hence fairly
widely distributed.
GEOMETRIC
Just out of curiosity, I also found the hypotenuse defined by the
numbers
of each combination, treating them as a fourdimensional triangle of sorts.
This was done by taking the difference between successive numbers in each
combination, squaring each, summing the squares and taking the square root
of the sum. Results were:
(1,14,26,39,52) hypotenuse= 25.51
(23,25,43,46,49) hypotenuse= 18.60, to standard =73%
(1,15,50,51,52) hypotenuse= 37.72, to standard 148%
Under this system of measure, the winning numbers are still more compact
than the standard, although not as much as under the statistical method.
However, the purposely distorted combination now has a higher spread value
than the standard.
While I trust the statistical results more than the geometric, it seems that
the geometric method has the germ of a meaningful statistic somewhere within
it. Any insights will be appreciated.
Paul
====
Subject: Re: Measuring Spread of Combinations
Hi everybody
After a megasized blunder BOB turned tail and ran with his tail between
legs. We do not hear from him anymore, I guess.
====
Subject: Re: Measuring Spread of Combinations
Correction
My counterexample is in the thread
I invite everybody to visit it.
Bye
====
Subject: Re: Measuring Spread of Combinations
Scandal
This post is intend to comment the BOB«s following
statements:(2/11/05)
>There are two completely separate problems here.
>1. Probability. If the RANDOM drawing mechanism is indeed random,
>then EVERY combination of 5 numbers is equally likely. Nothing
>more can be said about (23,25,43,46,49) other than it's probability
>is 1/C(52,5), and is as likely as (1,2,3,4,5) or (3,17,29,40,42) or
>any combination actually drawn.
>2. Statistics. Can you draw some statistical inference based on the
>observed numbres whether the generating process is random of not.
>NO! Absolutely not! In view of (1), when the generating process
>is truly random, every observed quintuple is equally like.
Being the first paragraph merely a ÒtruismÓ
the second is SCANDALOUS, deserving an absolute and severe repudiation. .
(I do not know what is the BOB«s professional activity but
if by chance is a TEACHER he case seems CATASTROPHIC.
This ÒGuyÓ showing the nimbleness of the
unlearned people make the calamitous inference:
HERE IS THE ERROR.
I could myself be sure by Monte Carlo, in this thread, that the RANGES
(defined there that the maximum number minus the minimum plus 1) have a
unimodal distribution right skewed.
This is not, surely, the only one that is not even.
Therefore
Sample unit Òequally likelyÓ DOES NOT leads,
necessarily, to a statistics which Probability Function (or density) is a
constant.
====
Subject: Re: Measuring Spread of Combinations
kFZg3Q0AAAAs_reLZ5CFIlGAro0MFDgD
You can determine how random a sequence is by using an appropriate test
for randomness of sequences. For instance if the sequence you got had
only 0's or 1's, you could use the runs test. Observing a sequence
1111111 would give strong evidence against underlying generating
process being random.
In your case there are no regular runs, but there is a run with step 3
(43,46,49). So if you devised a runs test which used runs of this kind
before seeing the data, and then saw the sequence, you'd have evidence
against the process being random.
An important issue is to devise the test before seeing the data. If you
pick runs test because your sequence has runs, or pick some test on the
histogram because distribution of digits seems skewed, the type1 and
type2 errors associated with the hypothesis test are no longer valid.
This means that you don't know whether results of those tests carry any
statistical significance.
====
Subject: Re: Measuring Spread of Combinations
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
In your case there are no regular runs, but there is a run with step
3
> (43,46,49). So if you devised a runs test which used runs of this
kind
> before seeing the data, and then saw the sequence, you'd have
evidence
> against the process being random.
No! Not in a SINGLE occurrence of a random combination of 5 numbers
from 1 to 52.
Each combination has the same probability of being observed.
An important issue is to devise the test before seeing the data.
That's a nonissue in the winning number observed by the OP.
Read my original followup, the 2nd post in this thread, on April 24,
2005.
This is NEIHER a probability or statistics problem based on the
occurrence
of a SINGLE combination.
 Bob.
====
Subject: Re: Measuring Spread of Combinations
XRFC2646: Format=Flowed; Original
This is NEIHER a probability or statistics problem based on the
> occurrence
> of a SINGLE combination.
their contributions.
However, what I was originally trying to get at is not a test of the
randomness of the draw or the odds of getting a specific combination but
just a way of measuring the spread within a combination. Apparently I didn't
do a good job of stating my goal.
Starting with the original premise of drawing five numbers without
replacement from the set of integers 152. If you got the combination
12345, you'd probably think it a bit unusual that the numbers are packed
so closely together. Not that it indicates an unrandom process or that
these combinations are less likely to occur than any others, just that they
look strangely compact.
If you drew the numbers 513273948, you'd probably think that they were
fairly evenly spread out over the set from which you drew, even though you
know statistically that this combination is no more or less likely to turn
up than is 12345.
So what I was looking for was just a measure of relative spread between two
combinations. If I take the ratios of the standard deviation to the mean of
each of the two groups above, I get .527 for the compact group and .673
for the dispersed group. The dispersed ratio is only 28% greater
than
the compact ratio. It just feels that this is not enough of a difference
in spread measurement between the two combinations so I wondered if there is
some generally accepted method of computing such a concept.
Paul
====
Subject: Re: Measuring Spread of Combinations
XRFC2646: Format=Flowed; Original
I've corrected the program for calculating standard deviation on the 5digit
lottery draw program. The results are posted at
http://mywebpages.comcast.net/pavel314/index.html
Just click on the Distribution of Lottery Numbers link on the home page.
I
included the UBasic code I used to generate the results.
Mean standard deviation on combinations of five numbers in the 152 range
came out to about 14.65, based on random samples of about 260,000. Standard
deviation on those was around 3.89.
Comments, corrections or questions are welcome.
Paul
====
Subject: Re: Measuring Spread of Combinations
<99k571dc969b019fb2paqoi2kr8coroq8o@4ax.com>
<547c71to5sll0amlhem3cdmhotkdn2qg3p@4ax.com>
IjHFTQ0AAADk2zrLfzxmyhHq2eBTXOUO
> Mean standard deviation on combinations of five numbers
> in the 152 range came out to about 14.65, based on random
> samples of about 260,000. Standard deviation on those was
> around 3.89.
There is no reason to sample. It raises questions about
whether the sample is representative. The exhaustive
computation of C(52,5) combinations  about 2.6 million
 is easily computable on modern computers. My (slow)
workstation does the job in less than 30 sec.
The average spread (computed using the std dev of the
combination) is 13.10, with a std dev (from the average
spread) of 3.48.
By the way, it appears that you are using the wrong std
dev formula to compute the spread.
The min and max of the spread is actually 1.41 and
24.26. This is computed based on the population std
dev, following your paradigm. The (population) std dev
is computed by SQRT(SUM((x[i]  avg)^2) / n).
It appears that you used n1 as the divisor  or an
application function that does. That is the sample std
dev. But your spread is computed based on the entire
population, namely all 5 numbers in a drawing.
If you are relying on a function that can only compute
the sample std dev, you can compute the population std
dev by adding the avg as a 6th data point, according
to the user manual for my calculator. For example:
x = AVERAGE(b1,...,b5)
sd = STDEV(b1,...,b5, x)
By the way, if you are using Excel, you can use
STDEVP(b1,...,b5) to compute the population std dev
directly. If you are using another application, you
might see if it has a similar alternative.
====
Subject: Re: Measuring Spread of Combinations
XRFC2646: Format=Flowed; Original
> There is no reason to sample. It raises questions about
> whether the sample is representative. The exhaustive
> computation of C(52,5) combinations  about 2.6 million
>  is easily computable on modern computers. My (slow)
> workstation does the job in less than 30 sec.
The average spread (computed using the std dev of the
> combination) is 13.10, with a std dev (from the average
> spread) of 3.48.
You're right, there's no need to sample. I ran the whole 2.6 million two
ways, one using 4 as the denominator in the standard deviation calculation
and the other using 5. I match your results with my 5divisor run.
4divisor 5divisor
Mean 14.646 13.100
StdDev 3.894 3.483
By the way, it appears that you are using the wrong std
> dev formula to compute the spread.
The min and max of the spread is actually 1.41 and
> 24.26. This is computed based on the population std
> dev, following your paradigm. The (population) std dev
> is computed by SQRT(SUM((x[i]  avg)^2) / n).
It appears that you used n1 as the divisor  or an
> application function that does. That is the sample std
> dev. But your spread is computed based on the entire
> population, namely all 5 numbers in a drawing.
I see why you could use 5 as the divisor. I had been considering each draw
as a sample of all possible draws, hence using n1 as the divisor. However,
I am not trying to use the sample standard deviation as an approximation of
the standard deviation of the universe of all possible draws but instead am
looking for an actual, absolute measure of the spread of those five numbers.
you think that the skewed results I obtained for my sample set could be
caused by having used the n1 divisor?
Paul
====
Subject: Re: Measuring Spread of Combinations
<99k571dc969b019fb2paqoi2kr8coroq8o@4ax.com>
<547c71to5sll0amlhem3cdmhotkdn2qg3p@4ax.com>
IjHFTQ0AAADk2zrLfzxmyhHq2eBTXOUO
> I see why you could use 5 as the divisor.
> [....]
> I'll have to revise my programs and rerun.
> Do you think that the skewed results I obtained
> for my sample set could be caused by having
> used the n1 divisor?
Not that I can tell. Looking at all 2.6 million, I still
see a normallike curve skewed to the right, with an
average to the left of the peak.
There is still the question of what value your analysis has.
I understand what you are trying to do, I believe. But I am
not convinced it achieves a useful result for your purposes
 at least, not the way that you are applying it.
====
Subject: Re: Measuring Spread of Combinations
XRFC2646: Format=Flowed; Original
>> I see why you could use 5 as the divisor.
>> [....]
>> I'll have to revise my programs and rerun.
>> Do you think that the skewed results I obtained
>> for my sample set could be caused by having
>> used the n1 divisor?
Not that I can tell. Looking at all 2.6 million, I still
> see a normallike curve skewed to the right, with an
> average to the left of the peak.
Using the n divisor gave the same slightlyskewed result as the n1. That's
interesting, although unexpected; I can't think of any intuitive reason why
that should happen. One would think that taking random combinations from a
set of evenlydistributed numbers would result in a normal distribution.
> There is still the question of what value your analysis has.
> I understand what you are trying to do, I believe. But I am
> not convinced it achieves a useful result for your purposes
>  at least, not the way that you are applying it.
Use mathematics to achieve a useful result? Heaven forbid! ;) Although
my degrees are in mathematics, I concentrated on pure rather than applied
math so my formal statistical training is minimal, as is probably obvious
from my approach to this problem. The input I've received from these
newsgroups has been very helpful and much appreciated.
The original question arose because the winning 5digit lottery combination
for the big jackpot drawing seemed abnormally compact to me. I wondered if
there were some sort of measure I could apply to check the expected
compactness of such groupings. The standard deviation method seems
reasonable and I'm satisfied that the combination in question is not as
abnormal as I thought.
Paul
====
Subject: Re: Measuring Spread of Combinations
XAntivirus: avast! (VPS 05175, 29/04/2005), Outbound message
XAntivirusStatus: Clean
>
>>This is NEIHER a probability or statistics problem based on the
>>occurrence
>>of a SINGLE combination.
> their contributions.
However, what I was originally trying to get at is not a test of the
> randomness of the draw or the odds of getting a specific combination but
> just a way of measuring the spread within a combination. Apparently I
didn't
> do a good job of stating my goal.
Starting with the original premise of drawing five numbers without
> replacement from the set of integers 152. If you got the combination
> 12345, you'd probably think it a bit unusual that the numbers are
packed
> so closely together. Not that it indicates an unrandom process or that
> these combinations are less likely to occur than any others, just that
they
> look strangely compact.
If you drew the numbers 513273948, you'd probably think that they were
> fairly evenly spread out over the set from which you drew, even though you
> know statistically that this combination is no more or less likely to turn
> up than is 12345.
So what I was looking for was just a measure of relative spread between
two
> combinations. If I take the ratios of the standard deviation to the mean
of
> each of the two groups above, I get .527 for the compact group and
.673
> for the dispersed group. The dispersed ratio is only 28% greater
than
> the compact ratio. It just feels that this is not enough of a
difference
> in spread measurement between the two combinations so I wondered if there
is
> some generally accepted method of computing such a concept.
Paul
>
Why divide by the mean?
Duncan
====
Subject: Re: Measuring Spread of Combinations
XRFC2646: Format=Flowed; Response
>> So what I was looking for was just a measure of relative spread between
>> two combinations. If I take the ratios of the standard deviation to the
>> mean of each of the two groups above, I get .527 for the compact
group
>> and .673 for the dispersed group. The dispersed ratio is only 28%
>> greater than the compact ratio. It just feels that this is not enough
>> of a difference in spread measurement between the two combinations so I
>> wondered if there is some generally accepted method of computing such a
>> concept.
>> Paul
>
> Why divide by the mean?
Duncan
I don't know why I did that. It doesn't make much sense, now that you
mention it. When I take the standard deviations of 12345 and
513273948, I get 1.58 and 17.77, respectively. The second one is 11.24
times the first, which sure seems like a better description of the relative
Paul
====
Subject: Re: Measuring Spread of Combinations
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> This problem arose from losing the Mega Millions lottery drawing last
> Friday. The game is played by picking a set of five numbers from 1 to
52,
> I noticed that the winning five nonMega numbers (23,25,43,46,49)
were
> bunched up in the higher range of possibilities
There are two completely separate problems here.
1. Probability. If the RANDOM drawing mechanism is indeed random,
then EVERY combination of 5 numbers is equally likely. Nothing
more can be said about (23,25,43,46,49) other than it's probability
is 1/C(52,5), and is as likely as (1,2,3,4,5) or (3,17,29,40,42) or
any combination actually drawn.
2. Statistics. Can you draw some statistical inference based on the
observed numbres whether the generating process is random of not.
NO! Absolutely not! In view of (1), when the generating process
is truly random, every observed quintuple is equally like.
All such odd outcomes can suggest is for one to examine whether
the physical process that generated the outcome has flaws in terms
of making them all equally like.
3. Mathematics and Number theory. There is something interesting
about every one of the numbers drawn, as some examples of such
were mentioned in the book The Man Who Loved Only Numbers. In
the observed numbers, 23 and 43 are primes, 25 and 49 are perfect
squares, and 46? 46 can have lots of different interesting
properties. For one, it is the sum of the Fibonnaci numbers
(1,3,8,13,21) < I found that just now. It is also the
sum of these 4 PRIME numbers (3+5+7+31), three of which are the
smallest Mersenne primes < my discovery this morning too, about
the number 46. :) 46 is also the sum of 4 perfect numbers
(6+6+6+28). And this could go on and on and on ... that every
integer has many interesting properties.
So, what's so interesting about numbers like 714 or 715?
Well, on April 8, 1974, Hank Aaron's 715th home run eclipsed
Babe Ruth's 1935 record of 714. Pomerance, a Georgia Asst Prof,
also noticed that 714x715= 2x3x5x7x11x13x17, the product of the
first 7 primes!
Albert Wilanski was the only one in the world who noticed that
the phone number of his brotherinlaw had the peculiar property
the sum of its digits is equal to the sum of its prime factors!
The phone number was 4937775. 4,937,775 can be expressed as the
product of its prime factors 3x5x5x65837. The sum of the original
digits (4+9+3+7+7+7+5) was 42, so was the sum of the digits in the
prime factors (3+5+5+6+5+8+3+7).
Take another phone number, say 6411024. Paul Erdos will be able
to tell you immediately that it is 2532 squared. Erdos knows the
square of any 4digit number, and in his words, sorry I am getting
old and cannot tell you the cube.
An example of (2) was in the draft lottery used by Uncle Sam. Those
born early in the year noticed many more of them were drafted than
those
born in the second half of the year.
But in the random SEQUENCE, all 365! sequences are equally likely. So,
even if the sequence drawn turned out to be 1,2,3,4,...,365 in perfect
it's
an exercise in futility if one tries to analyze the observed sequence
to
argue whether the generating process is random or not.
But it DID point to the examination of how the numbers were selected,
and
it pointed to certain noticeable flaws that explained the anamoly of
the
observed sequence.
If one wanted equal representation in whatever respect, all one needs
to do is to have a stratefied random sample (or sequence).
What if you threw up a set of wood blocks of letters, and it spelled
Christmas? That's Jimmie Savage's favorite example about
randomization.
Your statistical and geometric analyses of the OBSERVD numbers
sounds
interesting, but so does numerology, which has no probability or
statistical base or content. Try NUMBER THEORY. You may find very
interesting properties of those numbers. :)
 Bob.
> STATISTICAL
I used three combinations for this test, took the mean and standard
> deviation of each combination, then divided standard deviation by
mean to
> get a measure of spread around the mean. The first combination was
chosen so
> that the results would be evenly spread across the possible values;
its
> ratio is taken as the standard. The second is the winning combination
and
> the third is a purposely distorted combination. Results were:
(1,14,26,39,52) m=26.40, sd=20.08, ratio= 0.76
> (23,25,43,46,49) m=37.20, sd=12.26, ratio=0.33, to standard =43%
> (1,15,50,51,52) m=33.80, sd=24.08, ratio=0.71, to standard 94%
This seems to indicate that the spread on the winning numbers was 43%
of the
> spread of the standard, fairly bunched up, while the third, purposely
> distorted combination had 94% of the spread of the standard, hence
fairly
> widely distributed.
GEOMETRIC
Just out of curiosity, I also found the hypotenuse defined by the
numbers
> of each combination, treating them as a fourdimensional triangle of
sorts.
> This was done by taking the difference between successive numbers in
each
> combination, squaring each, summing the squares and taking the square
root
> of the sum. Results were:
(1,14,26,39,52) hypotenuse= 25.51
> (23,25,43,46,49) hypotenuse= 18.60, to standard =73%
> (1,15,50,51,52) hypotenuse= 37.72, to standard 148%
Under this system of measure, the winning numbers are still more
compact
> than the standard, although not as much as under the statistical
method.
> However, the purposely distorted combination now has a higher spread
value
> than the standard.
> While I trust the statistical results more than the geometric, it
seems that
> the geometric method has the germ of a meaningful statistic somewhere
within
> it. Any insights will be appreciated.
> Paul
====
Subject: Re: Measuring Spread of Combinations
XRFC2646: Format=Flowed; Original
> So, what's so interesting about numbers like 714 or 715?
> Well, on April 8, 1974, Hank Aaron's 715th home run eclipsed
> Babe Ruth's 1935 record of 714. Pomerance, a Georgia Asst Prof,
> also noticed that 714x715= 2x3x5x7x11x13x17, the product of the
> first 7 primes!
714 is one of my favorite numbers. Besides being the number of home runs hit
by Babe Ruth, it was also the badge number of Joe Friday on the original
Dragnet. And 7/14 in American date notation is July 14, Bastille Day!
There's no such thing as an uninteresting number.
Paul
====
Subject: All Integers are Interesting (with Proof)
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
So, what's so interesting about numbers like 714 or 715?
> Well, on April 8, 1974, Hank Aaron's 715th home run eclipsed
> Babe Ruth's 1935 record of 714. Pomerance, a Georgia Asst Prof,
> also noticed that 714x715= 2x3x5x7x11x13x17, the product of the
> first 7 primes!
> 714 is one of my favorite numbers. Besides being the number of home
runs hit
> by Babe Ruth, it was also the badge number of Joe Friday on the
original
> Dragnet. And 7/14 in American date notation is July 14, Bastille
Day!
>
I am glad I stumbled into interest and your interesting number.
Hardy (a great mathematician by his own record) rated himself 20 on a
scale of 1 to 100, and the selftaught Indian postal clerk Ramamujan,
100.
When Ramanujan, was lying in a nursinghome with a mysterious illness,
Hardy called to see him. Finding making conversation difficult, Hardy
observed lamely that he had come in Taxi no. 1729, which he considered
to be an uninteresting number. Ramanujan immediately perked up, and
said that on the contrary, 1729 was a very interesting number: It was
the SMALLEST positve integer that could be expressed as the sum of two
cubes in two different ways:
1729 = 1^3 + 12^3 = 9^3 + 10^3
> There's no such thing as an uninteresting number.
Actually, that statement can only be PROVED if the number is an
INTEGER.
Proof:
We proceed by the method of reductio ad absurdum
Suppose the set U of uninteresting integers is nonempty. Then, since
it is a set of integers, there is a least member of U, u, say. u has
the property of being the smallest uninteresting integer, which is
interesting  a logical contradiction. Thus we have disproved the
hypothesis that U is nonempty, hence empty. The set of uninteresting
integers is empty means there are no uninteresting integers.
QED.
 Bob.
====
Subject: Re: All Integers are Interesting (with Proof)
> There's no such thing as an uninteresting number.
Actually, that statement can only be PROVED if the number is an
> INTEGER.
Proof:
We proceed by the method of reductio ad absurdum
Suppose the set U of uninteresting integers is nonempty. Then, since
it is a set of integers, there is a least member of U, u, say. u has
> the property of being the smallest uninteresting integer, which is
> interesting  a logical contradiction. Thus we have disproved the
> hypothesis that U is nonempty, hence empty. The set of uninteresting
> integers is empty means there are no uninteresting integers.
QED.
 Bob.
Have you considered this classic response to your proof?
Theorem: All integers are boring.
Proof (by contradiction):
Suppose the set of nonboring integers is nonempty, and x is the least
member of this set.
Who cares?
QED. ;)
Carl G.
====
Subject: Re: All Integers are Interesting (with Proof)
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> There's no such thing as an uninteresting number.
Actually, that statement can only be PROVED if the number is an
> INTEGER.
Proof:
We proceed by the method of reductio ad absurdum
Suppose the set U of uninteresting integers is nonempty. Then,
since
it is a set of integers, there is a least member of U, u, say. u
has
> the property of being the smallest uninteresting integer, which is
> interesting  a logical contradiction. Thus we have disproved
the
> hypothesis that U is nonempty, hence empty. The set of
uninteresting
> integers is empty means there are no uninteresting integers.
QED.
 Bob.
> Have you considered this classic response to your proof?
Theorem: All integers are boring.
Not really.
Proof (by contradiction):
Suppose the set of nonboring integers is nonempty, and x is the
least
> member of this set.
Who cares?
Apparently Carl G. did.
QED. ;)
You need to patch your proof because you haven't proved that YOUR
x (the least number of the set) exists.
Carl G.
Perhaps this interests you even less, though it CAN be proven by
reductio ad absurdum because there are only 8700 threads in all
newsgroups posted by Carl G (according to Google search) and most
of them are not even by YOU:
Theorem: All postings in newsgroups authored by Carl G are boring.
Buenos tardes,
la Poisson.
====
Subject: Re: All Integers are Interesting (with Proof)
> > There's no such thing as an uninteresting number.
> > Actually, that statement can only be PROVED if the number is an
> > INTEGER.
> > Proof:
> > We proceed by the method of reductio ad absurdum
> > Suppose the set U of uninteresting integers is nonempty. Then,
> since
> > it is a set of integers, there is a least member of U, u, say. u
> has
> > the property of being the smallest uninteresting integer, which is
> > interesting  a logical contradiction. Thus we have disproved
> the
> > hypothesis that U is nonempty, hence empty. The set of
> uninteresting
> > integers is empty means there are no uninteresting integers.
> > QED.
> >  Bob.
> Have you considered this classic response to your proof?
Theorem: All integers are boring.
Not really.
> Proof (by contradiction):
Suppose the set of nonboring integers is nonempty, and x is the
> least
> member of this set.
Who cares?
Apparently Carl G. did.
> QED. ;)
You need to patch your proof because you haven't proved that YOUR
> x (the least number of the set) exists.
> Carl G.
Perhaps this interests you even less, though it CAN be proven by
> reductio ad absurdum because there are only 8700 threads in all
> newsgroups posted by Carl G (according to Google search) and most
> of them are not even by YOU:
Theorem: All postings in newsgroups authored by Carl G are boring.
Buenos tardes,
la Poisson.
I didn't create this proof (or spoof). It has been around for many
years (I found it in a list of mathematics jokes). I actually find some
integers interesting (for example: 7101001000).
I agree that many (if not most) people in the world would find my posts
boring. The exact number might be interesting to some people, but not to
me. ;)
Carl G.
====
Subject: OT: Why some integers are interesting
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> I actually find some integers interesting (for example: 7101001000).
Since I had already proved that every integer is interesting, there
must be many reasons why 7101001000 is interesting.
It is interesting because it is 1000 times the prime number 7101001.
What's your reason?
 Bob.
====
Subject: Re: OT: Why some integers are interesting
In a package of integers, how many crums are there?
====
Subject: OT: Re: OT: Why some integers are interesting
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
In a package of integers, how many crums are there?
subgroup H of G, and cosets X and Y,
WE> Do you mean 'for x,y in G, let X = x+H, Y = y+H' ?
WE> Then Y = y+H, XY = xy + H, c(XY) = c(xy) + cH ?
You're definitely FULL of crums, William. :)
 Bob.
====
Subject: Re: Why some integers are interesting
> I actually find some integers interesting (for example: 7101001000).
Since I had already proved that every integer is interesting, there
> must be many reasons why 7101001000 is interesting.
It is interesting because it is 1000 times the prime number 7101001.
What's your reason?
 Bob.
reader):
Define the ten digit checksum of a ten digit sequence as follows:
If all ten digits in the sequence are the same, the checksum is undefined,
otherwise the first digit in the checksum is the number of zeros in the
sequence, the second digit in the checksum is the number of ones in the
sequence, ..., and the tenth digit in the checksum is the number of nines
in
the sequence.
For example, if the ten digit sequence was 2718281828 the checksum
would
be 0230000140, because there are 0 zero's , 2 ones, 3 twos, 0 threes, 0
fours, 0 fives, 0 sixes, 1 seven, 4 eights, and 0 nines.
Problem 1: Which ten digit sequence is same as its checksum?
Problem 2: I selected a particular ten digit sequence. I then replaced
this sequence with its checksum. I kept replacing the sequence with its
checksum until the resulting checksum matched one of the previously
encountered checksums. Following this procedure, I was able to obtain over
seven different checksums before stopping. What was the final (different
from previous) checksum?
Problem 3: What is most number of times that one can replace a sequence by
its checksum before the result is either undefined or matches a previously
encountered sequence?
Carl G.
====
Subject: Re: OT: Why some integers are interesting
UtgH7gwAAACpBhTelVPOXNP7RAfbtQrK
I actually find some integers interesting (for example:
7101001000).
Since I had already proved that every integer is interesting, there
> must be many reasons why 7101001000 is interesting.
It is interesting because it is 1000 times the prime number 7101001.
What's your reason?
It's rich with harmonic resonance:
: you have one 7 (lucky) and six (perfect) 0's
: perfect (6) + lucky (7) = unlucky (13)
: you also have three (sacred) 1's, which, when reversed (profane)
becomes 13!
A very scary number, eh?
 Bob.
====
Subject: Re: OT: Why some integers are interesting
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> I actually find some integers interesting (for example:
> 7101001000).
Since I had already proved that every integer is interesting, there
> must be many reasons why 7101001000 is interesting.
It is interesting because it is 1000 times the prime number
7101001.
The notion of interesting numbers originated from those well versed
in Number Theory in Mathematics, in which PRIME numbers play a
dominant roll. These include Gauss, Fermat, Goldbach, and more recent
mathematicians as Ramanujan, Erdos, and others.
Not many people would know that 7101001 is a prime number! :)
The number 7101001000 is interesting because it has this
primenumber factorization:
7101001000 = 2^3 x 5^3 x 7101001.
What's your reason?
It's rich with harmonic resonance:
: you have one 7 (lucky) and six (perfect) 0's
: perfect (6) + lucky (7) = unlucky (13)
: you also have three (sacred) 1's, which, when reversed (profane)
> becomes 13!
A very scary number, eh?
Only to the Numerologist. :)
But I think that's a better reason than that advanced by Carl G, who
obviously accidentally got lost from alt.geek.comp.lang.java into one
of the mathematical ngs. Number Theory is already OT here. His
checksum reason is interesting, but at least (OT)^2.
 Bob.
====
Subject: Re: All Integers are Interesting (with Proof)
XRFC2646: Format=Flowed; Original
> Actually, that statement can only be PROVED if the number is an
> INTEGER.
Not necessarily. Using the Axiom of Choice, every set can be well ordered,
that is, every set S has a linear ordering such that every nonempty subset
of S has a minimal member. Your proof can be modified to show that any set
that can be well ordered has no uninteresting members.
====
Subject: Re: All Integers are Interesting (with Proof)
> Actually, that statement can only be PROVED if the number is an
> INTEGER.
Not necessarily. Using the Axiom of Choice, every set can be well
ordered,
> that is, every set S has a linear ordering such that every nonempty
subset
> of S has a minimal member. Your proof can be modified to show that any
set
> that can be well ordered has no uninteresting members.
This only works if the well ordering is a particular well ordering that
is
interesting in some way... :)
====
Subject: Re: All Integers are Interesting (with Proof)
<426ff588$0$538$ed2e19e4@ptnnntpreader04.plus.net>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> > Actually, that statement can only be PROVED if the number is an
> > INTEGER.
Not necessarily. Using the Axiom of Choice, every set can be well
ordered,
> that is, every set S has a linear ordering such that every
nonempty
> subset
> of S has a minimal member. Your proof can be modified to show that
any set
> that can be well ordered has no uninteresting members.
This only works if the well ordering is a particular well ordering
that is
> interesting in some way... :)
Even THEN, the set of all intergers, well ordered into its natural
order,
which is rather interesting, has no minimal member.
And if anyone else is going to be pedantic about this, I'll have to
bring my
friend Godel here to lecture you on HIS principle, which pulled the rug
out of 20 years of hard labor by Russell and Whitehead on Principia
Mathematica! :)
While we are at it, here are still other interesting facts about the
numbers
714 and 715, besides having the Pomerance property that 714 x 715 is
the product of the first seven primes
714 + 715 = 1429, which was the year Columbus stumbled onto America.
:^)
1429 is also a backwardsforwardssideways prime: 1429, 9241, 1249,
9421, 4129, 4219 are all prime numbers.
Finally, a PAIR of consecutive integers that has the property that the
sum of the prime factors of one equals the sum of the prime factors
of the other:
714 = 2 x 3 x 7 x 17 2 + 3 + 7 + 17 = 29
715 = 5 x 11 x 13 5 + 11 + 13 = 29
is called a Ruth Aaron pair. Paul Erdos proved that there are
INFINITELY many RuthAaron pairs.
Do you know ANY RuthAaron pair greater than (714, 715)? :)
 Bob.
====
Subject: Re: All Integers are Interesting (with Proof)
<426ff588$0$538$ed2e19e4@ptnnntpreader04.plus.net>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> > Actually, that statement can only be PROVED if the number is an
> > INTEGER.
Not necessarily. Using the Axiom of Choice, every set can be well
ordered,
> that is, every set S has a linear ordering such that every
nonempty
> subset
> of S has a minimal member. Your proof can be modified to show that
any set
> that can be well ordered has no uninteresting members.
This only works if the well ordering is a particular well ordering
that is
> interesting in some way... :)
Even THEN, the set of all intergers, well ordered into its natural
order,
which is rather interesting, has no minimal member.
And if anyone else is going to be pedantic about this, I'll have to
bring my
friend Godel here to lecture you on HIS principle, which pulled the rug
out of 20 years of hard labor by Russell and Whitehead on Principia
Mathematica! :)
While we are at it, here are still other interesting facts about the
numbers
714 and 715, besides having the Pomerance property that 714 x 715 is
the product of the first seven primes
714 + 715 = 1429, which was the year Columbus stumbled onto America.
:^)
1429 is also a backwardsforwardssideways prime: 1429, 9241, 1249,
9421, 4129, 4219 are all prime numbers.
Finally, a PAIR of consecutive integers that has the property that the
sum of the prime factors of one equals the sum of the prime factors
of the other:
714 = 2 x 3 x 7 x 17 2 + 3 + 7 + 17 = 29
715 = 5 x 11 x 13 5 + 11 + 13 = 29
is called a Ruth Aaron pair. Paul Erdos proved that there are
INFINITELY many RuthAaron pairs.
Do you know ANY RuthAaron pair greater than (714, 715)? :)
 Bob.
====
Subject: Re: All Integers are Interesting (with Proof)
>>> Actually, that statement can only be PROVED if the number is an
>>> INTEGER.
>> Not necessarily. Using the Axiom of Choice, every set can be well
ordered,
>> that is, every set S has a linear ordering such that every nonempty
subset
>> of S has a minimal member. Your proof can be modified to show that any
set
>> that can be well ordered has no uninteresting members.
> This only works if the well ordering is a particular well ordering
that is
> interesting in some way... :)
 Even THEN, the set of all intergers, well ordered into its natural
 order,
 which is rather interesting, has no minimal member.

