Subject: Re: Q: Gambling Theory Result from Bell Labs
From: Jive Dadson
Date: Wed, 23 Oct 1996 05:44:02 +0000
Alex Castaldo wrote:
>
> Have you ever seen the following theorem before:
>
> "A gambler takes repeated binomial gambles. At each step he/she invests
> a fraction alpha of their current wealth. Researchers at Bell Labs have
> proved that the optimal strategy in this situation is to set alpha
> equal to p - q ".
>
> Is this correct?
Only if the proposition is made at even money.
To maximize his longterm growth rate of bankroll, the gambler should
bet a proportion of his bankroll equal to edge/odds for each isolated proposition.
given that the probability of winning is independent of the odds offered.
For multiple mutually exclusive propositions (like betting on two or more
horses in a horse race), the formula is more complicated.
> Who proved this and where is it published?
J.L. Kelly Jr., "A New Interpretation of Information Rate", Bell System
Technical Journal, v 35 (1956), pp. 917-926.
J.
Subject: Some probability questions.
From: Darren Pamatat
Date: Wed, 23 Oct 1996 09:42:30 -0400
I am posting this for a friend, who is a student.
He received this project and is totally lost. If anyone,
can offer any guidance, ways to approach, or reference books
it would be most appreciated.
Here are the three questions:
1. There are red and white balls in two containers. Container #1 has 5
red and 5 white. Container #2 has 3 red and 7 white. One container is
chosen at random and 6 balls are randomly chosen from this container. If
among the chosen balls, there are equal number of white and red balls,
what is the probablity that they came from container #2.
2. Consider the following game at a casino. To enter each round of the
game, you put one dollar on the table theh choose one of the following 3
dice (you and the casino can see all three)
Die #1: 5,10,15,20,25,30
Die #2: 2,12,13,22,28,30
Die #3: 4,9,14,19,29,43
After you have chosen, the casino host will choose on of the other 2
dice and also put one dollar on the table. Then you will throw your die
and the host throws his. The one that gets the higher number gets both
dollars on the table.
1. If you enter the game playing against the casino, what is the
probability of your winning?
2. What is your expected win/loss?
3. Desing a computer simulation of this game using random number
generator.
(just design is sufficient)
3. The next is a coin toss game. An unfair coin with head turns up at
the probability p=0.6 is used. You pay $x to enter the game and then
you toss the coin 10 times. You win $n if there are n heads. Let H be
the random variable which is the number of heads in this 10 tosses.
1. Compute and plot the probability distribution of H.
2. What should be the premium x so that the game is fair?
3. Design a computer simulation of this game.
Subject: Re: covariance
From: aacbrown@aol.com (AaCBrown)
Date: 23 Oct 1996 09:40:54 -0400
Jordi Riu in <326DE27D.37CA@quimica.urv.es> wants
to find the covariance of a and b+c given the variances and covariances of
a, b, and c.
The covariance of a and b+c is equal to:
E[a(b+c)] - E(a)E(b+c)
= E(ab) + E(ac) - E(a)E(b) - E(a)E(c)
= E(ab) - E(a)E(b) + E(ac) - E(a)E(c)
= Cov(a,b) + Cov(a,c)
Aaron C. Brown
New York, NY
Subject: Re: Weibull distribution : 1) What kind of distribution is it? 2) Pls suggest a program to fit it
From: aacbrown@aol.com (AaCBrown)
Date: 23 Oct 1996 09:59:07 -0400
"HAMEL, Jean" in <326A9B04.7D17@total.net> asks about the
Weibull Distribution.
The c.d.f. for a Weibull is 1-exp[-(x/b)^c] where x ranges from 0 to
infinity, b is called the "characteristic life" and c is called the
"shape". With c=1 a Weibull is just an exponential variate, with c=2 it is
a Rayleigh variate.
The mean is b times Gamma[(c+1)/c].
The probability that a Weibull variate is less than the characteristic
life (b) is 1-exp(-1) = 0.632 for any shape parameter (c).
Weibull variates are used to model failure times. With shape parameter 1,
the time to next failure is independent of time. In other words the amount
of time something has already lasted has no effect on how much longer it
will last.
With shape parameter greater than 1, failure probability increases with
time. Failures will show a bell-shaped distribution in time.
With a shape parameter less than 1, failure probability decreases with
time.
If something "wears out" it will have a shape parameter greater than 1, an
automobile tire is an example. If something "breaks in" or there is a wide
variation in initial quality, the shape parameter will be less than 1.
These are things that either break early or last forever.
