Subject: Re: Probability and Wheels: Connections and Closing the Gap
From: nveilleu@NRCan.gc.ca (Normand Veilleux)
Date: Mon, 13 Jan 1997 17:47:07 GMT
>From: bm373592@muenchen.org (Uenal Mutlu)
>I think this posting contains useful hints for a successful play
>strategy! Read on!
>
>On Thu, 9 Jan 1997 14:38:13 GMT, nveilleu@NRCan.gc.ca (Normand Veilleux)
>wrote:
>>consecutive drawings if you buy 1 ticket per draw. And even after 168
>>draws, there still is 0.042398 probability of having lost all draws.
>
>That's saying 95.76 % chance of winning (>= 3) if playing the same 1 ticket
>in 168 consecutive draws. IMHO an important conclusion from this would be:
> Playing the same 1 ticket in x consecutive draws is better than playing
> x different tickets (or a wheel) in 1 draw.
>Isn't it?
Nope, it's the inverse. Which is highest, 95.76% for 168 draws of 1
ticket each or 100% for 168 tickets in one draw?
You can also see this with a very small lottery. Say a certain
lottery has only 2 possible combinations and only 1 combination
wins a prize (like a coin flip). Obviously, if you buy all 2
combinations in one draw, then you are guaranteed to win. But if
you buy 1 combination for 2 consecutive draws, you only have 75%
chance of winning at least one of the prizes. The big difference
between the 2, like has been mentioned already, is that in the
second case you have the opportunity to win the "jackpot" twice,
but only once in the first case.
The two factors, when taken together result in exactly the same
average expected return.
>If yes, then the further practical generalization of this statement
>would be:
> Don't change your numbers; ie. play always the same numbers (tickets or
> wheel) until you have a win.
> --> So one should also very well think of analysing the past draws for
> choosing the 'right' expected numbers (it's normally a one-time task)
Looks like you missed something. The probabilities do not care which
ticket you buy, so you can keep the same ticket all the time or keep
it for some time and then change it or even change it for every drawing.
The probabilities remain the same because every ticket has 260,624
ways of winning out of 13,983,816 combinations.
>>If you do come up with the same number, then it implies that wheeling
>>does not change, in any way, the average number of winning tickets.
>
>But then also the opposite is true: wheeling is at least equal to using
>the same number of any different randomly chosen single tickets. True?
>
>Are there any situations where wheeling behaves worser than using
>randomly or even any some otherwise chosen different tickets of
>same size?
Maybe it's just because you are new at this Uenal, but this has been
stated a million times. If the lottery is random, then every imaginable
system will have the exact same average expected gain as would a system
based on randomly selecting numbers. Of course, it will take a lot of
draws to prove it to deluded system authors, but that's what the math
predicts: all systems will be equivalent within statistical significance.
Subject: Re: 1000 Terabytes ?
From:
Date: Tue, 14 Jan 1997 11:21:17 +1000
On Mon, 13 Jan 1997, Alexander Schatten wrote:
> On Tue, 07 Jan 1997 14:42:18 +0000, "\"j.a.steele\""
> wrote:
>
> >Can anyone tell me if 1000 Terabytes is 1 Petrabyte ?. If not what is it
> >?
> >Thanks
> >Jason :)
>
> first of all, it is called peta, not petra. usually it should. the
> names are:
>
> 10^6 mega
> 10^9 giga
> 10^12 tera
> 10^15 peta
> 10^18 exa
>
> but i dont know exactly if it is used in information theory in the
> same way.
>
> alex
2^10 kilo
2^20 mega
2^30 giga
etc.
This is because 2^10 = 1024 which is approximately 1000 = 10^3.
In this case 1024 terabytes is a petabyte = 2^50 bytes, much *greater
than* 10^15.