 And if anyone else is going to be pedantic about this, I'll have to
 bring my
 friend Godel here to lecture you on HIS principle, which pulled the rug
 out of 20 years of hard labor by Russell and Whitehead on Principia
 Mathematica! :)

 While we are at it, here are still other interesting facts about the
 numbers
 714 and 715, besides having the Pomerance property that 714 x 715 is
 the product of the first seven primes

 714 + 715 = 1429, which was the year Columbus stumbled onto America.
 :^)
Before he was even born? _________________________________________Gerard S.
 1429 is also a backwardsforwardssideways prime: 1429, 9241, 1249,
 9421, 4129, 4219 are all prime numbers.

 Finally, a PAIR of consecutive integers that has the property that the
 sum of the prime factors of one equals the sum of the prime factors
 of the other:

 714 = 2 x 3 x 7 x 17 2 + 3 + 7 + 17 = 29
 715 = 5 x 11 x 13 5 + 11 + 13 = 29

 is called a Ruth Aaron pair. Paul Erdos proved that there are
 INFINITELY many RuthAaron pairs.

 Do you know ANY RuthAaron pair greater than (714, 715)? :)
====
Subject: Re: All Integers are Interesting (with Proof)
<426ff588$0$538$ed2e19e4@ptnnntpreader04.plus.net>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> 
>  While we are at it, here are still other interesting facts about
the
>  numbers
>  714 and 715, besides having the Pomerance property that 714 x 715
is
>  the product of the first seven primes
> 
>  714 + 715 = 1429, which was the year Columbus stumbled onto
America.
>  :^)
Before he was even born?
_________________________________________Gerard S.
Yes! That's why he discovered it in his reincarnation in 1492! :)
Actually, it is now commonly accepted (outside of the USA) that America
was discovered before Columbus was born!
http://www.apol.net/dightonrock/CodFish/discovery_of_north_america.htm
LOL! You caught my hidden Dyslexic Devil!
Actually there are many theories about who First discovered America.
One theory was that a Chinese explorer discovered America during
14211423.
> http://english.people.com.cn/200203/06/eng20020306_91553.shtml
The Portuguese, unaware of the Chinese claim, claimed they discovered
America in 1924. Here's another link about the same claim:
> http://www.thornr.demon.co.uk/kchrist/portam.html#COLOM
All of this made 1429 all the more interesting as a number, doesn't it?
 Bob.
 1429 is also a backwardsforwardssideways prime: 1429, 9241,
1249,
>  9421, 4129, 4219 are all prime numbers.
> 
>  Finally, a PAIR of consecutive integers that has the property that
the
>  sum of the prime factors of one equals the sum of the prime factors
>  of the other:
> 
>  714 = 2 x 3 x 7 x 17 2 + 3 + 7 + 17 = 29
>  715 = 5 x 11 x 13 5 + 11 + 13 = 29
> 
>  is called a Ruth Aaron pair. Paul Erdos proved that there are
>  INFINITELY many RuthAaron pairs.
> 
>  Do you know ANY RuthAaron pair greater than (714, 715)? :)
====
Subject: Re: All Integers are Interesting (with Proof)
snipped
> While we are at it, here are still other interesting facts about the
numbers
> 714 and 715, besides having the Pomerance property that 714 x 715 is
> the product of the first seven primes
> 714 + 715 = 1429, which was the year Columbus stumbled onto America.
> :^)
> Before he was even born? _________________________________________Gerard
S.
 Yes! That's why he discovered it in his reincarnation in 1492! :)

 Actually, it is now commonly accepted (outside of the USA) that America
 was discovered before Columbus was born!
snipped
When America was discovered wasn't my point, I was pointing out the
error when Christopher stumbled onto America (before he was born?).
______________________________________________________________________Gerard
S.
====
Subject: Re: All Integers are Interesting (with Proof)
<426ff588$0$538$ed2e19e4@ptnnntpreader04.plus.net>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> snipped
> > While we are at it, here are still other interesting facts about
the numbers
> > 714 and 715, besides having the Pomerance property that 714 x 715
is
> > the product of the first seven primes
> > 714 + 715 = 1429, which was the year Columbus stumbled onto
America.
> > :^)
> > Before he was even born?
_________________________________________Gerard S.
 Yes! That's why he discovered it in his reincarnation in 1492!
:)
That was my JOKE. See the SMILEY :) ? Columbus discovered it in
his previous life. Now reread the preceding sentence.
> 
>  Actually, it is now commonly accepted (outside of the USA) that
America
>  was discovered before Columbus was born!
> snipped
When America was discovered wasn't my point, I was pointing out the
> error when Christopher stumbled onto America (before he was born?).
>
______________________________________________________________________Gerard
S.
RF> LOL! You caught my hidden Dyslexic Devil!
Let me explain. A dyslexic person is one who is prone to having
problems
with leftright distinction and tends to permute letters or numerals.
last two digits.
See if you get this dyslexlic joke:
The Dyslexic Agnostic stayed up nights wondering if there is a Dog.
I rather suspect you're not THAT humor challenged, but rather English
is not your native or commonly used language, and hence the meanings
of those words like reincarnation and dyslexic did not register
in intended jokes.
English is not my native language either. But I manage, with or
without the help of my Keyboard Devil, Dyslexic Devil, and other
Devils.
Did you know that the Devil number 666 is VERY VERY Interesting?
http://users.aol.com/s6sj7gt/mike666.htm
 Bob.
====
Subject: Re: All Integers are Interesting (with Proof)
<426ff588$0$538$ed2e19e4@ptnnntpreader04.plus.net>
The Dyslexic Agnostic stayed up nights wondering if there is a Dog.
^
Insomniac