Aaron C. Brown
New York, NY
Subject: Re: 0.5*infinity
From: aacbrown@aol.com (AaCBrown)
Date: 23 Oct 1996 10:05:18 -0400
Bill Shipley and Lyne Labrecque in
<326C24B3.7F06@interlinx.qc.ca> writes:
> Consider an X-Y graph (#1) in which both X and Y are REAL
> variables that can vary from -infinity to +infinity. The area of
> this graph is therefore infinity*infinity (...?...). Now, restrict
> Y to be greater than, or equal to, zero. Is the area of this
> new graph (#2) 1/2infinity*infinity?
No. You can take the old graph and place it on top of the new graph with
no overlap. So they must have the same area. It is strange that cutting
something in half does not reduce its area. Infinity is strange.
It's easier to explain with integers. A hotel has an infinite number of
rooms numbers 1, 2, 3, . . . and so on. It is full. An infinite number of
new guests arrive. The manager simply tells all the existing guests to
move to a room twice the number of their current room. So 1 moves to 2, 2
to 4, 3 to 6 and so on. Now all the odd rooms are empty the the new guests
can be accomodated.
It is strange that a full hotel can still add an infinite number of
guests. But that is what infinity is.
Aaron C. Brown
New York, NY
Subject: Re: fitting function without independent variable
From: jarausch@numa1.igpm.rwth-aachen.de (Helmut Jarausch)
Date: 23 Oct 1996 10:38:08 GMT
In article <54jlv5$sq7@news.nyu.edu>, mjy@cns.nyu.edu (Mark Young) writes:
|>
|> I am looking for a treatment of the problem
|> of curve fitting in the case where there is
|> NO INDEPENDENT variable. For example, you
|> have a sensor system that measures space and
|> time (all subject to errors) and you need to fit
|> a curve to the data.
|>
SNIP
You have to choices,
either you design an implicit curve (like (x/a)^2+(y/b)^2)-r^2= 0 for an ellipse)
and fit a,b and r
OR
you need an independent variable to represent a curve.
The problem is, you must be able to order the measured points in increasing
arc-length of the (final) curve. Then you can take e.g. just the sum of the distances
of the points as an artificial parameter (preliminary arc length, pseudo arc length).
i.e. if your points are x[i], i=0,...,N then assign the parameter
\sqrt{\sum_1^k{ |x[k]-x[k-1]|^2 }} to t[k]. Now you can make a vector valued spline ansatz s(t) for the mapping t->x and use an orthongal direction regression like ODR from netlib
to estimate the unknown spline coefficients. AFterwards you can plot the curve given
(piecewiese) by t->s(t) .
Helmut Jarausch
Subject: Re: Looking for a better estimator for a simple expectation
From: Helene Thygesen
Date: Wed, 23 Oct 1996 17:24:23 +0200
Hein Hundal wrote:
> Once again I am seeking some knowledge and/or a reference to confirm
> a rumor. I am conducting an experiment with the following possible
> outcomes: {-11, -9, -7, -5, ..., 9, 11} (odd numbers between -12 and
> 12.) I will perform the experiment approximately 5000 times.
[..]
> During the interview the
> applicant mentioned that there was a better estimator available for this
> kind of experiment. I didn't believe him at the time, but then he
> mentioned a paper that he had written on the subject, so I took his word
> for it. I really wish I had written down the paper's title because a
> better estimator would be very useful for me.
>
> So the questions is "Is there a better estimate for the expectation than
> the average?"
[..]
Depends what you mean by "better" and what you know about the
distribution.
If you expect many "outliers" a robust estimator such as the median may
be better than the average.
If you know that your data a gausian distributed, the average and the sd
are maximum likelyhood parameters which is often taken as an argument
for considering the "best" estimators.
Helene Thygesen
Schaepmanstraat 111
6702 AS Wageningen
The Netherlands
+31(0)654 655 631
mailto:helene@pobox.org.sg
http://www.pobox.org.sg/~helene
Subject: Re: Some probability questions.
From: Jive Dadson
Date: Wed, 23 Oct 1996 10:42:33 +0000
Darren Pamatat wrote:
>
> I am posting this for a friend, who is a student.
> He received this project and is totally lost. If anyone,
> can offer any guidance, ways to approach, or reference books
> it would be most appreciated.
Certainly. I will be glad to help. Tell your friend to schedule
an appointment with his teacher to discuss the difficulties
he is having.