John Foster
Subject: Re: Combining Neural/Fuzzy Models with Statistical Models
From: saswss@hotellng.unx.sas.com (Warren Sarle)
Date: Tue, 14 Jan 1997 00:31:36 GMT
In article <32d84448.82298631@news.otago.ac.nz>, agray@commerce.otago.ac.nz (Andrew Gray) writes:
|> I'm working on combining neural networks and fuzzy logic models
|> with statistical techniques (regression and data reduction) for
|> software metrics (for example, predicting development time based on
|> the type and size of system). While there has been a lot of work on
|> neural-fuzzy, neural-genetic, fuzzy-genetic, etc. type systems I've
|> only ever found a small number of researchers using AI/statistical
|> techniques (presumably at least partially an indication of how few AI
|> researchers follow the statistical side of things, and vice versa).
See "How are NNs related to statistical methods?" (in part 1) and
"What about Fuzzy Logic?" (in part 2) in the Neural Network FAQ at
ftp://ftp.sas.com/pub/neural/FAQ.html
--
Warren S. Sarle SAS Institute Inc. The opinions expressed here
saswss@unx.sas.com SAS Campus Drive are mine and not necessarily
(919) 677-8000 Cary, NC 27513, USA those of SAS Institute.
*** Do not send me unsolicited commercial or political email! ***
Subject: Expected values in binomial distribution
From: tvaughan@athena.mit.edu (Timothy E. Vaughan)
Date: 14 Jan 1997 14:27:56 GMT
Sorry to those who read this in sci.math. I did not know this group
existed when I posted there. I am hoping this is an easy question for
somebody in this group!
To set notation, here is the binomial distribution:
p(n) = B(N,n) p^n (1-p)^(N-n),
where B(N,n) is (obviously) the binomial coefficient. One can easily
look up the expected value of n, or n^2. Does anyone know if there
are tables of expected values for more complicated expressions, such
as n! or B(N,n)?
I would appreciate an e-mail, but I will also monitor the group.
Tim
Subject: Expected values in binomial distribution
From: tvaughan@athena.mit.edu (Timothy E. Vaughan)
Date: 14 Jan 1997 14:27:56 GMT
Sorry to those who read this in sci.math. I did not know this group
existed when I posted there. I am hoping this is an easy question for
somebody in this group!
To set notation, here is the binomial distribution:
p(n) = B(N,n) p^n (1-p)^(N-n),
where B(N,n) is (obviously) the binomial coefficient. One can easily
look up the expected value of n, or n^2. Does anyone know if there
are tables of expected values for more complicated expressions, such
as n! or B(N,n)?
I would appreciate an e-mail, but I will also monitor the group.
Tim
Subject: 1997 New Researchers' Conference
From: cocteau@bell-labs.com (Mark Hansen)
Date: Tue, 14 Jan 1997 13:33:04 GMT
CONFERENCE ANNOUNCEMENT
The Third North American Conference of New Researchers
July 23-26, 1997
Laramie, Wyoming.
The purpose of this meeting is to provide a venue for recent
Ph.D. recipients in Statistics and Probability to meet and share their
research ideas. All participants will give a short expository talk or
poster on their research work. In addition, three senior speakers
will present overview talks. Anyone who has received a Ph.D. after
1992 or expects to receive one by 1998 is eligible. The meeting is to
be held immediately prior to the IMS Annual Meeting in Part City, Utah
(July 28--31, 1997), and participants are encouraged to attend both
meetings. Abstracts for papers and posters presented in Laramie will
appear in the IMS Bulletin.
The New Researchers' Meeting will be held on the campus of the
University of Wyoming in Laramie, and housing will be provided in the
dormitories. Transportation to Park City will be available via a
charter bus. Partial support to defray travel and housing costs is
available for IMS members who will also be attending the Park City
meetings, and for members of sponsoring sections of the ASA.
Additional information on the conference and registration is available
at the website: http://www.math.unm.edu/NR97.html. Or contact
Prof. Snehalata Huzurbazar, Department of Statistics, University of
Wyoming, Laramie, WY 82071-3332, USA; email: lata@uwyo.edu; fax:
307-766-3927.