Odysseus
====
Subject: Re: All Integers are Interesting (with Proof)
The Dyslexic Agnostic stayed up nights wondering if there is a Dog.
> ^
> Insomniac
> 
> Odysseus
I read this several times and didn't understand what was so fnnuy
RJP
====
Subject: Re: All Integers are Interesting (with Proof)
<426ff588$0$538$ed2e19e4@ptnnntpreader04.plus.net>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> 
>  While we are at it, here are still other interesting facts about
the
>  numbers
>  714 and 715, besides having the Pomerance property that 714 x 715
is
>  the product of the first seven primes
> 
>  714 + 715 = 1429, which was the year Columbus stumbled onto
America.
>  :^)
Before he was even born?
_________________________________________Gerard S.
Yes! That's why he discovered it in his reincarnation in 1492! :)
Actually, it is now commonly accepted (outside of the USA) that America
was discovered before Columbus was born!
http://www.apol.net/dightonrock/CodFish/discovery_of_north_america.htm
LOL! You caught my hidden Dyslexic Devil!
Actually there are many theories about who First discovered America.
One theory was that a Chinese explorer discovered America during
14211423.
> http://english.people.com.cn/200203/06/eng20020306_91553.shtml
The Portuguese, unaware of the Chinese claim, claimed they discovered
America in 1924. Here's another link about the same claim:
> http://www.thornr.demon.co.uk/kchrist/portam.html#COLOM
All of this made 1429 all the more interesting as a number, doesn't it?
 Bob.
 1429 is also a backwardsforwardssideways prime: 1429, 9241,
1249,
>  9421, 4129, 4219 are all prime numbers.
> 
>  Finally, a PAIR of consecutive integers that has the property that
the
>  sum of the prime factors of one equals the sum of the prime factors
>  of the other:
> 
>  714 = 2 x 3 x 7 x 17 2 + 3 + 7 + 17 = 29
>  715 = 5 x 11 x 13 5 + 11 + 13 = 29
> 
>  is called a Ruth Aaron pair. Paul Erdos proved that there are
>  INFINITELY many RuthAaron pairs.
> 
>  Do you know ANY RuthAaron pair greater than (714, 715)? :)
====
Subject: Re: All Integers are Interesting (with Proof)
> > So, what's so interesting about numbers like 714 or 715?
> > Well, on April 8, 1974, Hank Aaron's 715th home run eclipsed
> > Babe Ruth's 1935 record of 714. Pomerance, a Georgia Asst Prof,
> > also noticed that 714x715= 2x3x5x7x11x13x17, the product of the
> > first 7 primes!
> 714 is one of my favorite numbers. Besides being the number of home
> runs hit
> by Babe Ruth, it was also the badge number of Joe Friday on the
> original
> Dragnet. And 7/14 in American date notation is July 14, Bastille
> Day!
> I am glad I stumbled into interest and your interesting number.
Hardy (a great mathematician by his own record) rated himself 20 on a
> scale of 1 to 100, and the selftaught Indian postal clerk Ramamujan,
> 100.
> When Ramanujan, was lying in a nursinghome with a mysterious illness,
> Hardy called to see him. Finding making conversation difficult, Hardy
> observed lamely that he had come in Taxi no. 1729, which he considered
> to be an uninteresting number. Ramanujan immediately perked up, and
> said that on the contrary, 1729 was a very interesting number: It was
> the SMALLEST positve integer that could be expressed as the sum of two
> cubes in two different ways:
1729 = 1^3 + 12^3 = 9^3 + 10^3
> There's no such thing as an uninteresting number.
Actually, that statement can only be PROVED if the number is an
> INTEGER.
Proof:
We proceed by the method of reductio ad absurdum
Suppose the set U of uninteresting integers is nonempty. Then, since
it is a set of integers, there is a least member of U, u, say. u has
> the property of being the smallest uninteresting integer, which is
> interesting  a logical contradiction. Thus we have disproved the
> hypothesis that U is nonempty, hence empty. The set of uninteresting
> integers is empty means there are no uninteresting integers.
QED.
>
Oldie, but goodie.
I think this proof could be expanded to any set of numbers which is
denumerable.
Actually, more interesting IMO is the following
**Please restrict the following to Restricting to positive integers..**
Suppose that Dustin Hoffman found nothing interesting about anything except
1,2,
Someone points out that the number 3 is the first uninteresting number,
then.
So Dustin admits this and groups all numbers this way.
so if you name any number whatever, it is now interesting to HIM because of
its residue mod 2.
someone else says , I don't find any numbers interesting except 1.
The argument falls apart here.
The question immediately arises that the concept Interesting need to be
examined.
In the context of the original problem it means a UNIQUE property.
The premise is that somehow correspondence to some subset of integers
having a common property would be intrinsically interesting
But if this is admitted, then Even ness or odness should do very
nicely!
( reducing Dustin's world to binary)
Even *I* think this post is getting odd!!
Bob Pease
====
Subject: Re: All Integers are Interesting (with Proof)
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
Suppose that Dustin Hoffman found nothing interesting about anything
except
> 1,2,
> Someone points out that the number 3 is the first uninteresting
number,
> then.
> So Dustin admits this and groups all numbers this way.
> so if you name any number whatever, it is now interesting to HIM
because of
> its residue mod 2.
This joke is almost as bad as the joke of Cauchy's dog leaving his
residue at the pole.
> ( reducing Dustin's world to binary)
Another oldie:
There are 10 kinds of people in the world:
those who understand binary and those who don't.
> Even *I* think this post is getting odd!!
On even and odd, Goldback's conjecture that all EVEN numbers greater
than 2 can be expressed as the sum of two (ODD of course) primes
is still up for grabs.
The conjecture had been verified to all even numbers up to 100 million,
but has not been proved to be universally true for all even numbers.
Bob Pease
A final interesting number for today. Mersennes conjectured that
2^67  1 was a prime, after it was found that 2^p 1 were prime for
p = 2,3,5,7 resulted in primes, but failed when p =11.
The conjecture stood for 250 years unchallenged until Frank Nelcon Cole
gave a talk at the American Mathematics Society in 1903. Cole, a man
of few words, did not say a single during the entire presentation.
He went to the blackboard. raised 2 to the 67th power and subtracted 1
to get 147,573,952,589,676,412,927.
Without a word, he moved to the clear side of the blackboard and
multiply out long hand,
195,707,721 x 761,838,257,287
which was 147,573,952,589,676,412,927.
That poor sap had more time on his hand than any of us! :) But
he certainly made the Mersenne number 147,573,952,589,676,412,927
interesting.
 Bob.
====
Subject: Re: All Integers are Interesting (with Proof)
XRFC2646: Format=Flowed; Original
You guys are out there.
I'm just happy when I can help my 10 year old with a
I did find this newsgroup interesting. Just reading the stuff you genius
people write is amazing.
word problem.
> > Suppose that Dustin Hoffman found nothing interesting about anything
> except
>> 1,2,
>> Someone points out that the number 3 is the first uninteresting
> number,
>> then.
>> So Dustin admits this and groups all numbers this way.
>> so if you name any number whatever, it is now interesting to HIM
> because of
>> its residue mod 2.
This joke is almost as bad as the joke of Cauchy's dog leaving his
> residue at the pole.
>> ( reducing Dustin's world to binary)
Another oldie:
> There are 10 kinds of people in the world:
> those who understand binary and those who don't.
>> Even *I* think this post is getting odd!!
On even and odd, Goldback's conjecture that all EVEN numbers greater
> than 2 can be expressed as the sum of two (ODD of course) primes
> is still up for grabs.
The conjecture had been verified to all even numbers up to 100 million,
> but has not been proved to be universally true for all even numbers.
> Bob Pease
A final interesting number for today. Mersennes conjectured that
> 2^67  1 was a prime, after it was found that 2^p 1 were prime for
> p = 2,3,5,7 resulted in primes, but failed when p =11.
The conjecture stood for 250 years unchallenged until Frank Nelcon Cole
> gave a talk at the American Mathematics Society in 1903. Cole, a man
> of few words, did not say a single during the entire presentation.
> He went to the blackboard. raised 2 to the 67th power and subtracted 1
> to get 147,573,952,589,676,412,927.
Without a word, he moved to the clear side of the blackboard and
> multiply out long hand,
195,707,721 x 761,838,257,287
which was 147,573,952,589,676,412,927.
That poor sap had more time on his hand than any of us! :) But
> he certainly made the Mersenne number 147,573,952,589,676,412,927
> interesting.
 Bob.
====
Subject: $1,000,000 Prize
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
On even and odd, Goldback's conjecture that all EVEN numbers greater
> than 2 can be expressed as the sum of two (ODD of course) primes
> is still up for grabs.
Faber and Faber offered a $1,000,000 prize prize to anyone who proved
Goldbach's conjecture between March 20, 2000 and March 20, 2002, but
the prize went unclaimed and the conjecture remains open. Not sure if
the prize is still open, but I am sure the PROOF will be more than $1M
to the methematician, on just Nike sponsored ads. :)
The conjecture had been verified to all even numbers up to 100
million,
> but has not been proved to be universally true for all even numbers.
This number is way out of date.
http://www.ieeta.pt/~tos/goldbach.html
By March 20, 2005, all even numbers through 2^17 or
10,000,000,000,000,000
had been doublechecked, and still going strong. But this will never
constitute a proof, though a counterexample may DISPROVE the
conjecture.
I had a proof written on the margin of a note book, but I couldn't find
the notebook or remember the proof. :)
 Bob.
====
Subject: Re: $1,000,000 Prize
mmiamAwAAAATmtxVYi9NGy7tls83IKO3
> [about Goldbach's conjecture]
> I had a proof written on the margin of a note book, but I
> couldn't find the notebook or remember the proof. :)
Or remember what language it's in. 8)
 Christopher Heckman
Lunatic idea of the week: The Voynich Manuscript is really a proof of
Goldbach's Conjecture.
====
Subject: Re: All Integers are Interesting (with Proof)
...
Actually, that statement can only be PROVED if the number is an
> INTEGER.
Proof:
We proceed by the method of reductio ad absurdum
Suppose the set U of uninteresting integers is nonempty. Then, since
You need to say _positive_ integers, else U can be
{1, 2, 3, 4, ...}
> it is a set of integers, there is a least member of U, u, say. u has
> the property of being the smallest uninteresting integer, which is
> interesting  a logical contradiction. Thus we have disproved the
> hypothesis that U is nonempty, hence empty. The set of uninteresting
> integers is empty means there are no uninteresting integers.
QED.
 Bob.
====
Subject: Re: All Integers are Interesting (with Proof)
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
...
Actually, that statement can only be PROVED if the number is an
> INTEGER.
Proof:
We proceed by the method of reductio ad absurdum
Suppose the set U of uninteresting integers is nonempty. Then,
since
You need to say positive integers, else U can be
{1, 2, 3, 4, ...}
negative integers too. Nothing in the proof below assumes U or u to
be positive integers only.
If the smallest uninteresting integer is 12345679, or any other
negative integer, the proof still holds.
it is a set of integers, there is a least member of U, u, say. u
has
> the property of being the smallest uninteresting integer, which is
> interesting  a logical contradiction. Thus we have disproved
the
> hypothesis that U is nonempty, hence empty. The set of
uninteresting
> integers is empty means there are no uninteresting integers.
QED.
 Bob.
1 is certainly an interesting integer. The square root of 1 takes
you
from the real domain to the complex domain is just one of the
interesting
facts about it. :)
25,361,761 is interesting because ... according to the Guiness Book
...
The largest slot machine payout is $39,713,982.25 (£25,361,761),
won
by
a 25yearold software engineer (hence 25,361,761 won by the slot
machine ) from Los Angeles after putting in $100 (£64) in the
Megabucks slot machine at the Excalibur HotelCasino (pictured),
 Bob.
====
Subject: Re: All Integers are Interesting (with Proof)
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> > ...
> > Actually, that statement can only be PROVED if the number is an
> > INTEGER.
> > Proof:
> > We proceed by the method of reductio ad absurdum
> > Suppose the set U of uninteresting integers is nonempty. Then,
> since
You need to say positive integers, else U can be
{1, 2, 3, 4, ...}
negative integers too. Nothing in the proof below assumes U or u to
> be positive integers only.
I stand corrected! The proof was indeed valid for positive integers
only, because it assumes there is a SMALLEST element u.
The proof can easily be fixed by amending a 2nd part for NEGATIVE
integers. Let U be the set of all NEGATIVE integers, ... and let u
be the LARGEST of the uninteresting negative integers ...
The method of reductio ad absurdum will prove that the set of
un=interesting negative integers is an empty set.
Combining the two separate proofs for positive and for negative
integers, we have proved that there are no uninteresting INTEGERS!
I think I have too much time on my hands ... must go do something
more interesting than this. :=))
 Bob.
If the smallest uninteresting integer is 12345679, or any other
> negative integer, the proof still holds.
> > it is a set of integers, there is a least member of U, u, say. u
> has
> > the property of being the smallest uninteresting integer, which
is
> > interesting  a logical contradiction. Thus we have disproved
> the
> > hypothesis that U is nonempty, hence empty. The set of
> uninteresting
> > integers is empty means there are no uninteresting integers.
> > QED.
> >  Bob.
1 is certainly an interesting integer. The square root of 1 takes
> you
> from the real domain to the complex domain is just one of the
> interesting
> facts about it. :)
25,361,761 is interesting because ... according to the Guiness Book
> ...
The largest slot machine payout is $39,713,982.25 (£25,361,761),
won
> by
> a 25yearold software engineer (hence 25,361,761 won by the slot
> machine ) from Los Angeles after putting in $100 (£64) in
the
> Megabucks slot machine at the Excalibur HotelCasino (pictured),
 Bob.
====
Subject: get a FREE IPOD!!!
dgptiQ0AAACIKrn5085HyNLrw4SpjEK
get a free ipod!!! just use this link, fill out one silly little offer,
and get your free ipod just like me!!!
http://www.freeiPods.com/?r=16673510
====
Subject: Variance of a correlation matrix
iERciQ0AAACOSGJqO0CmX3aKi0XwcyLS
I have a problem here, let e be the i, j th entry of matrix R'R, where
R is a random matrix of size mxm and distributed according to N(0,1).
R' is the transposition of R.
I understand that E[e] = m for i=j and E[e] = 0 for i~=j, but I have no
idea how to show that
var[e] = 2m for i=j and var[e] = m for i~=j
Any help is greatly appreciated.
Andrew
====
Subject: nonlinear regression
IKUkrQ0AAAChheIjdx1TO3pWD2M5mz3s
I need to find formula for this function:
http://qrange.150m.com/misc/plot.htm
What is good program for nonlinear regression that could help me?
At the moment, I'm using this formula:
Y*X=22,5
or
I*V=22,5 Watt
but its not very precise.
BTW, I'm a total newbie.
It seems that all programs require knowledge of function form and then
they calculate parameters, right? So what form should I use?
====
Subject: Re: nonlinear regression  NegAsymptotic.jpg 97.7 KBytes yEnc
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
I need to find a formula for this graph:
http://qrange.150m.com/misc/plot.htm
What is good program for nonlinear regression that could help me?
At the moment, I'm using this formula:
> Y*X=22,5
or
> I*V=22,5 Watt
but its not very precise.
I think a negative asymptotic function that descends to some lower
boundary
> would fit your data pretty well. I did a test fit of this type of
function
> to some of your data points, and the R^2 figure of 0.9854 shows that
it
> explained 98.54% of the variance.
It does not explain anything! it is the percent of variation of Y
FITTED
by the model in X, in a SIMPLE LINEAR regression (see below).
> I recommend that you use my NLREG program for the analysis because it
can
> perform general nonlinear regression.
While that may be the case, this is a SIMPLE LINEAR regression problem!
One of the common ills of the users (and now program author) of
regression programs and package is that of NOT knowing the difference
between a LINEAR regression and a NONLinear regression. Worse, not
recognizing s simple linear regression problem.
> You can download a demonstration copy
> of NLREG from http://www.nlreg.com The demo version should be
sufficient
> for your needs.
Here is the NLREG program to do the fit:
Title Negative Asymptotic Function: mA = a + b/V;
> Variables Vrms, mArms; // Two variables: x and y
> Parameters a, b; // Two parameters to estimate: a and
b
> Function mArms = a + b/Vrms; // Equation to be fitted to data
> Plot; // Plot equation and data
with grid lines
> Data;
> 24 1090
> 25 960
> 30 902
> 35 760
> 40 690
> 45 600
> 50 565
> 55 520
> 60 495
> 64 460
In the model you set up, it is a SIMPLE regression model Y = a + b X,
where Y is mArms,
and X is (1/Vrms).
Here's my handcaculation of your model and fit using the Speakeasy
language (created
by Stan Cohen circa 1960). See
http://www.speakeasy.com/about_speakeasy.htm
I used to have a program written in Speakez to do ALL POSSIBLE
regressions (for
classroom demo and pedagogical use) in about FOUR lines of raw code in
the BASIC
language, using the Hamiltonian path of SWPs for the computation.
Here is how I did my handcalculation of your Nonlinear fit with
your data
in a SIMPLE linear regression setup (WITHOUT a program) in the speakez
language.
The language is not only programmable, but supports userdefined
subroutines,
funtions, and other features of a programming language. I reviewed
Speakeasy
for the American Statistician, in the mid1980s.
TWO lines below did all the fitting and calculation of FITTED and
RESIDULS:
Vrms=24,5*integers(5,12,1),64; marms=1090 960 902 760 690 600 565 520
495
xp=mat(2,10:vrms.eq.vrms,(1/vrms));xpx=xp*transp(xp);y=vec(marms)
coeff=inverse(xpx)*xp*y; yhat=transp(xp)*coeff; res=yyhat
That's all! Now I can TABULATE transp(xp) y yhat res to exhibit
TRANSP(XP) Y YHAT RES
********** **** ******* ********
1 .041667 1090 1057.5 32.497
1 .04 960 1019.6 59.611
etc. 868.04 33.956
759.78 .21901
678.58 11.416
615.43 15.431
564.91 .091823
523.57 3.5715
489.12 5.8757
465.44 5.4418
Want R^2? just type (correlation(y, yhat))**2 to get
(CORRELTION(Y,YHAT))**2 = .98537.
> 
> Phil Sherrod
> (phil.sherrod 'at' sandh.com)
> http://www.dtreg.com (decision tree modeling)
> http://www.nlreg.com (nonlinear regression)
> http://www.NewsRover.com (Usenet newsreader)
> http://www.LogRover.com (Web statistics analysis)
 Bob.
====
Subject: LINEAR vs NONLINEAR regression
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
This is a repost with a change of subject AND the .jpg in the title
removed
the .jpg was completely unreadable jibberish in newsgroup textmoode:
RÌ´*RÌ´*RÌ´*R[Capital
IGrave]´*RÌ´*=M.a6EA
!î,.9fõ.b9±d?.99¸&]
Gu.88NÉëèQûfy9±&[Capi
talIAcute]dqÕ'.86Án
èwQîd~¸.b3Ó'á.99Ó,
åÌ...n,,Ài;(H¨[Hyphen]e(@è
f?.90ËeìÈIúæ.83
±`hRú&¡
4Ì~Û?ù.b3.9f)*2k§Q.b2^[Co
pyright]9´!n=@ÖW[Hyphen]'{[YAcute][CapitalThorn]2
10rÿW%Å.b3XüYY)*[Hyphen].9diy¸
I[Hyphen]?xç@í
=M7...)*¬.9f(ü)*ß.b9´é.8c)*ß.99N[EG
rave]æ[YAcute](0.a6[Hyphen].8f[YAcute]&+?Í
y9.9dï¤.be?8Ç[CapitalODoubleDot
]&w.a61
.83úÖt....b9;.89[Hyphen].81)*[RegisteredT
rademark]
HUNDREDS of lines like that in Phil's post.
Phil and others. A LINESR regression is a linear combinatoin of the
COEFFICIENTS.
Tht's why a polynomial regression with X^2, ..., X^k is a LINEAR
multiple regression.
Some nonlinear models can be linearized by a transformation. Others
cannot ...
> I need to find a formula for this graph:
> > http://qrange.150m.com/misc/plot.htm
> > What is good program for nonlinear regression that could help me?
> > At the moment, I'm using this formula:
> > Y*X=22,5
> > or
> > I*V=22,5 Watt
> > but its not very precise.
I think a negative asymptotic function that descends to some lower
> boundary
> would fit your data pretty well. I did a test fit of this type of
> function
> to some of your data points, and the R^2 figure of 0.9854 shows
that
> it
> explained 98.54% of the variance.
It does not explain anything! it is the percent of variation of Y
> FITTED
> by the model in X, in a SIMPLE LINEAR regression (see below).
> I recommend that you use my NLREG program for the analysis because
it
> can
> perform general nonlinear regression.
While that may be the case, this is a SIMPLE LINEAR regression
problem!
> One of the common ills of the users (and now program author) of
> regression programs and package is that of NOT knowing the difference
> between a LINEAR regression and a NONLinear regression. Worse, not
> recognizing s simple linear regression problem.
> You can download a demonstration copy
> of NLREG from http://www.nlreg.com The demo version should be
> sufficient
> for your needs.
Here is the NLREG program to do the fit:
Title Negative Asymptotic Function: mA = a + b/V;
> Variables Vrms, mArms; // Two variables: x and y
> Parameters a, b; // Two parameters to estimate: a and
b
> Function mArms = a + b/Vrms; // Equation to be fitted to
data
> Plot; // Plot equation and
data with grid lines
> Data;
> 24 1090
> 25 960
> 30 902
> 35 760
> 40 690
> 45 600
> 50 565
> 55 520
> 60 495
> 64 460
In the model you set up, it is a SIMPLE regression model Y = a + b X,
> where Y is mArms,
> and X is (1/Vrms).
Here's my handcaculation of your model and fit using the Speakeasy
> language (created
> by Stan Cohen circa 1960). See
> http://www.speakeasy.com/about speakeasy.htm
I used to have a program written in Speakez to do ALL POSSIBLE
> regressions (for
> classroom demo and pedagogical use) in about FOUR lines of raw code
in
> the BASIC
> language, using the Hamiltonian path of SWPs for the computation.
Here is how I did my handcalculation of your Nonlinear fit with
> your data
> in a SIMPLE linear regression setup (WITHOUT a program) in the
speakez
> language.
> The language is not only programmable, but supports userdefined
> subroutines,
> funtions, and other features of a programming language. I reviewed
> Speakeasy
> for the American Statistician, in the mid1980s.
TWO lines below did all the fitting and calculation of FITTED and
> RESIDULS:
Vrms=24,5*integers(5,12,1),64; marms=1090 960 902 760 690 600 565 520
> 495
> xp=mat(2,10:vrms.eq.vrms,(1/vrms));xpx=xp*transp(xp);y=vec(marms)
> coeff=inverse(xpx)*xp*y; yhat=transp(xp)*coeff; res=yyhat
That's all! Now I can TABULATE transp(xp) y yhat res to exhibit
TRANSP(XP) Y YHAT RES
> ********** **** ******* ********
> 1 .041667 1090 1057.5 32.497
> 1 .04 960 1019.6 59.611
> etc. 868.04 33.956
> 759.78 .21901
> 678.58 11.416
> 615.43 15.431
> 564.91 .091823
> 523.57 3.5715
> 489.12 5.8757
> 465.44 5.4418
Want R^2? just type (correlation(y, yhat))**2 to get
(CORRELTION(Y,YHAT))**2 = .98537.
> 
> Phil Sherrod
> (phil.sherrod 'at' sandh.com)
> http://www.dtreg.com (decision tree modeling)
> http://www.nlreg.com (nonlinear regression)
> http://www.NewsRover.com (Usenet newsreader)
> http://www.LogRover.com (Web statistics analysis)
 Bob.
====
Subject: card shuffling variance problem
XAbuseNotes: Abuse reports must be submited via the usenetabuse.com portal
listed above.
XAbuseNotes2: Reports sent via any other method will not be processed.
I'm looking at the following problem: suppose you have a deck of cards
numbered 1 to n and they are shuffled randomly and the random variable X_i
=
1 if the ith card has the value i and X_i = 0 otherwise. Then we want to
compute E[X] and Var[X] where X = sum( i=1 to n ) of X_i. For part of the
solution for Var[X], a solution that I'm looking at computes the Var[X_i]
and says Var[X_i] = E[X_i^2]  E[X_i]^2 = 1/n  (1/n)^2. It is basically
asserted (without justification) that E[X_i] = E[X_i^2] = 1/n. This is
obvious to me for E[X_i], but it is not obvious to me that E[X_i^2] = 1/n.
Can someone help me see why this is so?
====
Subject: Re: card shuffling variance problem
On 25Apr2005, Tino numbered 1 to n and they are shuffled randomly and the random variable
X_i
> =
> 1 if the ith card has the value i and X_i = 0 otherwise. Then we want to
> compute E[X] and Var[X] where X = sum( i=1 to n ) of X_i. For part of
the
> solution for Var[X], a solution that I'm looking at computes the Var[X_i]
> and says Var[X_i] = E[X_i^2]  E[X_i]^2 = 1/n  (1/n)^2. It is basically
> asserted (without justification) that E[X_i] = E[X_i^2] = 1/n. This is
> obvious to me for E[X_i], but it is not obvious to me that E[X_i^2] =
1/n.
> Can someone help me see why this is so?
Forget E[X_i] and Var[X_i]. It's easy to show directly that the
probability that X=m is p(X=m) = (1/m!)*f(nm) where f(nm)
depends only on the difference nm. Compute f(nm) for a few
small values of nm and guess what it is :), then verify the
guess by induction. The result is that p(X=m) =
straightforward to compute that E[X] = 1 (for n >= 1) and
Var[X] = 1 (for n >= 2).