With best regards,
Jive Dadson
Subject: UM Biostatistics Open House
From: Robert L Strawderman
Date: Wed, 23 Oct 1996 14:52:48 -0400
Hi all -
The University of Michigan Department of Biostatistics is having
its annual Student Open House on Friday Nov 8. Please inform
anyone that you think may be interested! Students unable to attend but
intertested in the department should contact the department directly
at the address below for additional information. Thanks much!
Announcement follows:
The University of Michigan Department of Biostatistics will host a
Student Open House to provide information to interested individuals
about graduate study in biostatistics.
Time and Place: Friday November 8 from 1:00 to 4:30 pm in Room M3024,
School of Public Health Building I (SPH I), 109 South Observatory, Ann
Arbor. If you need directions, contact Mike Kelly at the address below.
The Open House will include presentations by students, faculty, and
alumni, who will focus on what biostatistics is and what
biostatisticians do, on the outstanding job opportunities in
biostatistics, and on the admissions and financial support opportunities
in the Department of Biostatistics at Michigan. There also will be time
for questions and discussion.
To pre-register for the Open House, send e-mail to mikell@umich.edu, or
fill out and return the form at the bottom of this flyer. (The form is
also on the world wide web at www.sph.umich.edu/group/biostat) If you
decide at the last minute you would like to attend, please do so even if
you haven't pre-registered.
For more information, please call Michael Kelly at 313-764-5451.
------------------------------------------------------------------------
Name:
Address:
E-mail:
Major:
I plan to attend: Yes No
Please send me information about the Department: Yes No
Please return to: Admissions Committee, Department of Biostatistics,
School of Public Health, University of Michigan, 1420 Washington
Heights, Ann Arbor, MI 48109-2029
--
***************************************************************************
Robert Strawderman, Sc.D. Email: strawder@umich.edu
Department of Biostatistics Office: (313) 936 - 1002
University of Michigan Fax: (313) 763 - 2215
1420 Washington Heights
Ann Arbor, MI 48109-2029 Web: http://www.sph.umich.edu/~strawder/
***************************************************************************
Subject: Re: Prony's method, and the arithmetic of distributions
From: cbilbo@bham.mindspring.com (Claude D. Bilbo)
Date: Wed, 23 Oct 1996 18:08:41 GMT
In , Tony Corso wrote:
>
>In the 1986 SIGAPL Conf. Proceedings Groner and Cook Published “Arithmetic of
>statistical distributions”.
>
> In it they describe a suite of APL programs that uses “Prony’s method” to
>generate a representation of a set of distributions that they can then
>manipulate arithmetically.
Don't know about Prony's method.
>i.e. they can say something like
>
>Normal (1,3) + Normal ( 1.5,4)
>and get back the result
>Normal (2.5, 5)
>
>i.e. the sum of a normal distribution with mean=1 and stddev=3 with another
>independent normal distribution mean =1.5, stddev 4 is a normal distribution
>with mean=2.5 and stddev=5.
>
>I would very much like to do this sort of thing for LOGNORMAL distributions,
>(with a known covariance ).
>The article says that the authors would next work on multivariate
>distributions and lognormals, but I’ve been unable to locate any other work by
>them. They cite a 1981 article by Hellerman as reference #5, but provide only
>4 references.
I couldn't find much at all on multivariate lognormals when I needed
the info either. There's a book by Aitchison and Brown called "The
Lognormal Distribution" that may be of help. They developed theorems
that allow you to do the same sort of arithmetic for lognormals that
you've described for normals. But where sums of normals are normal,
products of lognormals are lognormal. There's a nice clean equation
that gives a result for products of multivariate lognormals. I read
once that someone else has written a more recent book on lognormals,
but can't remember the title. Should be easy enough to find.
Books on multivariate arithmetic for normal (gaussian) distributions
should be easy to find.
If you need to convert back and forth between gaussian and lognormal,
some files of mine are at ftp://ftp.mathworks.com/pub/contrib/stats/cbilbo/
>Unfortunately the article is a little vague as to what Prony’s method is, and
>a web search seems to indicate that Prony’s method has something to do with
>signal processing.
>
>might anybody point me in the right direction, (considering that I’m no EE
>signal processing gearhead)?
No comment.
>TIA
>Regards
>Tony
>
>
-----------------------------------------------------------------
| Claude D. Bilbo | |
| cbilbo@mindspring.com | All of my opinions are |
| bilboc02@eng.uab.edu | completely uncorrelated.|
| http://www.mindspring.com/~cbilbo/ | |
-----------------------------------------------------------------
Subject: Re: probability is relativistic
From: mma@goon.ux.softpro.de (Dr Michael Mattes)
Date: Wed, 23 Oct 1996 07:28:51 GMT
Christopher McKinstry (chris@clickable.com) wrote:
> I believe probability is relativistic.