Jim Heckman
====
Subject: Re: card shuffling variance problem
On 25Apr2005, Tino
I'm looking at the following problem: suppose you have a deck of cards
> numbered 1 to n and they are shuffled randomly and the random variable
X_i
> =
> 1 if the ith card has the value i and X_i = 0 otherwise. Then we want
to
> compute E[X] and Var[X] where X = sum( i=1 to n ) of X_i. For part of
the
> solution for Var[X], a solution that I'm looking at computes the
Var[X_i]
> and says Var[X_i] = E[X_i^2]  E[X_i]^2 = 1/n  (1/n)^2. It is
basically
> asserted (without justification) that E[X_i] = E[X_i^2] = 1/n. This is
> obvious to me for E[X_i], but it is not obvious to me that E[X_i^2] =
1/n.
> Can someone help me see why this is so?
Forget E[X_i] and Var[X_i]. It's easy to show directly that the
> probability that X=m is p(X=m) = (1/m!)*f(nm) where f(nm)
> depends only on the difference nm. Compute f(nm) for a few
> small values of nm and guess what it is :), then verify the
> guess by induction. The result is that p(X=m) =
> straightforward to compute that E[X] = 1 (for n >= 1) and
> Var[X] = 1 (for n >= 2).
Still easier is
E[X^2] = E[Sum_i X_i^2] = E[Sum_i X_i^2 + 2*Sum_{i=2 just using arithmetic and the linearity of E without guessing
and induction.

Horst
====
Subject: Re: card shuffling variance problem
> I'm looking at the following problem: suppose you have a deck of cards
> numbered 1 to n and they are shuffled randomly and the random variable X_i
=
> 1 if the ith card has the value i and X_i = 0 otherwise. Then we want to
> compute E[X] and Var[X] where X = sum( i=1 to n ) of X_i. For part of
the
> solution for Var[X], a solution that I'm looking at computes the Var[X_i]
> and says Var[X_i] = E[X_i^2]  E[X_i]^2 = 1/n  (1/n)^2. It is basically
> asserted (without justification) that E[X_i] = E[X_i^2] = 1/n. This is
> obvious to me for E[X_i], but it is not obvious to me that E[X_i^2] =
1/n.
> Can someone help me see why this is so?
>
X_i is either 1 or 0, so X_i^2 is either....
Bob

Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf H.8allstr.9amin katu 2b)
FIN00014 University of Helsinki
Finland
Telephone: +3589191 51479
Mobile: +358 50 599 0540
Fax: +3589191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results  EEB: www.jnreeb.org
====
Subject: Re: card shuffling variance problem
ONSuJQ0AAABDeuDwQ9FnSh1VIzGh74o
Does the solution hinge on whether you can assume X i to be
independent? This seems to require knowing what you mean by a deck
of n cards?
> I'm looking at the following problem: suppose you have a deck of
cards
> numbered 1 to n and they are shuffled randomly and the random
variable X i =
> 1 if the ith card has the value i and X i = 0 otherwise. Then we
want to
> compute E[X] and Var[X] where X = sum( i=1 to n ) of X i. For part
of the
> solution for Var[X], a solution that I'm looking at computes the
Var[X i]
> and says Var[X i] = E[X i^2]  E[X i]^2 = 1/n  (1/n)^2. It is
basically
> asserted (without justification) that E[X i] = E[X i^2] = 1/n.
This is
> obvious to me for E[X i], but it is not obvious to me that E[X i^2]
= 1/n.
> Can someone help me see why this is so?
X i is either 1 or 0, so X i^2 is either....
Bob

> Bob O'Hara
> Department of Mathematics and Statistics
> P.O. Box 68 (Gustaf H.8allstr.9amin katu 2b)
> FIN00014 University of Helsinki
> Finland
Telephone: +3589191 51479
> Mobile: +358 50 599 0540
> Fax: +3589191 51400
> WWW: http://www.RNI.Helsinki.FI/~boh/
> Journal of Negative Results  EEB: www.jnreeb.org
====
Subject: Re: card shuffling variance problem
Does the solution hinge on whether you can assume X_i to be
> independent? This seems to require knowing what you mean by a deck
> of n cards?
The solution for E[X] = E[Sum X_i] = 1 doesn`t require independency.
because E[Sum X_i] = Sum E[X_i] holds for any familiy of rvs,
The solution for V[X] = E[X^2]  E[X]^2 = 1 has to use the fact that a
pair (X_i,X_j) is not independent. E[X_i]*E[X_j] = 1/n^2 but
E[X_i*X_j] = 1/(n(n1)) if i and j are distinct.
A deck of cards is just a deck of n cards numbered from 1..n.

Horst
====
Subject: Biostatistics for Dummies?
Hi. I'm looking for a clear and simplified book for understanding the
basics of biostatistics. Something like Biostatistics for Dummies (I
know there's a Statistics for Dummies but the reviews don't seem to
regard it very highly). I'm afraid I lack in the mathematics
background as in my years in the medical profession I haven't used it
much and have forgotten most of what I learned in highschool and
during the medical training.
====
Subject: Re: Biostatistics for Dummies?
HDlx1hMAAACJdRVnPUojok2zLWEAR2Fqoe31CBgRxbUklLgYIPXeA
I take by your asking of *bio*statistics, rather than just
statistics, not that you imply there to be a substantive difference
among any various flavors of statistics, but rather simply a
differential applications emphasis.
But rather than implying a heavy reliance on tests of significance
and the like, particularly applicable to assessing clinical trials et
cetera, which I (IMO) associate with classical statistics, I'd guess
you instead mean applications such as gene sequencing, drug discovery,
microarray assay classification, etc? If so, here are some links (with
links to ...):
http://www.chemometrics.se/
http://www.qsar.org/
http://www.cheminformatics.org/
====
Subject: Re: Biostatistics for Dummies?
>Hi. I'm looking for a clear and simplified book for understanding the
>basics of biostatistics. Something like Biostatistics for Dummies (I
>know there's a Statistics for Dummies but the reviews don't seem to
>regard it very highly). I'm afraid I lack in the mathematics
>background as in my years in the medical profession I haven't used it
>much and have forgotten most of what I learned in highschool and
>during the medical training.
>
Suggest you have a look at Zar's _Biostatistical Analysis_.
====
Subject: Re: Biostatistics for Dummies?
>Hi. I'm looking for a clear and simplified book for understanding the
>basics of biostatistics. Something like Biostatistics for Dummies (I
>know there's a Statistics for Dummies but the reviews don't seem to
>regard it very highly). I'm afraid I lack in the mathematics
>background as in my years in the medical profession I haven't used it
>much and have forgotten most of what I learned in highschool and
>during the medical training.
>
I don't know how much statistics you want (or how much of a dummy
you consider yourself!), but an excellent overview of books is at:
http://wwwphm.umds.ac.uk/Statinfo/ways.htm
I'd recommend Practical Statistics for Medical Research by D. G.
Altman,
which has well setout introductions to all of its topics, and also
goes beyond the basics. Be aware that (at least in the 1st edition)
it has essentially nothing on Bayesian inference, which is finally
making serious inroads into biostatistical practice.
However it does discuss biases, ethics, and common fundamental
statistical errors in medical publications. With this book, you'll
at least be able to talk the same language as your friendly local
statistician.
Good hunting  Ewart Shaw

J.E.H.Shaw [Ewart Shaw] strgh@uk.ac.warwick TEL: +44 2476 523069
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
http://www.warwick.ac.uk/statsdept http://www.ewartshaw.co.uk
3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@:2^:2))&.>@]^:(i.@[) <#:3 6 2
====
Subject: Re: Biostatistics for Dummies?
>>Hi. I'm looking for a clear and simplified book for understanding the
>>basics of biostatistics. Something like Biostatistics for Dummies (I
>>know there's a Statistics for Dummies but the reviews don't seem to
>>regard it very highly). I'm afraid I lack in the mathematics
>>background as in my years in the medical profession I haven't used it
>>much and have forgotten most of what I learned in highschool and
>>during the medical training.
>I don't know how much statistics you want (or how much of a dummy
>you consider yourself!), but an excellent overview of books is at:
> http://wwwphm.umds.ac.uk/Statinfo/ways.htm
>I'd recommend Practical Statistics for Medical Research by D. G.
Altman,
>which has well setout introductions to all of its topics, and also
>goes beyond the basics. Be aware that (at least in the 1st edition)
>it has essentially nothing on Bayesian inference, which is finally
>making serious inroads into biostatistical practice.
>However it does discuss biases, ethics, and common fundamental
>statistical errors in medical publications. With this book, you'll
>at least be able to talk the same language as your friendly local
>statistician.
I am not sure that I would go along with this. I am
familiar with the misuse of statistics which is constantly
being made by the medical profession, and no practical
statistics book will do anything about it. There is even
_Statistics; the Religion of Medicine_. It is normally
used ritually by those who do not understand it.
Not much more is needed than high school algebra to
understand probability and decision theory. The biologist
should formulate the problem, giving the information needed
to make a reasonable analysis to the statistician for good
procedures to be used, which are not often in the grimoire.
If the person is a biostatistician, the roles should be
kept distinct here.
So learn probability, and learn to formulate your problems,
using prior information and assessment of the consequences.
Learn to formulate, not to solve; in practical problems, it
will take either someone who can do good manual and mental
arithmetic at least, or more likely a computer, to obtain
the actual statistical advice.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558
====
Subject: Re: Biostatistics for Dummies?
zuiTXwwAAADHDQA2vQPjoyoWimvkgeWk
> Hi. I'm looking for a clear and simplified book for understanding the
> basics of biostatistics. Something like Biostatistics for Dummies (I
> know there's a Statistics for Dummies but the reviews don't seem to
> regard it very highly). I'm afraid I lack in the mathematics
> background as in my years in the medical profession I haven't used it
> much and have forgotten most of what I learned in highschool and
> during the medical training.
>
Of the three on my bookshelf, I'd recommend _Biostatistics: A
Foundation for Analysis in the Health Sciences_ by Wayne Daniel,
published by Wiley. I have the 6th edition. I don't know if it's
for dummies, but IMO the exposition of the ideas is among the
clearest I've read.
Russell
====
Subject: Re: Biostatistics for Dummies?
> Hi. I'm looking for a clear and simplified book for understanding the
> basics of biostatistics. Something like Biostatistics for Dummies (I
> know there's a Statistics for Dummies but the reviews don't seem to
> regard it very highly). I'm afraid I lack in the mathematics
> background as in my years in the medical profession I haven't used it
> much and have forgotten most of what I learned in highschool and
> during the medical training.
>
There is a cartoon guide to statistics, that's pretty good, although it
might be too basic.
And don't worry about Reef Fish. I think he's metamorphosing into a
troll, poor dear.
Bob

Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf H.8allstr.9amin katu 2b)
FIN00014 University of Helsinki
Finland
Telephone: +3589191 51479
Mobile: +358 50 599 0540
Fax: +3589191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results  EEB: www.jnreeb.org
====
Subject: Re: Biostatistics for Dummies?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> Hi. I'm looking for a clear and simplified book for understanding
the
> basics of biostatistics. Something like Biostatistics for Dummies
(I
> know there's a Statistics for Dummies but the reviews don't seem to
> regard it very highly). I'm afraid I lack in the mathematics
> background as in my years in the medical profession I haven't used
it
> much and have forgotten most of what I learned in highschool and
> during the medical training.
> There is a cartoon guide to statistics, that's pretty good, although
it
> might be too basic.
I've even used one of those books as a recommended reading or
handout pages when I taught certain beginning course in statistics.
The one I used actually explained the elementary statistical terms
and concepts BETTER than most of the books I've seen that were
textbooks at that level!
> And don't worry about Reef Fish. I think he's metamorphosing into a
> troll, poor dear.
LOL! I think your brain had been frozen for having been in Finland
too long. :)
I have FORGOTTEN more in statistics than you've ever learned,
and what you see in my posts are what I haven't forgotten. :)
All my posts in sci.stat.math are 100% serious. If you have anything
of SUBSTANCE to debunk or rebut anything I've posted, by all means
do to.
Your gratuitous ad hominem attack is worthy of only those
village idiots I have encountered in NONstatistical newsgroups.
There!
 Bob la Poisson.

> Bob O'Hara
> Department of Mathematics and Statistics
> P.O. Box 68 (Gustaf H.8allstr.9amin katu 2b)
> FIN00014 University of Helsinki
> Finland
Telephone: +3589191 51479
> Mobile: +358 50 599 0540
> Fax: +3589191 51400
> WWW: http://www.RNI.Helsinki.FI/~boh/
> Journal of Negative Results  EEB: www.jnreeb.org
====
Subject: Re: Biostatistics for Dummies?
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> Hi. I'm looking for a clear and simplified book for understanding the
> basics of biostatistics. Something like Biostatistics for Dummies (I
> know there's a Statistics for Dummies but the reviews don't seem to
> regard it very highly). I'm afraid I lack in the mathematics
> background as in my years in the medical profession I haven't used it
> much and have forgotten most of what I learned in highschool and
> during the medical training.
>
I don't have any suggestion for such a book, but I have this comment
which I think is important for ALL who apply statistical methods.
There ain't such a thing as statistics for biology,
statistics for Engineers, statistics for Bueiness, etc. etc.
Statistics is statistics. Some disciplines do use certain stat
methods more so than others. But you MUST separate the expertise
in statistics from the expertise in biology or other areas of
substantive applications.
There must be dozens of Statistics for Dummies books. :)
But no matter how well such books are written, there's no substitute
for statistical expertise which you must rely on the help of
those statsticians who HAVE IT, rather than those who had read
a Statistics for Dummies book or an SPSS Manual. :)
I like my brain surgeon analogy which is NO HYPERBOLE. It takes no
less training to practice statistics (and not even necessarily well)
than it takes to train a brain surgeon to do brain surgery!
Would you let someone operate on your brain after reading a book
Brain Surgery for Dummies?
That's why Harvard has the unique 8year program for M.D.s who
expects to be RESEARCHERs  a 4yr Harvard M.D., and 4yr.
Harvard Ph.D. in Statistics. I taught one such Harvard M.D.
after his completion of M.D., and was talking an advanced course
in Data Analysis I taught at the Harvard Stat Department, when
he was completing his jointdegreeprogram there. I taught some
other M.D.s in my stat courses elsewhere.
 Bob.
====
Subject: Re: Biostatistics for Dummies?
On 25 Apr 2005 10:50:07 0700, Reef Fish
>But no matter how well such books are written, there's no substitute
>for statistical expertise which you must rely on the help of
>those statsticians who HAVE IT, rather than those who had read
>a Statistics for Dummies book or an SPSS Manual. :)
consulting firm. ;) I just want to gain more / update basic knowledge
in the field to speak the same language with our department's
statistician. Or are you suggesting we amateurs keep out of it
totally?
====
Subject: Re: Biostatistics for Dummies?
<9ubq61la0uoal94ot21p2732ketfeumube@4ax.com>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
> On 25 Apr 2005 10:50:07 0700, Reef Fish
But no matter how well such books are written, there's no substitute
>for statistical expertise which you must rely on the help of
>those statsticians who HAVE IT, rather than those who had read
>a Statistics for Dummies book or an SPSS Manual. :)
consulting firm. ;) I just want to gain more / update basic
knowledge
> in the field to speak the same language with our department's
> statistician.
That's fine. Be an educated CONSUMER of statistics. Learn the
basics, but don't try any doityourself stuff like all those
Multiple Regression abusers in sci.stat.math.
> Or are you suggesting we amateurs keep out of it totally?
Not at al. But do only those simple stuff you thoroughly understand,
such as how to wash the gloves and hand them to a brain surgeon
and let the surgeon do the cutting. :)
 Bob.
====
Subject: Re: Biostatistics for Dummies?
om6X7Q0AAAACiLemITlTL_hSSX2zvtG1
> Hi. I'm looking for a clear and simplified book for understanding the
> basics of biostatistics. Something like Biostatistics for Dummies (I
> know there's a Statistics for Dummies but the reviews don't seem to
> regard it very highly). I'm afraid I lack in the mathematics
> background as in my years in the medical profession I haven't used it
> much and have forgotten most of what I learned in highschool and
> during the medical training.
>
Here are some websites that may be helpful.
http://www.tufts.edu/~gdallal/LHSP.HTM
http://www.bmj.com/collections/statsbk/
http://collection.nlcbnc.ca/100/201/300/cdn_medical_association/cmaj/series
/stats.htm
http://wwwpersonal.umich.edu/~bobwolfe/560/index560.html