> Here’s a simple experiment you can try at home to demonstrate
> probability changing with speed:
> 1) Let "V" the maximum number of digits you can write per second.
> 2) In "T" seconds, write down a random number in decimal form.
> Now, the maximum number you could have written is "9" repeated VT times.
> This is your Reality Radius "RR". The fact you even have one proves
> probability behaves relativistically.
> Consider, as V decreases, there comes a point at which the only number
> you have time to write is "1". At this point another person would be
> able to guess your "random" number in 100% of all trials at that V. As V
> increases the probability that that same person could guess your
> "random" number approaches zero. Only at infinite V, could you truly
> pick a random number. What was thought to be random is thus
> deterministic. Probability changes with speed.
> A person traveling near the speed of light would be able to write many,
> many times more digits than a person at rest in a given time period,
> due to relativistic time dilation. The person moving at near light speed
> would thus have a much larger RR and could generate much more random
> numbers than the person at rest. At the speed of light, a person could
> write an infinite number of numbers and thus choose an actual random
> number.
I don't think so. If i would look at a fast moving passenger, i would
see "his time" passing by very slow. Thats "his" proper time. On the
other hand, if he looks at my clock, he would see a very fast running
clock. Thats "my" proper time. And when he returns (e.g. after a year
in ** his ** reference system) for me (in ** my ** reference system
there have passed a lot of more than one year (e.g. some millions
year, if he was travelling at near light speed). This means ** I **
would be able to write much more digits than the moving passenger.
> Unless you’re moving at the speed of light you can’t generate a random
> number.
> --
> -K. Christopher McKinstry : Homepage
> http://www.clickable.com/employees/chris/index.html
> -Join In The World's Largest AI Effort
> http://www.clickable.com/mist_corpus.html
--
************************************************************************
* SOFTPRO GmbH Phone : Germany-7031-6606-85 *
* Wilhelmstrasse 34 Fax : Germany-7031-6606-88 *
* D-71034-Boeblingen E-mail : mma@softpro.de *
************************************************************************
Subject: Announcement of Student Contest in Clinical Trials
From: chappell@becrux.biostat.wisc.edu (Rick Chappell)
Date: 23 Oct 1996 21:51:33 GMT
Please distribute to interested parties. Thanks,
Rick.
--------------------------------
Rick Chappell <> Associate Professor, Depts. of Statistics and Biostatistics
University of Wisconsin at Madison Medical School <> chappell@stat.wisc.edu
K6/430 Clinical Science Center <> 600 Highland Ave <> Madison, WI 53792
Work (608) 263-5572 / FAX 263-1059 / Home 233-3664 <> take logs
***************
STUDENT SCHOLARSHIP PROGRAM
SOCIETY FOR CLINICAL TRIALS / INTERNATIONAL SOCIETY FOR CLINICAL BIOSTATISTICS
JOINT MEETING
JULY 6 - 10, 1997
BOSTON, MA
The Society for Clinical Trials Student Scholarship Program was established
to stimulate student involvement in the Society. Because the 1997
meeting will be held jointly with the International Society for Clinical
Biostatistics, the contest will be sponsored by both societies. Students are
invited to submit abstracts, along with a short manuscript (not to exceed three
pages). To be eligible, the presentation should concern clinical trial -
related issues.
ELIGIBILITY
All students enrolled in a degree program of an accredited college or
university, post-doctoral fellows, or physicians enrolled in an accredited
residency program. The manuscript must relate to original work that has not
yet been published. Student eligibility will be assessed by the committee
at the time of submission.
TOPIC
The presentation can describe a completed study, one in progress, or a
proposal for carrying out a clinical trial. Sample topics include (but are
not limited to):
Design or analysis of a specific trial or class of trials.
Review of results or methods of a class of trials.
Medical, legal or ethical issues related to clinical trials.
Data entry, management, and computing as applied to clinical trials.
PRESENTATION
A session at the Joint Meeting will be set aside for Student
Scholarship paper presentations followed by discussion.
SUBMISSION PROCEDURE
Manuscript should be no more than three double-spaced pages.
Abstracts should be submitted on an official form obtained from the Society
for Clinical Trials Business Office and should conform to the rules it states.
Seven (7) copies of both abstract and short manuscript should be submitted.