Bruce Weaver
bweaver@lakeheadu.ca
www.angelfire.com/wv/bwhomedir
====
Subject: how to evaluate the questionaire for survey?
I am going to design a survey questionaire to evaluate a tool for
collecting patient profiles. This survey will ask for the feedbacks from
those who used the tool. The purpose of my survey is to:
1. evaluate the usefulness of the tool.
2.evaluate the usability of the tool.
3. evaluate the frequency of use.
4. decide when this tool should be used and when should not accoding to the
size of clinical trial.
Kun
====
Subject: MatLab randn and Simulation Step Numbers
P77RgA0AAACc6AiMlTdskcmY8pXoJG6q
I am testing the MatLab routine randn which is supposed to generate
rv's ~ N(0,1). The test for lack of correaltion looks good, but when I
run a chisquare test to check that the simulated distbtn is the same
as N(0,1) I run into a strange problem: as the number of simulated data
points increases, my chisquare statistics increases.
My simulation is performed so simulated data points are binned in
intervals of 0.01 units (in units of sdev) from 3.52 hours of hell...actually, it wasn't that bad :). There was one
problem
>>that I just did not know how to answer (20 points! Ouch!).
>> Did you do anything on it? Do you remember what it was about?
I did as much as I possibly could, which consisted of drawing a few
> preliminary diagrams and formulas. The instructor gives very difficult
> tests, but he is sometimes generous if we at least make an attempt to
answer
> a problem.
An observer on the ground sees an airplane at 4000 feet altitude. The
plan
> is at an angle of x radians, and approaches at a rate such the angle
> increases by 1/10 radian per minute. I'm not sure that is exactly right,
but
> it was something like that. And for some reason I had no idea how to
> approach it. If I had more time I might have figured it out, but I put
that
> off until the end because I recognized it as a problem I would have
> difficulty with.
OK. Do you recall what the question was and whether they said the plane was
flying horizontal? It's OK if you do not recall.
>> I would think that is very unusual. And you were failing before the
test,
> if I
>> recall correctly. And others among the 12 might have been also. What
type
> of
>> school are you at?
This is the local community college. I've taken several classes there,
and
> found the quality of instructors overall to be very good. It is true I
was
> failing before the test. So was almost everyone else. The class average
of
> the third test was in the 40's, and the fourth test it was in the 60's.
All
> of us have very low grades because of the difficulty of the last two
tests,
> which gives me cause to believe the the tests may be unreasonably
difficult.
> The final, by comparison, was much easier. Of course, several days of
> intense studying didn't hurt me either :)
Is this a new teacher? I think few people will want to take his courses if
almost everyone flunks them or drops out.
Bill
====
Subject: Re: Statistics and stock market historical data
<6rqdnUgm7pf67jzfRVnytQ@pipex.net>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
This is the 2nd post I overlooked, on which I should have followed
up before now.
>> A model of stocks with an absolute return of +1 or 1 is a bad idea as
>> among
>> other things it allows prices to go negative.
The bad thing is the +1 and 1 wrongly assumed. That's the CHANGE of
> stock prices from one period to the next. Why is it a bad idea that a
> change can be negative?
> Not change, the model is bad because the price of a stock can go
negative.
> That is one reason we should model percentage returns rather than
absolute
> returns.
By absolute return you mean the price. Now I see how inappropriately
and literally mind you were when you made your statement about
negative
returns.
You are saying the NORMAL (Gaussian) distribution is inappropriate
as an approximation of anything that can take on negative values,
aren't you?
Your point would be analogous to saying the normal distribution
should be used on IQ, height, weight, and all the other things
that are approximated by the normal distribution simply because
these measurements cannot be NEGATIVE.
Don't be so literal minded and naive!
forward explanation of how percentage returns tends to a lognormal
> distribution just as absolute returns would tend to a normal distribution
> via the CLT. This is just an approximate model. No one is saying it is
> exact.
inexactness of the CLT, but the ERRORS about the random walk model, and
the inappropriate application of the CLT.
>> The effect of the Efficient Market hypothesis is to make stock prices
non
>> path dependent / Markov Processes.
No. Not a Markov Processes. Markov Process is a process WITH memory,
> as opposed to a Bernoulli Process which has no memory. Random Walk is
> still another process which is neither Markov nor Bernoulli. This is
> YOUR error, a new one, not a case of oversimplification but an
> error about random processes.
> No the Markov property means the process is not affected by history. This
is
> the way we view a Stocks current valuation as containing all information
> about its expected future value. A Random Walk is a markov process.
You had better get yourself educated about the difference between a
Markov process (which has memory) and a Bernoulli Process (which has
no memory). In the Bernoulli process (of coin flips say), the
probability of success (H) is the same whether the previous flip
resulted in H or T. For the Markov Process on coin flips P(H!H)
is different from P(H!T). To say that the random walk is a Markov
process you would be saying it HAS memory on the latest return.
>> All stocks tend to follow a random walk with DRIFT, why would we buy
them
>> if
>> we didn't expect to make some money? After all we can go and buy
>> government
>> bonds which are almost all drift and no risk. Dividends lead to
>> discontinuities and consequently jump processes.
That was my DIRECT criticism of Rosenkrantz's Lecture Notes cited by
> joeu2...@hotmail.com and you seem to be doing the same!
> No these lecture notes are just an introduction to basic ideas. We teach
> Newton's laws of motion before we teach adjustments for relativity.
But we were talking about a SPECIFIC lecture of Rosenkratz, the
particular one that was referenced. Whatever other lectures he may
have are irrelevant to the present discussion. He was simply DEAD
WRONG in his various assertions about the stock market, in that
particular lecture.
> I can't remember the efficient market hypothesis
and you can't remember lots of other things such as what constitues
a Markov process. You should have stopped right there; or find
out before you start speculating.
>> but I'm pretty sure we
>> need
>> to remove the risk free interest rate (Drift) when measuring it. Maybe
>> you
>> mean dividends have the effect of changing stocks drift to be
different
>> from
>> the risk free rate?
See your preceding paragraph which started with
Robert> All stocks tend to follow a random walk with DRIFT
I'm having difficulty understanding your point?
See below.
> It was my DIRECT criticism of Rosenkrantz's Lecture Notes cited by
> joeu2...@hotmail.com which assumes all random walks are WITHOUT drifts,
> and move in i.i.d. steps of +1 or 1.
That was in Rosenkrantz's notes IN QUESION, on the web link reference.
I must have read a different set of notes? I can't see either the steps
of
> +1 or 1 or the assumption of 0 drift?
Now you don't even know that you reading the wrong set of notes. LOL.
>> helpful web links. You just happened to have found possibly the
>> WORSE one.
That was my typo. I meant the WORST one.
>> Try Pareto and other distributions. Try look up some links that
>> explain better the Efficient Market hypothesis and how it relates
>> to the notion of random walk.
> The above were my advice to joeu2...@hotmail.com who cited
> Rosenkrantz's Lecture Notes as his source of authority.
> You are right that the LOGNORMAL distribution isn't a perfect fit, it
>> does
>> tend to undervalue the tails. In practice when valuing derivatives
>> dependent
>> on the stock price an adjustment is made to variance to compensate.
Nothing has a perfect fit  that's not the criticism. The criticism
> is
> that the lognormal is not the only longtailed distrition used in the
> theory of stock prices and returns.
> The lognormal is used instead of normal because investment is base on
> percentage return not absolute return.
> In short, you put all your eggs in one basket, the one you cited,
>> which happened to contain more ERRORS than having anything right 
>> the only thing correct in that link is that the LOGNORMAL
>> distribution is sometimes used.
That was my EXPLCIT criticism of joeu2...@hotmail.com for his citation
> of Rosenkrantz's web page as his sole source.
I hope THIS post unravelled all the multiple >>>>s some of which
> were things said by YOU (Robert) and others said by the source cited
> by joeu2...@hotmail.com. Most of my criticism were about what was
> in Rosenkrantz's web link, which was his Lecture Notes to a class in
> Mathematics and Statistics, about probability distributions and
> the central limit theorem, but INCORRECTLY applied to the stock
> market prices, returns, or the Efficient Market hypothesis.
Read the above paragraphs again, and more carefully, in the light of
my additional comments to your comments this time.
 Bob.
> I still don't see why you think it was incorrect. It is just a model.
Once
> this model is understood it is easier to consider why other distributions
> should be used.
Are the distributions you mention for the stock price of for the log of
the
> daily returns?
>  Bob.
>
====
Subject: Re: Statistics and stock market historical data
<6rqdnUgm7pf67jzfRVnytQ@pipex.net>
7EEacAwAAACAxOPs71C36KOSRcb3o0fT
In the lull of the LINEAR regression models thread (I am still waiting
for someone to point out the CONTEXT or JUSTIFICATION of the model
in Kendall and Stuart's book), I came across two followups of my
posts in this thread that I overlooked but should have responded.
Here is the response to one now.
> I was talking about Walter Rosenkrantz of the Department of Mathematics
> and Statistics, whom joeu2...@hotmail.com cited as the sole source
> his previous post.
of references. As I said, I simply picked Rosenkrantz's
The sole source was referring to YOUR reference. Of course
there are zillions of references in Google.
> (I confess: I did not read it in detail.)
That made it all the worse. Either you didn't read it or you
didn't know anything about the subject of stock returns yourself
(probably both), else you wouldn't have overlooked all the ERRORS
about the stock market in that link.
> Since he is a statistics professor with a PhD
> since 1963 and author of a Prob & Stat text (McGrawHill),
> I thought that might lend some credance to the content of
> that supports the thesis that Robert asserted, at least
> in concept.
The first part of your paragraph is known as the informal
Logical Fallacy of Argumentum ad Verecundium (appeal to
authority), except you were appealing to one who is not
only not an authority on the subject, but one who makes
blunders about it.
More to the point, you picked the WORST reference you
could have picked on the web, given that you picked only
one.
You, on the other hand, could be anybody. Even if you
> identified yourself and offered your alleged qualifications,
> there is no way for me to confirm you are who you say
> you are.
As I always say about what I post and what others post,
It's not WHO you are, or what your name is, or what posting
handle you use that matters. It's the SUBSTANCE of you SAY
in your post that matters.
If I post something on which my statistical credentials may
be relevant, I would attach something like Yale Ph.D. in
Statistics (1970); elected Fellow of the ASA (1984) below
my sig. I've done that about 15 times in about 20,000 posts
in the past 15 years.
That is not intended to be an ad hominem attack. The same
> is true about me. It is simply the reality of newsgroups.
> I accept your insights when they make sense and they are
> helpful.
Strictly your argument is not the Argumentum ad Hominem
(abusive) or the Argumentum ad Hominem (circumstantial) types
of Logical Fallacies, sometimes called ad hominem attacks.
You post showed only other fallacies and your apparent
ignorance about the subject.
I just wanted to point the readership of this thread to
> additional information so that they could weigh and
> interpret your comments appropriately.
As I have said, you couldn't have picked a worse source to
cite. It was arguably the WORST you could have picked
among the tens of thousands of web references you could
have chosen.
 Bob.
====
Subject: Resistance of infinite sheet
XRFC2646: Format=Flowed; Original
I wonder if someone can help me with this: Imagine an infinite sheet of
material. The material has some electrical resistivity Rho  meaning there
are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
rectangle of the material L units long by W units wide. Imagine also that
the sheet is connected to electrical ground around its' periphery. (I
know this is kind of a mindbender for some  the EE's at this point are
bailing for the next post, and the mathematicians are wondering what the
fuss is about.)
My question is, what is the resistance from a point on this sheet to ground?
I set up an integral based on concentric rings, each of whose radial extent
(L) is dr and circumference is 2*pi*r, I end up with something like
R=Integral[0infinity](1/(2*pi*r) dr), which is
(rho/2*pi)*[ln(infinity)ln(0)].
I'm stumped. Anyone have any ideas?
Joel
====
Subject: Re: Resistance of infinite sheet
> I wonder if someone can help me with this: Imagine an infinite sheet of
> material. The material has some electrical resistivity Rho  meaning
there
> are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
> rectangle of the material L units long by W units wide. Imagine also
that
> the sheet is connected to electrical ground around its' periphery.
(I
> know this is kind of a mindbender for some  the EE's at this point are
> bailing for the next post, and the mathematicians are wondering what the
> fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
> I set up an integral based on concentric rings, each of whose radial
extent
> (L) is dr and circumference is 2*pi*r, I end up with something like
> R=Integral[0infinity](1/(2*pi*r) dr), which is
> (rho/2*pi)*[ln(infinity)ln(0)].
I'm stumped. Anyone have any ideas?
Joel
If you are truly talking about the ground connection made at infinity, the
resistance is infinite. It is also infinite if the connection is made as a
point contact. The cylindrical symmetry leads to a logarithmic potential as
a funtion of radius.
To turn your problem into a real problem it needs to be modified.
The problem is relatated to that of calculating the dc inductance of an
infinite long wire of finite diameter. In essence, such two dimenisonal
problems are dealt with by using analytic functions and conformal
transformation. Look up the Schwartz transformation.
Finite resistance per unit length will be found between two wires that can
be of different diameters. The field configurations for such problems have
been widely published. They look like a tansmission impedance chart in
rectangular coordinates. Such a chart is the equivalent of a Smith chart
transformed from the Smith chart's unit circle to an infinite plane.
It is also possible to solve for the resistance of a finite wire to the
edges of a rectangle in which the perimiter is grounded. A Schwartz
transformation for such a problem has been published decades ago. Be
prepared, however, that it requires knowledge of elliptic functions to
understand what is going on.
Bill
====
Subject: Re: Resistance of infinite sheet
Your result is fine but:
You have added a complication. your inner radius is 0. The effective cross
section at this point is 0 so the cross section of the material is also 0
so
(rho) l/area is infinite.
In other words the integral from 0 to a finite r also blows up to infinity.
Why not look at an inner radius rmin and outer radius rmax and get an
expression for this case, then see what happens as rmin goes to 0 or rmax
goes to infinity.
EE's are not necessarily bailing for the next post I certainly hope that
they are not.

Don Kelly
dhky@peeshaw.ca
remove the urine to answer
> I wonder if someone can help me with this: Imagine an infinite sheet of
> material. The material has some electrical resistivity Rho  meaning
there
> are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
> rectangle of the material L units long by W units wide. Imagine also
that
> the sheet is connected to electrical ground around its' periphery.
(I
> know this is kind of a mindbender for some  the EE's at this point are
> bailing for the next post, and the mathematicians are wondering what the
> fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
> I set up an integral based on concentric rings, each of whose radial
extent
> (L) is dr and circumference is 2*pi*r, I end up with something like
> R=Integral[0infinity](1/(2*pi*r) dr), which is
> (rho/2*pi)*[ln(infinity)ln(0)].
I'm stumped. Anyone have any ideas?
Joel
====
Subject: Re: Resistance of infinite sheet
>I wonder if someone can help me with this: Imagine an infinite sheet of
>material. The material has some electrical resistivity Rho  meaning there
>are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
>rectangle of the material L units long by W units wide. Imagine also that
>the sheet is connected to electrical ground around its' periphery. (I
>know this is kind of a mindbender for some  the EE's at this point are
>bailing for the next post, and the mathematicians are wondering what the
>fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
>I set up an integral based on concentric rings, each of whose radial extent
>(L) is dr and circumference is 2*pi*r, I end up with something like
>R=Integral[0infinity](1/(2*pi*r) dr), which is
>(rho/2*pi)*[ln(infinity)ln(0)].
I'm stumped. Anyone have any ideas?
Joel
>
Resistance to ground is infinite  the path being infinitely long.
Brian Whatcott
====
Subject: Re: Resistance of infinite sheet
>I wonder if someone can help me with this: Imagine an infinite sheet of
>material. The material has some electrical resistivity Rho  meaning there
>are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
>rectangle of the material L units long by W units wide. Imagine also that
>the sheet is connected to electrical ground around its' periphery. (I
>know this is kind of a mindbender for some  the EE's at this point are
>bailing for the next post, and the mathematicians are wondering what the
>fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
>I set up an integral based on concentric rings, each of whose radial extent
>(L) is dr and circumference is 2*pi*r, I end up with something like
>R=Integral[0infinity](1/(2*pi*r) dr), which is
>(rho/2*pi)*[ln(infinity)ln(0)].
It might be helpful to start with an easier question. Let's say you had a
sheet that was grounded at both ends across the width and had a terminal
across the entire center width. The resistance from terminal to ground
would be Rho*(L/W)/4.
Can we expand on that answer to some kind of discrete model which
approaches
the continuous one?
Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
====
Subject: Re: Resistance of infinite sheet
> I wonder if someone can help me with this: Imagine an infinite sheet of
> material. The material has some electrical resistivity Rho  meaning
there
> are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
> rectangle of the material L units long by W units wide. Imagine also that
> the sheet is connected to electrical ground around its' periphery. (I
> know this is kind of a mindbender for some  the EE's at this point are
> bailing for the next post, and the mathematicians are wondering what the
> fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
> I set up an integral based on concentric rings, each of whose radial
extent
> (L) is dr and circumference is 2*pi*r, I end up with something like
> R=Integral[0infinity](1/(2*pi*r) dr), which is
> (rho/2*pi)*[ln(infinity)ln(0)].
>
Assume you are at the centre, take a pieshaped segment, angle Theta,
Radius R, Resistivity Rho
Total resistance of segment = Rho * Int (Theta*r, r=0..R)
Theta * R^2 / 2, this does not converge as R > Infinity
Total resistance from the centre of the infinite plane,
sum of all segments: = Rho * Int (Theta* R^2/2, Theta=0..2*Pi).
For an infinitely large plane, you have an infinite resistance to ground.
Niall
====
Subject: Re: Resistance of infinite sheet
dWyaYg0AAABUdUvz_483ZCEP0m1OnB
> I wonder if someone can help me with this: Imagine an infinite sheet
of
> material. The material has some electrical resistivity Rho  meaning
there
> are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
> rectangle of the material L units long by W units wide. Imagine also
that
> the sheet is connected to electrical ground around its' periphery.
(I
> know this is kind of a mindbender for some  the EE's at this point
are
> bailing for the next post, and the mathematicians are wondering what
the
> fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
> I set up an integral based on concentric rings, each of whose radial
extent
> (L) is dr and circumference is 2*pi*r, I end up with something like
> R=Integral[0infinity](1/(2*pi*r) dr), which is
> (rho/2*pi)*[ln(infinity)ln(0)].
> Assume you are at the centre, take a pieshaped segment, angle Theta,
> Radius R, Resistivity Rho
Total resistance of segment = Rho * Int (Theta*r, r=0..R)
> Theta * R^2 / 2, this does not converge as R > Infinity
Total resistance from the centre of the infinite plane,
sum of all segments: = Rho * Int (Theta* R^2/2, Theta=0..2*Pi).
For an infinitely large plane, you have an infinite resistance to ground.
I don't dispute your conclusion, but the segments wouldn't be summed
they'd be in parallel, so would combine as 1/(1/seg1+1/seg2...etc.)
Also, as R is increased in a single segment, the contribution of each
increase in radius to the total resistance of the segment would be less
because of broader parallel path.