A letter from the student's faculty advisor stating that he/she is a bona
fide student and briefly describing the student's course of study should
accompany the submission. If the manuscript is coauthored, this letter
should also include an indication of the level of involvement of the various
authors.
The deadline for student submissions is JANUARY 15, 1997.
REVIEW
Selections are made by the Student Scholarship Committee and are final.
Between three and five students are expected to be named as presenters.
Winners will be notified by March 1. They are required to provide
Scholarship Committee members with a copy of the complete paper to be
presented at the Annual Meeting by May 15, 1997. This paper will be used
by the Committee for post-presentation discussion.
AWARDS
Those students selected to present papers will be invited to the meeting
with all fees waived and travel and living expenses paid, subject to a
negotiable $1750 US limit and the guidelines provided by the Society
Business Office.
The student judged to have the best paper will receive the Thomas C.
Chalmers Student Scholarship prize and a $500 cash award.
MAIL SUBMISSION OF MANUSCRIPT TO: FOR FURTHER INFORMATION CONTACT:
Secretariat Rick Chappell, Ph.D.
Society for Clinical Trials, Inc. University of Wisconsin - Madison
600 Wyndhurst Avenue Department of Biostatistics
Baltimore, Maryland 21210 600 Highland Ave., K6/430
Madison, WI 53792 USA
e-mail address: chappell@stat.wisc.edu
FAX (608) 263-1059
Subject: Announcement of applied statistics contest
From: chappell@becrux.biostat.wisc.edu (Rick Chappell)
Date: 23 Oct 1996 21:54:32 GMT
Please distribute to interested parties. Thanks,
Rick.
--------------------------------
Rick Chappell <> Associate Professor, Depts. of Statistics and Biostatistics
University of Wisconsin at Madison Medical School <> chappell@stat.wisc.edu
K6/430 Clinical Science Center <> 600 Highland Ave <> Madison, WI 53792
Work (608) 263-5572 / FAX 263-1059 / Home 233-3664 <> take logs
***************
THE INTERNATIONAL BIOMETRIC SOCIETY EASTERN NORTH AMERICAN REGION CASE STUDIES
COMPETITION ANNOUNCEMENT
ENAR will sponsor the third annual Case Studies Competition at its upcoming
Spring Meeting. Winning presentations will be highlighted in a poster session
at the meeting. The purpose of the competition, in addition to fostering
excellence in biometric endeavors, is to encourage participation by practicing
statisticians in industry, government, research organizations, and academic
research centers both as entrants in the competition and as attendees at the
conference. Papers should represent interesting applications of existing or
new statistical methods to datasets arising from scientifically relevant
studies. Awards will be made based on originality and thoroughness in
accomplishing one or more of the following:
Illustration of the use of new statistical methodology or innovative application of existing methodology with real data from a biological field of study;
Application of sound statistical methods to an unusual or complex dataset from a biological field of study;
Presentation of new data or data from new sources that make a significant
contribution to a biological field of study; and
Comparison of competing analysis strategies for a particular type of dataset
pertinent to biology.
REQUIREMENTS
Eligible participants include practicing statisticians with a Bachelor's or
Master's degree in statistics or a related field who are not pursuing a
doctorate degree. All entrants should be able to attend the Spring Meeting, to be held in Memphis, Tennessee, March 23-26, 1997. Datasets upon which the
analyses are based are to be supplied by the entrants and may be disguised
for purposes of confidentiality.
Selection of awards will be based on a manuscript describing the analysis and
presenting results. Manuscripts should be no longer than 25 pages, inclusive of tables and graphs. An annotated version of the poster is an acceptable
submission. The entrant should be the first author of the manuscript. The
manuscript and abstract (in standard ENAR format) should be submitted by
November 15, 1996. Two title pages should be included with the manuscript,
one with title, authors, and contacting information, and a second with only
the title and no identifying information.
SELECTION AND AWARDS
A review committee will judge the submitted manuscripts in a blinded fashion.
The application should be of scientific relevance and of interest to the
audience. The author should demonstrate a thorough understanding of the methods employed. The results should be well explained and well illustrated. Innovative uses of statistical methods and/or novel applications are particularly
encouraged.
The winners will be notified in January, 1997. A first-place winner and up to four additional winners will be selected. All winners will receive a one-year
membership in the Biometric Society that includes a subscription to the journal Biometrics. Awardees will be recognized at the Presidential address and
receive an invitation to the President's reception.