john
====
Subject: Re: Resistance of infinite sheet
XRFC2646: Format=Flowed; Original
This is why the obvious answer (resistance is infinite) didn't match my
intuition. As r increases, the additional resistance added to the total for
each unit increase in radius drops, so you have a sum of an infinite
sequence of values, each of which get ever closer to zero. Seems like I
dimly remember from college calculus a lot of Taylor/Maclaurin series like
this that are bounded and converge to some constant, but I could be
mistaken.
>> I wonder if someone can help me with this: Imagine an infinite sheet
>> of
>> material. The material has some electrical resistivity Rho  meaning
>> there
>> are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
>> rectangle of the material L units long by W units wide. Imagine also
>> that
>> the sheet is connected to electrical ground around its' periphery.
>> (I
>> know this is kind of a mindbender for some  the EE's at this point
>> are
>> bailing for the next post, and the mathematicians are wondering what
>> the
>> fuss is about.)
>> My question is, what is the resistance from a point on this sheet to
>> ground?
>> I set up an integral based on concentric rings, each of whose radial
>> extent
>> (L) is dr and circumference is 2*pi*r, I end up with something like
>> R=Integral[0infinity](1/(2*pi*r) dr), which is
>> (rho/2*pi)*[ln(infinity)ln(0)].
>> Assume you are at the centre, take a pieshaped segment, angle Theta,
>> Radius R, Resistivity Rho
>> Total resistance of segment = Rho * Int (Theta*r, r=0..R)
>> Theta * R^2 / 2, this does not converge as R > Infinity
>> Total resistance from the centre of the infinite plane,
>> sum of all segments: = Rho * Int (Theta* R^2/2, Theta=0..2*Pi).
>> For an infinitely large plane, you have an infinite resistance to
ground.
I don't dispute your conclusion, but the segments wouldn't be summed
> they'd be in parallel, so would combine as 1/(1/seg1+1/seg2...etc.)
> Also, as R is increased in a single segment, the contribution of each
> increase in radius to the total resistance of the segment would be less
> because of broader parallel path.
> 
> john
>
====
Subject: Re: Resistance of infinite sheet
> This is why the obvious answer (resistance is infinite) didn't match my
> intuition. As r increases, the additional resistance added to the total
for
> each unit increase in radius drops, so you have a sum of an infinite
> sequence of values, each of which get ever closer to zero. Seems like I
> dimly remember from college calculus a lot of Taylor/Maclaurin series
like
> this that are bounded and converge to some constant, but I could be
> mistaken.
True and false. Just because the terms get smaller does not mean that they
converge. The classic example is that of the harmonic series:
1 + 1/2 +1/3 + 1/4 + 1/5 + ...
Bill
====
Subject: Re: Resistance of infinite sheet
XRFC2646: Format=Flowed; Response
>> My question is, what is the resistance from a point on this sheet to
>> ground?
>> I set up an integral based on concentric rings, each of whose radial
>> extent (L) is dr and circumference is 2*pi*r, I end up with something
>> like R=Integral[0infinity](1/(2*pi*r) dr), which is
>> (rho/2*pi)*[ln(infinity)ln(0)].
>
> Assume you are at the centre, take a pieshaped segment, angle Theta,
> Radius R, Resistivity Rho
Total resistance of segment = Rho * Int (Theta*r, r=0..R)
> Theta * R^2 / 2, this does not converge as R > Infinity
Total resistance from the centre of the infinite plane,
sum of all segments: = Rho * Int (Theta* R^2/2, Theta=0..2*Pi).
For an infinitely large plane, you have an infinite resistance to ground.
>
This is similar to the integral which occurs in the characteristic impedance
of coaxial cables, which all electrical engineers know, which finishes up as
something like Zo.log(R2/R1) as I remember. Zo is the characteristic
impedance of the dielectric, R2 is the radius of the outer and R1 is the
radius of the innner.
So for a circular sheet of radius R2 and a central contact of radius R1 the
impedance will have this form. Resistive sheets are used to terminate radio
frequency coaxial cables as dummy loads.
rusty.
====
Subject: Re: Resistance of infinite sheet
> I wonder if someone can help me with this: Imagine an infinite sheet of
> material. The material has some electrical resistivity Rho  meaning
there
> are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
> rectangle of the material L units long by W units wide. Imagine also that
> the sheet is connected to electrical ground around its' periphery. (I
> know this is kind of a mindbender for some  the EE's at this point are
> bailing for the next post, and the mathematicians are wondering what the
> fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
> I set up an integral based on concentric rings, each of whose radial
extent
> (L) is dr and circumference is 2*pi*r, I end up with something like
> R=Integral[0infinity](1/(2*pi*r) dr), which is
> (rho/2*pi)*[ln(infinity)ln(0)].
I'm stumped. Anyone have any ideas?
Joel
I would look in the charming little book:
RANDOM WALKS AND ELECTRIC NETWORKS
====
Subject: Re: Resistance of infinite sheet
<090620051123273942%anniel@nym.alias.net.invalid>
y3wZYhMAAABYsCtaDBjCWE5oFd14ElQZbfvQjxC1czdFUKdrfKUl4g
I wonder if someone can help me with this: Imagine an infinite sheet
of
> material. The material has some electrical resistivity Rho  meaning
there
> are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
> rectangle of the material L units long by W units wide. Imagine also
that
> the sheet is connected to electrical ground around its' periphery.
(I
> know this is kind of a mindbender for some  the EE's at this point
are
> bailing for the next post, and the mathematicians are wondering what
the
> fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
> I set up an integral based on concentric rings, each of whose radial
extent
> (L) is dr and circumference is 2*pi*r, I end up with something like
> R=Integral[0infinity](1/(2*pi*r) dr), which is
> (rho/2*pi)*[ln(infinity)ln(0)].
I'm stumped. Anyone have any ideas?
Joel
I would look in the charming little book:
> RANDOM WALKS AND ELECTRIC NETWORKS
Second the recommendation. It is freely available (under GPL)
on the Web:
[arXiv:math  Random Walks and Electric Networks]
http://front.math.ucdavis.edu/math.PR/0001057
In brief, for dimensions higher than two the answer is finite.
====
Subject: Re: Resistance of infinite sheet
BoVIJQwAAABWQmiBreBpIBK6U9cCf57f
> I wonder if someone can help me with this: Imagine an infinite sheet of
> material. The material has some electrical resistivity Rho  meaning
there
> are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
> rectangle of the material L units long by W units wide. Imagine also
that
> the sheet is connected to electrical ground around its' periphery.
(I
> know this is kind of a mindbender for some  the EE's at this point are
> bailing for the next post, and the mathematicians are wondering what the
> fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
> I set up an integral based on concentric rings, each of whose radial
extent
> (L) is dr and circumference is 2*pi*r, I end up with something like
> R=Integral[0infinity](1/(2*pi*r) dr), which is
> (rho/2*pi)*[ln(infinity)ln(0)].
I'm stumped. Anyone have any ideas?
I can't speak for the correctness of your model, but that integral is
infinite, which presumably isn't much use.

Larry Lard
Replies to group please
====
Subject: Re: Resistance of infinite sheet
>I wonder if someone can help me with this: Imagine an infinite sheet of
>material. The material has some electrical resistivity Rho  meaning there
>are Rho (L/W) Ohms of resistance in traversing (in the L direction) a
>rectangle of the material L units long by W units wide. Imagine also that
>the sheet is connected to electrical ground around its' periphery. (I
>know this is kind of a mindbender for some  the EE's at this point are
>bailing for the next post, and the mathematicians are wondering what the
>fuss is about.)
My question is, what is the resistance from a point on this sheet to
ground?
>I set up an integral based on concentric rings, each of whose radial extent
>(L) is dr and circumference is 2*pi*r, I end up with something like
>R=Integral[0infinity](1/(2*pi*r) dr), which is
>(rho/2*pi)*[ln(infinity)ln(0)].
I'm stumped. Anyone have any ideas?
Joel
When you find such a sheet jusr stick a meter on it!
====
Subject: Waneeta Eden Marchand  July 3rd 1971
xTuwsg0AAAAJvUJEaPgOGiJgKaup0yZ5
M A R C H A N D
13 1 18 3 8 1 14 4 = 62
A bit of a space cadet, she couldn't remember which particular year in
the 1950's that her mom was born, and like most people in Saskatchewan,
likely never even met her dad. She offered to pay me $2 for my work but
in the end she just walked away and didn't give me anything.
? Mom 30 10 /62
159 Waneeta 3 7 71 184/181 5249
Waneeta 69 Eden 28 Marchand 62
? Sis 14 10 75 287/78 6813
Waneeta's last name adds to 62, while her mom was born with 62 days
remaining in the year. Mom gave birth a total of 595 days after her
birthdays, or 1.62 years. Perhaps mom and the sister also share the 62
valued last name.
Waneeta was born a multiple of 23 days into the year (184=8x23), her
first name begins with the 23rd letter of the alphabet and adds to a
multiple of 23 (69=23+23+23). Her last name adds to 62 (the 23rd Book
of the New Testament).
Mom was born on the 30th and gave birth in years adding to the 146
verses of Bible Book 30, Amos.
Waneeta was born on day 184... the 184th prime (1097) and the 184th
nonprime (235) averages 666. She was born in 71, there are 71 verses
in Bible chapters 993 and 1005, together for 1998 (666+666+666). Her
last pair of names add together for 90 (66th nonprime).
Primes NonPrimes Numbers
2 1 1
3 4 2
5 6 3
7 8 4
11 9 5
13 10 6
17 12 7
19 14 8
23 15 9
29 16 10
31 18 11
37 20 12
41 21 13
43 22 14
47 24 15
53 25 16
59 26 17
61 27 18
67 <19th> 28 <19th> 19
  
568 306 190
Mom generally has her birthday on the 303rd day of the year, it's
the number of verses in Hebrews, Bible Book 58 (the 19th Book of the
New Testament). The kids were together born 471 days into their years,
it's 67 (the 19th prime) weeks and 2 days. Waneeta has 19 letters, her
first name adds to 69 (Exodus 19), her middle name adds to 28 (19th
nonprime). Her given initials add to 28 (19th nonprime). The
different letters in her given names add to 67 (19th prime). The
different letters in her full name add to 109 (Leviticus 19). The last
letters of each of her names add together for 19. Waneeta gave birth on
the 28th (19th nonprime), Bible Book 28 contains 197 verses. Psalms is
Bible Book 19 with 2460 verses, or 7x19x19 minus the 19th prime (67).
Old Testament Book 19 and New Testament Book 19 together contain 163
chapters (the 38th or the 19+19th prime).
159 Waneeta 3 7 71 184/181 5249
Waneeta 69 Eden 28 Marchand 62
62+ Kid 28 1 94 28/337 13494
Waneeta's names have an average value of 53, she and her kid were
born on days of the year adding to 212 (53+53+53+53).
Marchand begins with the 13th letters of the alphabet and adds to
62, or the 13th prime (41) plus the 13th nonprime (21). Waneeta's
given names differ in value by 41 (13th prime). Her last 13 letters add
to 91 (1 through 13). Her first 13 and last 13 letters average 101 (the
13+13th prime). Her initials add to 41 (13th prime). Her names add to
69, 28 and 62, these are the 50th, 19th and 44th nonprimes, together
for 113. Her little sister was born in 75, or 13 plus the 13th prime
(41) plus the 13th nonprime (21). The little sister was born exactly
41 weeks into the year (13th prime) and she was born with 78 (6x13)
days remaining in the year. The sisters were born on days of the
century adding to 53796, it's 147.28 years (147 is the 113th
nonprime). Waneeta was born 246 days after mom's birthday, or 6 times
the 13th prime (41).
Primes NonPrimes Fibonacci Lucas
2 1 0 1
3 4 1 3
5 6 1 4
7 8 2 7
11 9 3 11
13 10 5 18
17 12 8 29
19 14 13 47
23 15 21 76
29 16 34 123
31 18 55 199
37 20 89 322
41 <13th> 21 <13th> 144 <13th> 521
 
238 154 <Lamentations
Mom generally has her birthday on the 303rd day of the year, it's
the number of verses in Hebrews, Bible Book 58 (the 7 primes up to 17).
The kids were born in months adding to 17 and on days of the month
adding to 17. The kids were together born 212 days closer to the
beginning of their years than to the end of their years, it's 1 through
17 (153) plus the 17th prime (59) and is the opening chapter of Bible
Book 7. The kids were together born with 259 days remaining in their
years (59 is the 17th prime). Wanetta was born on day 184, it's the 167
verses of Book 17 plus 17 more and is the location of the first two 17
versed chapters in the Bible, Leviticus 1 (chapter 91) and Leviticus 3
(chapter 93). Her name adds to 159, it's the 618 verses of Book 7 short
of 777 and is the 7x7th prime (227) minus the 7x7th nonprime (68). Her
prime valued leters add to 59 (the 17th prime). Her first 7 and last 7
letters average 59 (the 17th prime). Her 159 valued name adds with her
184th day of birth for 343 (7x7x7). Her name adds to 159, she was born
on the 3rd (Leviticus with 859 verses). Her day, month and year of
birth adds to 81 (59th nonprime). Mom and the little sister generally
have their birthdays on days of the year adding to 590. . Mom gave
birth a total of 595 days after her birthdays, corresponding to Psalm
117, the 595 days is 7 times the 17th prime (59) plus 7 times the 17th
nonprime (26).
Primes NonPrimes Numbers
2 1 1
3 4 2
5 6 3
7 8 4
11 9 5
13 10 6
17 12 7
19 14 8
23 15 9
29 16 10
31 18 11
37 20 12
41 21 13
43 22 14
47 24 15
53 25 16
59 <17th> 26 <17th> 17
  
440 251 153
Waneeta and her sister were together born with 259 days remaining in
their years while Waneeta and her kid were born with an average of 259
days remaining in their years. Waneeta and her kid were born an average
of 153 days closer to the beginning of their years than to the end of
their years (1 through 17 and is the 117th nonprime). Waneeta and her
kid were born on days of the year adding to 212 (1 through 17 plus the
17th prime, it's the opening chapter of Bible Book 7). Grandma and the
kid were born on days of the month adding to 58 (the 7 primes up to
17).
Primes
In Prime
Primes Positions
1 2
2 3 < 3
3 5 < 5
4 7 <17 is the 7th prime
5 11 < 11 while the primes up
6 13 to 7 add to 17
7 17 < 17
8 19
9 23
10 29
11 31 < 31
12 37
13 41 < 41
14 43
15 47
16 53
17 59 < 59 <the 7th prime in
 prime position
167
Esther
Book 17 <the 7th prime
17 is the 7th prime while the primes up to 7 add to 17. There are 7
primes in prime positions up to the 17th prime and they add to the 167
verse of Bible Book 17, Esther. Esther become Queen in Book 17 and Q is
the 17th letter of the alphabet. Psalm 59 (the 17th prime) not only
contains 17 verses, it is the 17th chapter in the Bible to contain the
length of 17 verses. James is Book 59 (the 17th prime), it's 108 verses
is the 17th prime short of the 167 verses of Book 17.
Primes
In Prime
Primes Positions
1 2
2 3 < 3
3 5 < 5
4 7
5 11 < 11
6 13
7 17 < 17
8 19
9 23
10 29
11 31 < 31
12 37
13 41 < 41

108
James
Book 59
Leviticus begins with 17 verses and terminates at chapter 117 with
17+17 verses. There are 17 verses at chapters 1 and 3, and 59 (the 17
prime) verses at chapter 13, so the 17's and the 17th prime are at
chapter numbers adding to 17 (1+3+13=17). The first 17 versed chapters
in the Bible are at chapters 91 and 93, together for 184, or the 167
verses of Book 17 plus 17 more. Leviticus contains 859 verses, it ends
in 59 (the 17th prime). The first 17's in the Bible surround chapter 92
(the 4x17th nonprime):
Leviticus

91 1 17
92 2 <68th (4x17th) nonprime
93 3 17
94 4
95 5
96 6
97 7
98 8
99 9
100 10
101 11
102 12
103 13 59 <17th prime
104 14
105 15
106 16
107 17
108 18
109 19
110 20
111 21
112 22
113 23
114 24
115 25
116 26
117 27 34 <17+17
The sisters are separated by 4.28 years. The sisters were born on
days of the century adding to 53796, it's 147.28 years. The little
sister was born on day 287. Waneeta's middle name adds to 28, she gave
birth on the 28th day of the month.
NonPrimes
1 27 50
4 28 51
6 30 52
8 32 54
9 33 55
10 34 56
12 35 57 <41st
14 36 58
15 38 60
16 39 62
18 40 63
20 42 64
21 44 65
22 45 66
24 46 68
25 48 69
26 49 70
The little sister was born exactly 41 weeks into the year (57 is the
41st nonprime), and she was born with 78 days remaining in the year
(the 57th nonprime). The little sister was born in 75... the 57's are
at Genesis 41, Leviticus 14, Judges 9 and John 11, together for 75.
Waneeta and her kid were born on the 26116th and 34361st days of the
century, the latter is 131.57% of the former, pretty as Waneeta's
common name adds to 131. Waneeta was 22.57 years old when she gave
birth.
The Four 57's
Genesis 41 > 41
Leviticus 14 > 104
Judges 9 > 220 <I dreamt of 220 roofs blown
John 11 > 1008 off homes in the Dakotas

1373 <220th prime
Chapter 57 is Exodus 7 with 25 verses
Book 57 is Philemon with 25 verses
 