SUBMISSION OF MANUSCRIPTS
Papers should be received no later than 11/15/96 or postmarked no later than
11/13/96. The submission should include:
1) A cover letter;
2) One complete title page with author, institutional affiliation, address,
phone/fax numbers;
3) Three copies of the paper with only a title on the first page; and
4) The ENAR abstract form.
ALL ITEMS should be sent to:
ENAR Data Analysis Competition
ENAR Office
Suite 502
1730 North Lynn Street
Arlington, VA 22209-2004
Tel (703) 525-1191
FAX (703) 276-8196
-----------------------------------------------
Thanks for your interest, and I wish you well.
Kent R. Bailey, Ph. D.
Biostatistics, Mayo Clinic
200 SW 1st. Ave.
Rochester, MN 55905
507-284-5581
baileyk@mayo.edu
Subject: Basic question on rxy
From: David Tjeder
Date: Tue, 22 Oct 1996 18:41:26 +0200
I am having some trouble with the rxy measure. The thing is, I have =
completed an analysis in economic history and my teacher has told me I =
should also analyse rxy (and r2) with the variables switched; i.e. =
exchanging x for y and vice versa. This would enable me to see whether =
the causal effect goes from x to y, or from y to x, she claims. Now, =
from what little statistics I know, this seems absurd. Is it not so, =
that since rxy is a measure on to what extent x and y are connected to =
each other, it does not matter which variable is put into the analysis =
as "x" and which we choose to call "y"? (x and y are of course, it =
seems to me, correlated to each other to same extent as y and x are =
correlated.) I have computed the rxy measure with the variables =
swithched, which left me with the same result as when I had not =
switched them (0,46).
Also, if one looks at the formula for rxy, it seems to me, again, that =
what variable is chosen as y and which is chosen as x has no effect on =
the outcome of the calculation:
N=85xy - =85x=85y =
divided by
=88N=85x2 - (=85x)2 =88N=85y2 - (=85y)2
Since the two parts from which one is supposed to extract the root =
(this sign =88, if my mailing program can't handle it) are multiplied =
anyway, it does not matter what variable we choose to treat as y, and =
which we choose to treat as x - am I right? i.e., my teacher is out in =
the blue telling me it matters and has anything to do with causality - =
or?
I would be most grateful if anyone could help me with this problem. =
Thank you,
David Tjeder
Subject: Re: 0.5*infinity
From: Ellen Hertz
Date: Wed, 23 Oct 1996 21:15:04 -0400
Bill Shipley and Lyne Labrecque wrote:
>
> Consider an X-Y graph (#1) in which both X and Y are REAL variables that can vary from
> -infinity to +infinity. The area of this graph is therefore infinity*infinity
> (...?...). Now, restrict Y to be greater than, or equal to, zero. Is the area of this
> new graph (#2) 1/2infinity*infinity? What if Y is restricted to the range (1,10). What
> is the area of this third graph? (10-1)*infinity? What is the ratio of the area of this
> plane divided by the area of the first plane? Is it:
> 9*infinity/(infinity*infinity)=9/infinity?
> What is the area of graph #3/graph#2? Is it:
> 9*infinity/(0.5*infinity*infinity)=18/infinity?
> If all of this is true then does it follow that (18/infinity) is twice as large as
> (9/infinity)?
> A reference would be appreciated.
Your questions are addressed by the subject called set theory. There are many
books on the subject. A pretty good summary is in "Theory of Functions of
a Real Variable" by Henry P. Thielman, Chapter II.
Subject: Re: Royal Statistical Society Certificate
From: n.w.nelson@education.leeds.ac.uk (nick nelson)
Date: Thu, 24 Oct 1996 09:36:08 +0100 (BST)
Myron Hlynka wrote:
>
> A student from a country in the Caribbean has applied for admission
> for the undergraduate program here at the U. of Windsor. He has
> submitted a document indicating that he has received a Royal
> Statistical Society (London) Higher Certificate, which apparently
> can be obtained by passing a set of exams. The topics are fairly
> standard - statistical analysis, inference, nonparametrics, etc.
> Presumably these are at a lower undergraduate level.
>
> Can anyone give a more precise indication of the level of this
> certificate? Is it considered equivalent to [a] course[s] in
> any university?
>
> Or, can anyone give me a contact so I can find out (preferably
> am e-mail contact)?
The RSS has a www page at http://www.maths.ntu.ac.uk/rss/index.html
also, e-mail contact via rss@rss.org.uk
Nick.
Subject: SPC software for PC with EWMA capability?
From: "Michael J. Anderson"
Date: 24 Oct 1996 14:20:37 GMT
Hi:
My company is moving from MAC's to PC's and looking for a new SPC / control
chart package. We are using a 'no-name' package on the MAC that doesn't
have a Windows version. I have absolute requirements that in addition to
having data protection and standard XR charting the software must do EWMA
charting. Aside from that things are pretty much negotiable. I have done
some looking / calling and bought a copy of SPC PC-IV from Quality America,
which does this, but is really made to run on a single computer. We would
_prefer_ client server, as there will be many users.
Any ideas / suggestions?
I know we could get a custom SAS system built, but that isn't currently
feasible (timeline and cost constraints), and we use JMP for engineering
data analysis, but it isn't what we want for a 'shop floor' system.
Thanks in advance,
Mike
anderson@usa1.com
Subject: Re: Looking for a better estimator for a simple expectation
From: aacbrown@aol.com (AaCBrown)
Date: 24 Oct 1996 11:18:55 -0400
Michael Kamen in
<54ml3v$nhg@news.doit.wisc.edu> writes:
> My understanding is that expectation, E(x) is synonymous with
> the population mean. Both have the same definition. As such, the
> arithmetic mean would be the best estimator since it is essentially
> the same thing as the mean only with a sample of the population
> rather than the population as a whole.
The expected value of a random variable is an unobservable quantity, the
sample mean is something that can be measured. It is true that a sample
mean is often a good estimate of the expected value, but not always. Your
argument that they are "essentially the same thing" has some merit, all
other things being equal we prefer estimators that are directly related to
what we want to measure. But sometimes other considerations are more
important.
To give an artificial but simple example, suppose I know that X has a
uniform distribution from A to B with A and B unknown. If I have a sample
of x's my best estimate of the expected value of X is the average of the
minimum and maximum observations (for most general purposes).
Aaron C. Brown
New York, NY
Subject: Re: Looking for a better estimator for a simple expectation
From: aacbrown@aol.com (AaCBrown)
Date: 24 Oct 1996 12:02:27 -0400
Hein Hundal in <326D15DA.4898@kincyb.com> writes:
> I am conducting an experiment with the following
> possible outcomes: {-11, -9, -7, -5, ..., 9, 11}. . . . I will
> perform the experiment approximately 5000 times. The
> result of any one experiment does not affect the results
> of any later experiments. The goal is to find the expectation.
> I am rather certain the expectation is between -0.2 and +0.2,
> and the standard deviation is about 3.5. I have always been
> under the impression that the best estimator for the
> expectation was the average of a sample for this type of
> experiment. With 5000 trials I would expect the average to
> be accurate to within 2 * 3.5 / Sqrt(5000) <= 0.1, 95% of the
> time. . . . Is there a better estimate for the expectation than
> the average?
Unless you know more about the distribution that you said here, you cannot
do much better than the mean. Depending on your loss function (in other
words, depending on how you define "best estimator") you can do a little
better by using the knowledge that there are only 12 possible outcomes.
If you were sampling fewer times, or had fewer possible outcomes, or the
outcomes were less uniform, or you had an unusual loss function; there
could be something significantly better than the mean. But in this case, I
doubt it.
\
Aaron C. Brown
New York, NY
Subject: Re: Basic question on rxy
From: aacbrown@aol.com (AaCBrown)
Date: 24 Oct 1996 11:26:45 -0400
David Tjeder in
<326CF936.7444@mbox318.swipnet.se> writes:
> I have completed an analysis in economic history and my
> teacher has told me I should also analyse rxy (and r2) with
> the variables switched; i.e. exchanging x for y and vice versa.
> This would enable me to see whether the causal effect goes
> from x to y, or from y to x, she claims.
You are correct that the correlation coefficient of X and Y is the same as
the correlation coefficient of Y and X. And neither one has any direct
bearing on causality.
I suspect what your teacher meant was that you lag your variables. For
example you might notice that the inflation rate is negatively correlated
to the unemployment rate. You could then compute the correlation of this
month's inflation rate to next month's unemployment rate, also next
month's inflation rate to this month's unemployment rate.
If the first correlation were higher (in absolute value) than the second
you have some weak evidence that inflation causes unemployment rather than
the other way around. The evidence is weak because there are many other
possible explanations. But all other things being equal, causes tend to
appear before effects. And with a well-specified model you can refine this
conclusion.
Aaron C. Brown
New York, NY
Subject: Statistical Question . . .