41st nonprime 16th nonprime
<together for 57>
Major Books of EndTimes Prophecy (Daniel and Revelation are in part
about 666 while Isaiah contains 66 chapters):
Daniel  357 verses
Revelation  404 verses <57 plus the 57th prime
plus the 57th nonprime
Isaiah  1292 verses <an average of 19.575757...
verses per chapter
Genesis 41 contains 57 verses (the 41st nonprime), we are
encouraged here to accumulate food reserves in preparation for a
prolonged period of adversity. The Canadian government instead fined
farmers for failure to move their grain to port fast enough to fill the
waiting ships (and this was after the railway companies ripped out the
tracks, sold the land and then used the money to buy luxurious hotels).
The Canadian government promised to clean up the environment but
instead opened our borders to Americans trucking in their toxic wastes.
The Canadian government prevented the manufacture of energy efficient
cars (U of S Engineers built cars decades ago that obtained many
hundreds of miles per gallon of gas) and allows extremely dirty
gasoline to be sold, even though technology existed decades ago that is
able to remove the assorted pollutants (the dirty gas fouls the engine
oil, and requires the engine oil to be changed more often). The
Canadian government is complicit in the slave trade of women by trading
with slave nations (Brazil, India, Japan, Thailand and the Moslem
nations) and by allowing the mafia to bring captive women from Eastern
Europe to work here under the guise of being exotic dancers. The
Canadian government keeps wages low by flooding our country with Asian
and Latin American immigrants (many of these people are Catholics who
are directed to vote for the government who brought them here) and
allows their bank friends to create money out of thin air and charge
high interest rates, resulting in the loss of land and property (and
years of labour). The Canadian government under funds our military,
even though we live in the last days when wars are prophesied... and
after WWII the Canadian military was dismantled, making millionaires
out of many Liberal party members. Farmers were fined for failure to
get their grain to port fast enough while I was repeatedly arrested and
tortured for daring to criticize traditions in churches that are in
opposition to God's Commandments. Note that in the Bible, only Psalm 57
refers to storms in the plural.
Waneeta provided stats on Broadway Ave. in Saskatoon, it is the
street that is lined with poster poles made to resemble penises. In
1988 I stated that these phallic poles are representations of penises,
and the Egyptian obelisks on the roofs of churches, at The Vatican,
Whitehouse and in front of Saskatoon City Hall are similarly
representations of penises, all in opposition to God's Second
Commandment (Exodus 20:46). I said that the environmental destruction
was on purpose, that people in positions of power are purposely
destroying the earth (Revelation 12:12). And I stated that the churches
are censoring Scriptural references to cannibalism, and that witches
have in fact eaten many of the missing people in North America (Psalm
14:4, Micah 3:23, First Peter 5:8). I said that the Bible encourages
us to save food for a period of adversity (Genesis 41) and that we are
to give the land rest every 7th year and redistribute the land every 50
years (Leviticus 25). I said that Satanists erect obelisks and other
phalliclike objects because they believe the penis has a godlike
force through it's reproductive role, but Shawn knows that your penis
is closer to your anus than to God, and they responded by saying that I
think too much about penises and that I am under arrest. Protestants
and Catholics did not like my criticisms of their churches and lobbied
my abusive parents to have me arrested and tortured in psychiatric
facilities. These supposed Christians hired Hindus to torture me, every
three weeks I was allowed to plead my sanity in front of a panel of
middleclass Protestants and Catholics who loved their decorated trees
and Sunday day of worship considerably more than me (and even more than
Jesus), telling them that Scripture condemns turning trees into idols
(Deuteronomy 12:2, First Kings 14:23, Second Kings 16:4, 17:10, 2
Chronicles 28:4, Isaiah 57:5, Jeremiah 2:20, 3:6, 3:13, 17:2, Ezekiel
6:13, Hosea 14:8) was used as evidence by them that I was religiously
deluded. I begged in vain for people in the community to assist me to
flee the horrid rounds of psychiatric torture, but people closed their
hearts, mocked and assaulted me, and threatened to arrested and treat
(torture) me if I dared to continue to speak out against their
traditions. In place of compassion they offered me verbal and physical
abuse, and they repeatedly tried to provoke me to anger... the Broadway
merchants erected additional representations of penises along their
street, the city lined the 20th Street commercial district with
representations of penises, and a statue of Gandhi was erected in
downtown Saskatoon with his back turned to the facilities were I was
tortured by Hindus. Rather than support my ministry in the slightest
manner, I was repeatedly arrested and tortured, and while you people
tithe to churches that censor cannibalism and teach you to turn trees
into decorated idols, Saskatoon has grown to be among the most violent
cities in Canada. For years and incessantly Don Ocean and James
Takayama were calling me a pedophile on the usenet, rather than report
that my postings were laden with pedophilia. And so your police
officers and psychiatrists were unable to shut me up, so now let the
violent semiliterate street slime deal with me instead, it's a fine
reward for trying to inform you people that the churches substitute
traditions for Commandments... I'm sure your reward will come soon as
well. Instead of turning a 7 foot tall tree into a decorated idol, why
not get a bigger tree and decorate the damn thing to an even greater
degree?!!! I lost my summers year after year to psychiatric torture, I
begged in vain for assistance to flee the country and all you filthy
pieces of crap could do for me is erect a statue of Gandhi in downtown
Saskatoon with his back turned to the facilities where I was tortured
by Hindus. You made me a home in a psychiatric ward then close your
hearts and decorate your own homes with billions of dollars in
fertility symbols, and then fly off to some place warm while leaving me
in a state of shock and horror. You people deserve the government you
have, as you are the same as your government, just a different
pile, while the people of Saskatoon are the cream of the crop.
After showing Waneeta mathematical patterns linking her name to her
birthday and to the birthdays of her family members, and all of this to
numbers in the Bible (rather indication that the God of the Bible is
the God that provided for Waneeta), she wouldn't give me the $2 she
originally offered. She spends over $10 for a package of cigarettes and
over $3 for a beer, or about $5 for a cup of Booster Juice down the
block, yet couldn't toss me a couple of dollars for my work.
Saskatchewan has the highest rate of teen pregnancies in Canada, and it
follows that Saskatchewan would also have the highest number of
illegitimate children. I think that these women who give birth to
illegitimate children are often drug addicted, and the drug that they
are most addicted to is tobacco. It is nearly impossible to walk around
downtown Saskatoon without somebody begging a cigarette from you, or
begging a few coins so that they can buy a cigarette from the next
person who passes by. These drug addicted women are most apt to spread
their legs for a cigarette, but also for 50 cents worth of crack
cocaine or for 10 cents worth of crystal meth, or for a heavily taxed
$3 beer. The ignorant women in Saskatchewan are apt to befriend and
fornicate with the ignorant men who offer them drugs, while in
Saskatoon, women give birth out of their assholes.
187 Dar 17 2 57 48/317 00
Daryl 60 Shawn 65 Kabatoff 62
187 Marcia 6 8 80 219/147 8571
Marcia 45 Veronica 87 Acevedo 55
288 Melinda 23 3 83 82/283 9530
Melinda 58 Janelle 59 Elaine 46 Joyce 58 Jarocki 67
Anyway, if you people think that you have the right to use my
abusive parents as tools and arrest and torture me, then I think that I
should have the right to ask women to marry me, or to marry Marcia and
me. I have Scripture to support taking seven brides (Isaiah 4:1) and I
have Scripture to support sleeping with Melinda Jarocki outside of
wedlock (First Kings 1:15), while you people have a vast multitude of
Scriptures condemning your decorated trees, phalliccapped churches and
your violence against me for daring to point out your pagan traditions.
Good luck and may God bless you!!!
Daryl Shawn Kabatoff
Box 7134
Saskatoon Saskatchewan
Canada
S7K 4J1
Isaiah 45:4, Ephesians 3:15  God gives you your name!!!
Here are my Carlys:
1)
1936 Buick Coupe  I wanted to buy a coupe, when Sam discovered I found
one at a reasonable price, he insisted that he would take me to see it,
he then drove me to see this car on 7th Street. I think I was 17 years
old, the car was about $700. Sam ordered me in a very angry and gruff
voice not to buy the car, he said it needed king pins and that I would
never find king pins for it. Sam ordered me not to purchase it and
added that he would buy me a nice car some day
2)
1938 Cadillac LaSalle 4 door sedan  Ruby threw away the head lights
and the tail lights, the car is rolled and already missing the drive
train, now there isn't enough left of this car to attempt to fix. I
still have this car and need parts for it. Farmer cousin Jack never
gave me a bill of sale for it, maybe he forgot about
the transaction
3)
1940 Chevrolet 4 door sedan  no tears in the interior, gauges intact,
not rusted out, the engine needed work. Sam sold it for the $50 I paid
for it within 3 days after bringing it home (Lloyd Minion and Brian
Dent helped me get it home), I think that Sam sold it to one of the
alcoholic Saskatoon City Police officers that dropped by daily to drink
with Sam at his bar in the basement
4)
1952 Studebaker Coupe  Ran and drivable but the water pump was about
to fail, Sam ordered me to sell it. Sam sold it to the first person who
flashed any amount of money. When there was a car that needed to be
sold, Ruby would always become very threatening and speak in a shrill
voice that I would expect to hear as a child
before she would hit me. She slapped me around pretty good on the
morning of December 25th one year, this and acts like it resulted in me
stuttering when I was around 11 or 12 years old. About this time I did
not desire to dress up and go Halloweening, and Sam gave me a slap and
ordered me to get dressed and go door to door on my own for the sweet
treats
5)
1956 Ford 2 door Sedan  I went to Kelsey to learn motor mechanics, I
put a lot of work into the 390 V8 engine, also installed a 4 speed
manual transmission, Ruby went insane in her insistence that I sell the
vehicle (new brakes and exhaust), I put it up for sale to try to keep
peace in the family, sold it for about what the transmission was worth
6)
1957 Ford 2 door Sedan  And what a mistake to put this car in Sam's
precious back yard, the body school at Kelsey Institute repaired the
rustedout rocker panels, the parents insisted and insisted I should
not have this car
7)
1958 Ford School Bus camperized with stove and 3 way fridge  In the
late 1970's (or perhaps in 1980) I drove this over to show my parents,
Ruby became ballistic and repeatedly demanded I sell it, she would
phone me up and harp about it
8)
1965 Daimler Benz 40 Foot Bus V6 Cummins  As per Ruby's insistence I
sold the 58 Ford school bus. But then I immediately bought a bigger
bus, then year after year after year after year after year after year
after year I listened to Ruby ordering me to sell the bus (again she
would phone me up to harp at me about it, and pretty much every time I
saw her she would make it an issue). There was never any encouragement
from Sam, all my life he took away my vehicles and always promised that
he would help me get established in life and buy me a car. But all he
would do is feed steaks and booze to the rich relatives and to any of
his alcoholic friends
9)
1970(?) VW Station Wagon  Clark Henderson's sister sold me this VW
Wagon when I worked as a Social Worker in Whitecourt Alberta in 1987,
intoxicated Sam and insane Ruby came to see me in Whitecourt, Ruby
repeatedly demanded I sell the 1965 Daimler bus, Sam assaulted me
during the visit, they returned to Saskatoon and sold the Daimler for
$1000. Earlier Sam sent me $1000 when I went to school in Montreal and
finished my degree in Anthropology with Women's Studies Classes, he
used this amount to determine the selling price, sold the bus and took
the money. My job performance suffered after Sam assaulted me and sold
my bus, I lost my job in Whitecourt, this VW broke down and I had no
money to fix it (much of my money was going into my brother's
photography business)
10)
1966 Ford 2 door hardtop  The VW broke down, so at the end of 1987 I
bought a cheap Ford to leave Whitecourt and return to Saskatoon, but
during 1988 my words upset people in the community and they had my
abusive parents institutionalize me. Rather than make money to keep
this car running, I was drugged and tortured
11 and 12)
After a few years of psychiatric torture and a few years of absence
from my parents, I renewed limited contact with them late into year
2001, for Sam was in the hospital then with a hip replacement, I
thought to go to wish him well. Sam then told me that he bought a van,
and that he never really got anything in trade for the late 1990's
Crown Victoria. The contact with Sam results in contact with Ruby, and
together they took me for a drive looking around the streets of
Confederation Park to find my mother's 1984 Mustang, Ruby sold it to
some kid and so Sam drove us around in search of the car just to point
it out for me. I heard Ruby say many times since obtaining it, that she
would pass her Mustang down to her kids. Then Sam insisted on checking
my blood sugar and then promptly stuck me with a dirty needle. Ruby
said that Sam should have used a cleannew needle
For Further Reading:
Frances Farmer: Shadowland by William Arnold, 1978
A History of Gold and Money 14501920 by Pierre Vilar, 1991
The Grip of Death: A Study of Modern Money, Debt Slavery, and
Destructive Economics by Michael Rowbotham, 1998
Disposable People: New Slavery In The Global Economy by Kevin Bales,
1999
====
Subject: sine and imaginary numbers
XRFC2646: Format=Flowed; Original
Hello there
I read the following statement in the book called the music of the
primes... and I am just wondering what does it mean? It was on pg. 90
Euler had made the surprising discovery that feeding an imaginary number
into the exponential function produced a sine wave. The rapidly climbing
graph usually associated with the exponential function had been transformed
by the introduction of these imaginary ...
anyone know any good books for the not so advanced mathemathician where such
wierd and cool relationships are explored and connnect, stuff with e, i, pi,
phi, and so on. I am a book on each of the numbers, but I am looking for one
that connects a whole lot of mathematical enteties in one book. P.S. I
finished advanced calculus, linear algebra in university and that's it.
====
Subject: Re: sine and imaginary numbers
> Hello there
> I read the following statement in the book called the music of the
> primes... and I am just wondering what does it mean? It was on pg. 90
Euler had made the surprising discovery that feeding an imaginary number
> into the exponential function produced a sine wave. The rapidly climbing
> graph usually associated with the exponential function had been
transformed
> by the introduction of these imaginary ...
> anyone know any good books for the not so advanced mathemathician where
such
> wierd and cool relationships are explored and connnect, stuff with e, i,
pi,
> phi, and so on. I am a book on each of the numbers, but I am looking for
one
> that connects a whole lot of mathematical enteties in one book. P.S. I
> finished advanced calculus, linear algebra in university and that's it.
There is a useful identity
sin(a+ib) = sin(a)*cosh(b) + i*cos(a)*sinh(b)
In order to find z such that sin(z) = 2 you have to solve the
equations
2 = sin(a)*cosh(b)
0 = cos(a)*sinh(b)
cos(a)=0 or sinh(b)=0. If sinh(b)=0 then b=0 > cosh(b)=1 > sin(a)=2.
As this impossible we have to set cos(a)=0. As sin(a) must be positive
the possible values for a are pi/2+2kpi. and we have to solve
cosh(b)=2. This yields b = +ln(2+sqrt(3))
Thus the complete solution is
z = pi/2 + k*pi + i*ln(2+sqrt(3))

Horst
====
Subject: Re: sine and imaginary numbers
> Hello there
> I read the following statement in the book called the music of the
> primes... and I am just wondering what does it mean? It was on pg. 90
Euler had made the surprising discovery that feeding an imaginary number
> into the exponential function produced a sine wave. The rapidly climbing
> graph usually associated with the exponential function had been
transformed
> by the introduction of these imaginary ...
> anyone know any good books for the not so advanced mathemathician where
such
> wierd and cool relationships are explored and connnect, stuff with e, i,
pi,
> phi, and so on. I am a book on each of the numbers, but I am looking for
one
> that connects a whole lot of mathematical enteties in one book. P.S. I
> finished advanced calculus, linear algebra in university and that's it.
Start with the series expression
e^x = 1 + x + x^2/2 + x^3/6 + ... + x^n/n! + ...
If you plug in i*x where x is real and i = sqrt(1), and using i^2 = 1,
i^3 = 1, i^4 = 1, you end up with the DeMoivre relationship mentioned
by other posters (using the series for sin(x) and cos(x)).
In fact it's instructive to graph each successive term on the complex
plane. The 4n terms (0, 4, 8, ...) add a positive real number, so they
move you to the right. The 4n+1 terms (1, 5, 9, ...) are a positive real
times i, so they move you up. The 4n+2 terms all involve i^2 = 1 so
they move you to the left, and the 4n+3 terms move you downward. With
x=pi you get a spiral (consisting of line segments meeting at right
angles) converging in the complex plane to the point (1, 0) on the
xaxis. In other words you get a simple and dramatic geometric
visualization of the equation e^i*pi = 1.
Of course the real trick is to have derived the infinite series for exp,
sin, and cosine in the first place. Those 18thcentury guys were pretty
clever.
====
Subject: Re: sine and imaginary numbers
XRFC2646: Format=Flowed; Response
> Hello there
> I read the following statement in the book called the music of the
> primes... and I am just wondering what does it mean? It was on pg. 90
Euler had made the surprising discovery that feeding an imaginary number
> into the exponential function produced a sine wave. The rapidly climbing
> graph usually associated with the exponential function had been
> transformed by the introduction of these imaginary ...
> Does anyone know any good books for the not so advanced mathemathician
> where such wierd and cool relationships are explored and connnect, stuff
> with e, i, pi, phi, and so on. I am a book on each of the numbers, but I
> am looking for one that connects a whole lot of mathematical enteties in
> one book. P.S. I finished advanced calculus, linear algebra in university
> and that's it.
>
Exp [ i * x ] = Cos [ x ] + i * Sin [ x ]
De'Moivre's [ spelling? ] Theorem
 Geo. Michael Henry
Eat dessert first. Life is uncertain.
====
Subject: Re: sine and imaginary numbers
Exp [ i * x ] = Cos [ x ] + i * Sin [ x ]
De'Moivre's [ spelling? ] Theorem
>
No, Euler's and is established with analysis.
DeMoiver's theorem is
(cos x + i.sin x)^n = cos nx + i.sin nx
and is proven with algebra, trig and induction on n.
====
Subject: Re: sine and imaginary numbers
XRFC2646: Format=Flowed; Original
> Exp [ i * x ] = Cos [ x ] + i * Sin [ x ]
>> De'Moivre's [ spelling? ] Theorem
> No, Euler's and is established with analysis.
> DeMoiver's theorem is
> (cos x + i.sin x)^n = cos nx + i.sin nx
> and is proven with algebra, trig and induction on n.
of what I've been taught 40 years ago.
 Geo. Michael Henry
Eat dessert first. Life is uncertain.
====
Subject: Explicit from of general solution
yPy0yA0AAAASbSTLbngmB_Y2MPXTyEPO
I need to make y the subject of
36/7y^7/3 = 1/6cos(x)^6
====
Subject: Re: Explicit from of general solution
> I need to make y the subject of
36/7y^7/3 = 1/6cos(x)^6
>
====
Subject: Re: Explicit from of general solution
yPy0yA0AAAASbSTLbngmB_Y2MPXTyEPO
sorry, I'll try again
(36/7)y^(7/3) = (1/6)cos(x)^6
====
Subject: Re: Explicit from of general solution
I forget. What's the problem?
What's cos(x)^6 ? cos(x^6) or (cos x)^6 ?
====
Subject: Mathew William Shaw  November 13th 1966
xTuwsg0AAAAJvUJEaPgOGiJgKaup0yZ5
S H A W
19 8 1 23 = 51
Mathew provided stats for his family today, he valued my work at
$2.75 (Canadian), it's about what he spends on a bottle of beer or for
a handful of lights for his decorated tree. My interest in numbers was
repeatedly used as an excuse to arrest and torture me in psychiatric
facilities and at a cost of millions of dollars, now I am respected and
my work is recognized as being valid, and I am paid $2.75. Woo hoo!!!
200 Mathew 13 11 66 317/48 3556
Mathew 70 William 79 Shaw 51
195 Jeanine 7 10 77 280/85 7537
Jeanine 58 Marie 46 Taylor 91
131 Aidan 7 5 03 127/238 16880
Aidan 29 Michael 51 Shaw 51
Dad was born with 48 days remaining in 66 (48th nonprime). His
given names add together for the 149 verses of Galatians, Bible Book
48. Mom's common name adds to or the 149 verses of Galatians, Bible
Book 48. The family has names adding together for 526 (Psalm 48). The
kid's full name adds to the 32nd prime, pretty when considering that
Bible Book 32 contains 48 verses.
NonPrimes
1 27 50
4 28 51
6 30 52
8 32 54
9 33 55
10 34 56
12 35 57
14 36 58
15 38 60
16 39 62
18 40 63
20 42 64
21 44 65
22 45 66 <48th
24 46 68
25 48 69
26 49 70
Dad was born on the 317th day (the 66th prime) of year 66. His name
adds to 200, corresponding to Bible Book 6 chapter 13 (the 6th prime).
His names have an average value of 66.666... The parents were born in
years adding to 143, chapter 666 brings Ecclesiastes up to 143 verses.
The parents were born on days and in months and years adding to 184...
the 184th prime (1097) and the 184th nonprime (235) averages 666. Dad
and the kid were born with an average of 143 days remaining in their
years (chapter 666 brings Ecclesiastes up to 143 verses). The kid's
first name adds to 29, it's 6 plus the 6th prime (13) plus the 6th
nonprime (10), Bible Book 13 (the 6th prime) contains 29 (6+6p+6np)
chapters while Bible chapter 666 contains 29 (6+6p+6np) verses.
66.666...% of the kid's names add to 51 (the 6x6th nonprime). Dad and
the kid were born in years adding to 69 and have names differing in
value by 69. The family was born an average of 66% into their years.
Together they have 51 letters (6x6th nonprime). Dad was 36 years old
when the kid was born (6x6 while 1 through to 36 adds to 666). Today
dad is 13404 days old, there are 404 verses in Revelation, Bible Book
66.
150  Genesis
5190  Exodus
91117  Leviticus
118153  Numbers
154187  Deuteronomy
188211  Joshua
930957  Matthew
958973  Mark
974997  Luke
9981018  John
10191046  Acts
10471062  Romans
41 <The 13th prime while 13 in turn is the 6th
prime, it's the 6th prime in prime position
while one of the versions of Bible Book 41
contains 666 verses
123 <Numbers 6, it is three times the 13th
prime (41+41+41), keeping in mind that
13 is the 6th prime... it's 3 times the
6th prime in prime position
188 <the opening chapter of Book 6 is 6x6x6 short
of the 404 verses of Bible Book 66, it is the
6th prime squared (13x13) short of the 357
verses of Daniel (also in part about 666)
193 <Book 6 chapter 6 is the 44th prime,
while 44 is in turn 66.666...% of 66
211 <the terminating chapter of Book 6 is
approximately 66.6% of the 66th prime (317)
357 <the opening chapter of Book 6 plus the 6th
prime squared is the 357 verses of Daniel
(in part about 666)
404 <the 6th prime squared (13x13) plus the 6th
prime squared (13x13) plus 66 adds to the
404 verses of Bible Book 66
1062 <666 plus 6x66 is a combination of the 658
verses of Bible Book 6 plus the 404 verses
of Bible Book 66, and is the terminating
chapter of New Testament Book 6
1070 <666 plus the 404 verses of Book 66 is the
1070 verses of Job (Book 6+6+6)
1213 <Exodus terminates at chapter 90 (66th non
prime) with 1213 verses (the 198th or the
66+66+66th prime)
1292 <the 658 verses of Book 6 plus twice the
66th prime (317) is the 1292 verses of
Isaiah (the Book contains 66 chapters)
Dad was born on the 13th, he has 13 letters in his given names, his
full name adds to 200 (Joshua 13). The parents were born in months
adding to 21 (13th nonprime) and on days and in months adding to 41
(13th prime). The parents were born in years adding to 143 (11x13).
Mom's given names span a range of 13 while her last name adds to 91 (1
through 13), she was born on day 280 (Second Samuel 13). The kid was
born with 238 days remaining in the year (the first 13 primes), his
first name adds to the 29 chapters of Bible Book 13, his full name adds
to 131. Mom and the kid were together born 84 days closer to the end of
their years than to the beginning of their years (the first 13 primes
minus the first 13 nonprimes). Dad and the kid have f5rst names
differing in value by 41 (13th prime). The family was born in months
adding to 26 (13+13). There are 37 chapters in the Bible that contain
the length of 13 verses...
Primes NonPrimes Fibonacci Lucas Numbers
2 1 0 1 1
3 4 1 3 2
5 6 1 4 3
7 8 2 7 4
11 9 3 11 5
13 10 5 18 6
17 12 8 29 7
19 14 13 47 8
23 15 21 76 9
29 16 34 123 10
31 18 55 199 11
37 20 89 322 12
41 <13th> 21 <13th> 144 <13th> 521 <13th> 13
  
238 154 <Lamentations 91
Dad was born 37 days further into the year than mom. The kid was
born 111 (37+37+37) days closer to the beginning of the year than to
the end of the year. Their names add to 200, 195 and 131, these are the
154th and 151st nonprimes, and the 32nd prime, together for 337. Mom
was 7537 days old when she gave birth. Mom and the kid were born on
days of the year adding to 407 (11x37). All first names add together
for 157 (the 37th prime).
Primes
2 61 149
3 67 151
5 71 157 <37th
7 73 163
11 79 167
13 83 173
17 89 179
19 97 181
23 101 191
29 103 193
31 107 197
37 109 199
41 113 211
43 127 223
47 131 227
53 137 229
59 139 233
The kid's given names add to 80, and his common name also adds to
80, pretty as he and mom were born in years adding to 80. And this 80
is the 58th nonprime, pretty as mom's first name adds to 58.
Lucas
1
3
4
7
11
18
29

73 <the Lucas numbers up to 29 add to
the 73 verses of Bible Book 29
J O E L <Bible Book 29
10 15 5 12 = 42 <29th nonprime
C O P P E R <29th element
3 15 16 16 5 18 = 73 <Book 29 and is the Lucas
numbers up to 29, there
is a copper riding a
horse on the 1973
Canadian 25 cent piece
C E N T <made out of 29th element
3 5 14 20 = 42 <29th nonprime
Mom's first name adds to 58, it's 29+29 and is the 42nd nonprime
while 42 in turn is the 29th nonprime (58 is 29+29 and is the 29th
nonprime in nonprime position). Dad's middle name adds to 79 (Exodus
29), the kid's first name adds to 29.
NonPrimes
Non In NonPrime
Primes Positions
1 1 < 1
2 4
3 6
4 8 < 8
5 9
6 10 < 10
7 12
8 14 < 14
9 15 < 15
10 16 < 16
11 18
12 20 < 20
13 21
14 22 < 22
15 24 < 24
16 25 < 25
17 26
18 27 < 27
19 28
20 30 < 30
21 32 < 32
22 33 < 33
23 34
24 35 < 35
25 36 < 36
26 38 < 38
27 39 < 39
28 40 < 40
29 42
30 44 < 44
31 45
32 46 < 46
33 48 < 48
34 49 < 49
35 50 < 50
36 51 < 51
37 52
38 54 < 54
39 55 < 55
40 56 < 56
41 57
42 58 < 58 <29+29 and is also the
29th nonprime number
the is in nonprime
position
Dad is Mathew. Matthew is the first of the 27 Books of the New
Testament, it contains exactly 3 times the number of verses of the 27th
Book of the Old Testament. The family was born on days of the month
adding to 27. The kid was born on the 127th day of the year.
Mom was born in 77, her given names add together for 104 (77th
nonprime). Mom's first name adds to 58 (the 7 primes up to 17), the
parents have first names adding together for 128 (2 to the 7th). The
parents were born on days of the week adding to 7. Mom and the kid were
both born on the 7th day of the month. Mom was exactly 307 months old
when she gave birth. Mom and the kid were born on days of the year
adding to 407. Mom and the kid were born on days of the month adding to
14, pretty as the kid's name adds to 131 (Numbers 14). Mom was born on
day 280 and with 85 days remaining in the year, these are the number of
verses in Bible Book 15 and 8 (a difference of 7).
Mom was born in 77, her given names add together for the 77th
nonprime, note that 77 plus the 77th prime (389) plus the 77th
nonprime (104) adds to 570, pretty as chapter 104 (the 77th nonprime)
contains 57 verses. Mom's given names add together for 104 (Leviticus
14 with 57 verses). She was 25.57 years old when she gave birth,
prettier as Bible chapter 57 contains 25 verses and Bible Book 57
contains 57 verses. Dad was born 269 days closer to the end of the year
than to the beginning of the year (57th prime).
389 <77th prime
104 <77th nonprime
77 <77

570
The Four 57's
Genesis 41 > 41
Leviticus 14 > 104
Judges 9 > 220 <I dreamt of 220 roofs blown
John 11 > 1008 off homes in the Dakotas

1373 <220th prime
Chapter 57 is Exodus 7 with 25 verses
Book 57 is Philemon with 25 verses
 
41st nonprime 16th nonprime
<together for 57>
Major Books of EndTimes Prophecy (Daniel and Revelation are in part
about 666 while Isaiah contains 66 chapters):
Daniel  357 verses
Revelation  404 verses <57 plus the 57th prime
plus the 57th nonprime
Isaiah  1292 verses <an average of 19.575757...
verses per chapter
Genesis 41 contains 57 verses (the 41st nonprime), we are
encouraged here to accumulate food reserves in preparation for a
prolonged period of adversity. The Canadian government instead fined
farmers for failure to move their grain to port fast enough to fill the
waiting ships (and this was after the railway companies ripped out the
tracks, sold the land and then used the money to buy luxurious hotels).
The Canadian government promised to clean up the environment but
instead opened our borders to Americans trucking in their toxic wastes.
The Canadian government prevented the manufacture of energy efficient
cars (U of S Engineers built cars decades ago that obtained many
hundreds of miles per gallon of gas) and allows extremely dirty
gasoline to be sold, even though technology existed decades ago that is
able to remove the assorted pollutants (the dirty gas fouls the engine
oil, and requires the engine oil to be changed more often). The
Canadian government is complicit in the slave trade of women by trading
with slave nations (Brazil, India, Japan, Thailand and the Moslem
nations) and by allowing the mafia to bring captive women from Eastern
Europe to work here under the guise of being exotic dancers. The
Canadian government keeps wages low by flooding our country with Asian
and Latin American immigrants (many of these people are Catholics who
are directed to vote for the government who brought them here) and
allows their bank friends to create money out of thin air and charge
high interest rates, resulting in the loss of land and property (and
years of labour). The Canadian government under funds our military,
even though we live in the last days when wars are prophesied... and
after WWII the Canadian military was dismantled, making millionaires
out of many Liberal party members. Farmers were fined for failure to
get their grain to port fast enough while I was repeatedly arrested and
tortured for daring to criticize traditions in churches that are in
opposition to God's Commandments. Note that in the Bible, only Psalm 57
refers to storms in the plural.
Mathew provided stats on Broadway Ave. in Saskatoon, it is the
street that is lined with poster poles made to resemble penises. In
1988 I stated that these phallic poles are representations of penises,
and the Egyptian obelisks on the roofs of churches, at The Vatican,
Whitehouse and in front of Saskatoon City Hall are similarly
representations of penises, all in opposition to God's Second
Commandment (Exodus 20:46). I said that the environmental destruction
was on purpose, that people in positions of power are purposely
destroying the earth (Revelation 12:12). And I stated that the churches
are censoring Scriptural references to cannibalism, and that witches
have in fact eaten many of the missing people in North America (Psalm
14:4, Micah 3:23, First Peter 5:8). I said that the Bible encourages
us to save food for a period of adversity (Genesis 41) and that we are
to give the land rest every 7th year and redistribute the land every 50
years (Leviticus 25). I said that Satanists erect obelisks and other
phalliclike objects because they believe the penis has a godlike
force through it's reproductive role, but Shawn knows that your penis
is closer to your anus than to God, and they responded by saying that I
think too much about penises and that I am under arrest. Protestants
and Catholics did not like my criticisms of their churches and lobbied
my abusive parents to have me arrested and tortured in psychiatric
facilities. These supposed Christians hired Hindus to torture me, every
three weeks I was allowed to plead my sanity in front of a panel of
middleclass Protestants and Catholics who loved their decorated trees
and Sunday day of worship considerably more than me (and even more than
Jesus), telling them that Scripture condemns turning trees into idols
(Deuteronomy 12:2, First Kings 14:23, Second Kings 16:4, 17:10, 2
Chronicles 28:4, Isaiah 57:5, Jeremiah 2:20, 3:6, 3:13, 17:2, Ezekiel
6:13, Hosea 14:8) was used as evidence by them that I was religiously
deluded. I begged in vain for people in the community to assist me to
flee the horrid rounds of psychiatric torture, but people closed their
hearts, mocked and assaulted me, and threatened to arrested and treat
(torture) me if I dared to continue to speak out against their
traditions. In place of compassion they offered me verbal and physical
abuse, and they repeatedly tried to provoke me to anger... the Broadway
merchants erected additional representations of penises along their
street, the city lined the 20th Street commercial district with
representations of penises, and a statue of Gandhi was erected in
downtown Saskatoon with his back turned to the facilities were I was
tortured by Hindus. Rather than support my ministry in the slightest
manner, I was repeatedly arrested and tortured, and while you people
tithe to churches that censor cannibalism and teach you to turn trees
into decorated idols, Saskatoon has grown to be among the most violent
cities in Canada. For years and incessantly Don Ocean and James
Takayama were calling me a pedophile on the usenet, rather than report
that my postings were laden with pedophilia. And so your police
officers and psychiatrists were unable to shut me up, so now let the
violent semiliterate street slime deal with me instead, it's a fine
reward for trying to inform you people that the churches substitute
traditions for Commandments... I'm sure your reward will come soon as
well. Instead of turning a 7 foot tall tree into a decorated idol, why
not get a bigger tree and decorate the damn thing to an even greater
degree?!!! I lost my summers year after year to psychiatric torture, I
begged in vain for assistance to flee the country and all you filthy
pieces of crap could do for me is erect a statue of Gandhi in downtown
Saskatoon with his back turned to the facilities where I was tortured
by Hindus. You made me a home in a psychiatric ward then close your
hearts and decorate your own homes with billions of dollars in
fertility symbols, and then fly off to some place warm while leaving me
in a state of shock and horror. You people deserve the government you
have, as you are the same as your government, just a different
pile, while the people of Saskatoon are the cream of the crop.
187 Dar 17 2 57 48/317 00
Daryl 60 Shawn 65 Kabatoff 62
187 Marcia 6 8 80 219/147 8571
Marcia 45 Veronica 87 Acevedo 55
288 Melinda 23 3 83 82/283 9530
Melinda 58 Janelle 59 Elaine 46 Joyce 58 Jarocki 67
Anyway, if you people think that you have the right to use my
abusive parents as tools and arrest and torture me, then I think that I
should have the right to ask women to marry me, or to marry Marcia and
me. I have Scripture to support taking seven brides (Isaiah 4:1) and I
have Scripture to support sleeping with Melinda Jarocki outside of
wedlock (First Kings 1:15), while you people have a vast multitude of
Scriptures condemning your decorated trees, phalliccapped churches and
your violence against me for daring to point out your pagan traditions.
Good luck and may God bless you!!! Or not, your traditions are in
opposition to God's Commandments, may He honor Exodus 20:5 and Hosea
4:6 as promises and spread you and your heartless Goddamned family out
like dung over the surface of the earth. If I find any of
compassionless Goddamned assholes in the obituaries I will cheer with
utter glee and post your stats again.
Daryl Shawn Kabatoff
Box 7134
Saskatoon Saskatchewan
Canada
S7K 4J1
Isaiah 45:4, Ephesians 3:15  God gives you your name!!!
Here are my Carlys:
1)
1936 Buick Coupe  I wanted to buy a coupe, when Sam discovered I found
one at a reasonable price, he insisted that he would take me to see it,
he then drove me to see this car on 7th Street. I think I was 17 years
old, the car was about $700. Sam ordered me in a very angry and gruff
voice not to buy the car, he said it needed king pins and that I would
never find king pins for it. Sam ordered me not to purchase it and
added that he would buy me a nice car some day
2)
1938 Cadillac LaSalle 4 door sedan  Ruby threw away the head lights
and the tail lights, the car is rolled and already missing the drive
train, now there isn't enough left of this car to attempt to fix. I
still have this car and need parts for it. Farmer cousin Jack never
gave me a bill of sale for it, maybe he forgot about
the transaction
3)
1940 Chevrolet 4 door sedan  no tears in the interior, gauges intact,
not rusted out, the engine needed work. Sam sold it for the $50 I paid
for it within 3 days after bringing it home (Lloyd Minion and Brian
Dent helped me get it home), I think that Sam sold it to one of the
alcoholic Saskatoon City Police officers that dropped by daily to drink
with Sam at his bar in the basement
4)
1952 Studebaker Coupe  Ran and drivable but the water pump was about
to fail, Sam ordered me to sell it. Sam sold it to the first person who
flashed any amount of money. When there was a car that needed to be
sold, Ruby would always become very threatening and speak in a shrill
voice that I would expect to hear as a child
before she would hit me. She slapped me around pretty good on the
morning of December 25th one year, this and acts like it resulted in me
stuttering when I was around 11 or 12 years old. About this time I did
not desire to dress up and go Halloweening, and Sam gave me a slap and
ordered me to get dressed and go door to door on my own for the sweet
treats
5)
1956 Ford 2 door Sedan  I went to Kelsey to learn motor mechanics, I
put a lot of work into the 390 V8 engine, also installed a 4 speed
manual transmission, Ruby went insane in her insistence that I sell the
vehicle (new brakes and exhaust), I put it up for sale to try to keep
peace in the family, sold it for about what the transmission was worth
6)
1957 Ford 2 door Sedan  And what a mistake to put this car in Sam's
precious back yard, the body school at Kelsey Institute repaired the
rustedout rocker panels, the parents insisted and insisted I should
not have this car
7)
1958 Ford School Bus camperized with stove and 3 way fridge  In the
late 1970's (or perhaps in 1980) I drove this over to show my parents,
Ruby became ballistic and repeatedly demanded I sell it, she would
phone me up and harp about it
8)
1965 Daimler Benz 40 Foot Bus V6 Cummins  As per Ruby's insistence I
sold the 58 Ford school bus. But then I immediately bought a bigger
bus, then year after year after year after year after year after year
after year I listened to Ruby ordering me to sell the bus (again she
would phone me up to harp at me about it, and pretty much every time I
saw her she would make it an issue). There was never any encouragement
from Sam, all my life he took away my vehicles and always promised that
he would help me get established in life and buy me a car. But all he
would do is feed steaks and booze to the rich relatives and to any of
his alcoholic friends
9)
1970(?) VW Station Wagon  Clark Henderson's sister sold me this VW
Wagon when I worked as a Social Worker in Whitecourt Alberta in 1987,
intoxicated Sam and insane Ruby came to see me in Whitecourt, Ruby
repeatedly demanded I sell the 1965 Daimler bus, Sam assaulted me
during the visit, they returned to Saskatoon and sold the Daimler for
$1000. Earlier Sam sent me $1000 when I went to school in Montreal and
finished my degree in Anthropology with Women's Studies Classes, he
used this amount to determine the selling price, sold the bus and took
the money. My job performance suffered after Sam assaulted me and sold
my bus, I lost my job in Whitecourt, this VW broke down and I had no
money to fix it (much of my money was going into my brother's
photography business)
10)
1966 Ford 2 door hardtop  The VW broke down, so at the end of 1987 I
bought a cheap Ford to leave Whitecourt and return to Saskatoon, but
during 1988 my words upset people in the community and they had my
abusive parents institutionalize me. Rather than make money to keep
this car running, I was drugged and tortured
11 and 12)
After a few years of psychiatric torture and a few years of absence
from my parents, I renewed limited contact with them late into year
2001, for Sam was in the hospital then with a hip replacement, I
thought to go to wish him well. Sam then told me that he bought a van,
and that he never really got anything in trade for the late 1990's
Crown Victoria. The contact with Sam results in contact with Ruby, and
together they took me for a drive looking around the streets of
Confederation Park to find my mother's 1984 Mustang, Ruby sold it to
some kid and so Sam drove us around in search of the car just to point
it out for me. I heard Ruby say many times since obtaining it, that she
would pass her Mustang down to her kids. Then Sam insisted on checking
my blood sugar and then promptly stuck me with a dirty needle. Ruby
said that Sam should have used a cleannew needle
For Further Reading:
Frances Farmer: Shadowland by William Arnold, 1978
A History of Gold and Money 14501920 by Pierre Vilar, 1991
The Grip of Death: A Study of Modern Money, Debt Slavery, and
Destructive Economics by Michael Rowbotham, 1998
Disposable People: New Slavery In The Global Economy by Kevin Bales,
1999
====
Subject: Help for a novice please
Hello group,
I am needing to order a part for a home project and in the catalog the part
is listed in cm.
I am needing to know a diameter of a part in inches that is listed in cm.
The size spec. 2.3cm (with a little 2 in the upper corner after the cm).
What exactly does the little upper 2 stand for?
When it is converted into inches, is the inches with the little 2 also?
What is the formula for this conversion?
====
Subject: Re: Help for a novice please
XRFC2646: Format=Flowed; Original
> Hello group,
I am needing to order a part for a home project and in the catalog the
part
> is listed in cm.
I am needing to know a diameter of a part in inches that is listed in cm.
The size spec. 2.3cm (with a little 2 in the upper corner after the cm).
What exactly does the little upper 2 stand for?
When it is converted into inches, is the inches with the little 2 also?
What is the formula for this conversion?
>
The little 2 means square. Just as in square feet. Here is a little trick.
You
Type: 2.3 square centimeters to square inches
And you get: 2.3 (square centimeters) = 0.356500713 square inches
Bill
====
Subject: Re: Help for a novice please
> I am needing to know a diameter of a part in inches that is listed in cm.
The size spec. 2.3cm (with a little 2 in the upper corner after the cm).
> What exactly does the little upper 2 stand for?
>
2.3 cm^2 is 2.3 centimeters squared or 2.3 square centimeters.
> When it is converted into inches, is the inches with the little 2 also?
Yes, cm^2 is measurement of area and in^2 or square inches is again
measurement of area.
> What is the formula for this conversion?
>
Look up in back of dictionary for conversion units.
1 in = 2.54 cm
1 in^2 = (2.54 cm)^2 = 2.54^2 cm^2 = 6.45 cm^2
Thus
1 cm = (1/2.54) in
and similar for cm^2.
====
Subject: Help for a novice please again
Another question about the result of the answer in the previous post.
If I am measuring the diameter (from one side to the other) is the 2.3cm^2
telling me it is 2.3cm from one side to the other? Therefore when
converted
into inches and the answer is square inches, is it telling me the distance
from one side to the other?
Ex. 2.3cm^2 = .356500713001^2
Is the diameter .356500713001
====
Subject: Re: Help for a novice please again
XRFC2646: Format=Flowed; Original
Another question about the result of the answer in the previous post.
If I am measuring the diameter (from one side to the other) is the
2.3cm^2
> telling me it is 2.3cm from one side to the other? Therefore when
converted
> into inches and the answer is square inches, is it telling me the
distance
> from one side to the other?
Ex. 2.3cm^2 = .356500713001^2
Is the diameter .356500713001
>
No. You have not said the shape of the object, but I assume it is a circle.
If
so the formula for the area of a circle is
A = pi*(r squared) where A = area = .356 etc., pi =3.14159265 and r is the
radius of the circle which is half the diameter. So divide the area by pi,
take the square root of that, and multiply that result by 2 to get the
diameter.
Bill
====
Subject: Re: Help for a novice please again
> If I am measuring the diameter (from one side to the other) is the
2.3cm^2
> telling me it is 2.3cm from one side to the other? Therefore when
converted
> into inches and the answer is square inches, is it telling me the
distance
> from one side to the other?
>
You are very confused. A diameter has a length and is measured in
inches, centimeters, feet, meters, etc. 2.3cm^2 is a unit of area, it
is not a unit of lenght. So if you measure the diameter as 2.3 cm^2
you have big problem not understanding what you're doing or what the
problem is or how to express what the problem is.
> Ex. 2.3cm^2 = .356500713001^2
>
What happened to the dimension, ie the units of measurements
of the right side?
> Is the diameter .356500713001
>
The diameter of what?