From: mercurio@flagstaff.princeton.edu (Matthew G. Mercurio)
Date: 23 Oct 1996 14:18:43 GMT
I have a question regarding a statistical analysis of radio advertising
prices. I have observations on prices for 261 markets (i.e., New York,
Atlanta, etc.). I have four observations per market, corresponding to
four dayparts (AM drive, daytime, PM drive, night). The first run I
tried was:
price = A0 + A1*{daypart} + A2*{Z} + e
where {daypart} represents dummies for the different dayparts and {Z}
represents other independent variables which are market-specific (such
as population, total number of radio stations, etc.). The variables in
{Z} do not vary by market. Of course, I am aware of the classical
"dummy variable trap", so I dropped the first daypart dummy.
In the second run, I thought it might be useful to add market specific
dummy variables. Four observations per market is a little thin, but I
thought I would just give it a try. I knew that I would have to drop one
market to avoid the dummy variable trap. However, the X'X matrix was
*still* singular. Through a process of trial and error, I discovered that
the X'X matrix would not invert unless I dropped a number of markets equal
to the number of elements in {Z}, that is, the number of included
independent variables which do not vary within market.
I am unfamiliar with this problem. Is it completely useless to try
to estimate market specific constants when I have no r.h.s. variables
which vary within market? Is the dropping of markets in this manner valid?
The overall fit of the model *seems* to improve with the fixed effects, but
I don't know if it's just horseshit.
Please email or post a reply. Thanks,
-Matt
--
===============================================================================
Matthew G. Mercurio * ---***HOUSTON ROCKETS***---
mercurio@phoenix.princeton.edu *
Department of Economics * next year
Subject: Re: 0.5*infinity
From: mercurio@flagstaff.princeton.edu (Matthew G. Mercurio)
Date: 23 Oct 1996 20:03:55 GMT
In article <54l8mu$e9h@newsbf02.news.aol.com> aacbrown@aol.com (AaCBrown) writes:
>Bill Shipley and Lyne Labrecque in
><326C24B3.7F06@interlinx.qc.ca> writes:
>
>> Consider an X-Y graph (#1) in which both X and Y are REAL
>> variables that can vary from -infinity to +infinity. The area of
>> this graph is therefore infinity*infinity (...?...). Now, restrict
>> Y to be greater than, or equal to, zero. Is the area of this
>> new graph (#2) 1/2infinity*infinity?
>
>No. You can take the old graph and place it on top of the new graph with
>no overlap. So they must have the same area. It is strange that cutting
>something in half does not reduce its area. Infinity is strange.
>
>It's easier to explain with integers. A hotel has an infinite number of
>rooms numbers 1, 2, 3, . . . and so on. It is full. An infinite number of
>new guests arrive. The manager simply tells all the existing guests to
>move to a room twice the number of their current room. So 1 moves to 2, 2
>to 4, 3 to 6 and so on. Now all the odd rooms are empty the the new guests
>can be accomodated.
>
>It is strange that a full hotel can still add an infinite number of
>guests. But that is what infinity is.
>
>
>Aaron C. Brown
>New York, NY
Okay. Now a number of guests equal to the number of real numbers between
0 and 1 arrive at the hotel. All of a sudden, the inn is full!!
Not even 1% of the new guests can be accomodated!
I guess they just don't make infinite hotels as infinite as they
used too :)
-Matt
--
===============================================================================
Matthew G. Mercurio * ---***HOUSTON ROCKETS***---
mercurio@phoenix.princeton.edu *
Department of Economics * next year
Subject: Bias and Variance of Eigenvalues of a Covariance Matrix?
From: eric@gi.alaska.edu (Eric Breitenberger)
Date: 24 Oct 1996 03:04:10 GMT
Hello, all:
I am using principal components in my work (meteorology) and I have
some questions regarding the sampling variability of the results.
I'm currently using formulas for the bias and variance of the
eigenvalues which I got from a paper by Lawley (1956, Biometrika 43,
128-136). These formulas are good to O(1/n^2) for bias and O(1/n^3)
for variance.
My covariance matrices are usually of dimension ~500, with about
1000 samples, and Lawley's formulas often give me negative variances
for many eigenvalues. This disturbs me as I am not sure whether I
am somehow misusing the formula or if there is some other explanation.
In addition to the problems with the variance, I often find that my
_leading_ sample eigenvalues are consistently lower than the Lawley
formulas would indicate they should be. I have checked my code
carefully, including comparisons with some published results, and
buggy code does not appear to be the problem.
If anyone is still with me at this point (!) I would really appreciate
some help with this. Does anyone know of other good references on
this subject?
Thanks much,
Eric Breitenberger
Geophysical Institute
University of Alaska - Fairbanks