This meeting is sponsored in part by the Institute of Mathematical
Statistics; the National Science Foundation, Statistics and
Probability Program; the ASA Section on Bayesian Statistical Sciences;
the ASA Section on Statistical Computing; and the ASA Section on
Quality and Productivity.
-----------------------------------------------------------------------------
Room 2C-260, Bell Laboratories
Innovations for Lucent Technologies Phone: (908) 582-3868
700 Mountain Avenue Fax: (908) 582-3340
Murray Hill, NJ 07974 Email: cocteau@research.bell-labs.com
URL: http://cm.bell-labs.com/who/cocteau/index.html
Subject: Help required on Bartlett Estimation and confidence intervals.
From: kleong@tartarus.uwa.edu.au (Weng Chong Leong)
Date: 14 Jan 1997 15:35:58 GMT
Hi,
I’m testing for the long-run neutrality of money using the following model
(Fisher and Seater (1993)):
[y(t) - y(t-k-1)] = a (k) + b(k)[m(t)-m(t-k-1)] + u(kt)
where:
y = log of GNP
m = log of money supply
k = lag length.
If the estimated b(k) = 0, it can be said that money is neutral.
If the estimated b(k) not equal to 0, then money is not neutral to GNP.
My question is, what is a Bartlett estimator?
b(k) can be estimated using OLS, why then do people use the Bartlett
Estimator?
‘The estimates of b(k) were obtained for k = 1 to 30, and 95-percent
confidence intervals corrected by the Newey-West technique were
constructed from a t-distribution using n/k degrees of freedom’.
Why is the degrees of freedom = n/k where n = sample size?
Has it got anything to do with the Bartlett estimator?
Many thanks.
Replies via email will be much appreciated.
Kenneth.
Subject: Summer Institute in Statistical Genetics
From: basten@esssjp.stat.ncsu.edu (Christopher J. Basten)
Date: Tue, 14 Jan 1997 08:27:04 -0400
1997 SUMMER INSTITUTE IN STATISTICAL GENETICS
North Carolina State University
Raleigh, NC
June 1-14, 1997
Applications are invited for participation in the 1997 Summer
Institute in Statistical Genetics. The Institute has been
expanded this year to eleven modules. It is expected that some
scholarship funds will be available for graduate students and
postdocs: women and minority groups are encouraged to apply for
these funds.
MODULE DESCRIPTIONS
Module 1
Topic: Statistics for Geneticists I
Instructors: Roger Berger, NCSU Statistics
Dennis Boos, NCSU Statistics
Dates: June 1,2,3
Fee: $240
Module 2
Topic: Genetics for Statisticians
Instructors: Ted Emigh, NCSU Genetics
Henry Schaffer, NCSU Genetics
Dates: June 1,2,3
Fee: $240
Module 3
Topic: Statistics for Geneticists II
Instructors: Marie Davidian, NCSU Statistics
Dates: June 4,5,6
Fee: $240
Module 4
Topic: Population Genetic Data
Instructors: Bruce Weir, NCSU Statistics
Ian Painter, NCSU Statistics
Katy Simonsen, NCSU Statistics
Dates: June 4,5,6
Fee: $240
Module 5
Topic: Forensic & Paternity Data
Instructors: John Buckleton, New Zealand ESR:Forensic
Bruce Weir, NCSU Statistics
Dates: June 8,9,10
Fee: $240
Module 6
Topic: Quantitative Genetic Data
Instructors: Bill Louw, Stellenbosch Genetics
Trudy Mackay, NCSU Genetics
Dates: June 8,9,10
Fee: $160
Module 7
Topic: QTL Mapping I
Instructors: Christopher Basten, NCSU Statistics
Rebecca Doerge, Purdue Statistics
Zhao-Bang Zeng, NCSU Statistics
Dates: June 11,12
Fee: $160
Module 8
Topic: QTL Mapping II
Instructors: Ina Hoeschele, VPI Dairy Science
Zhao-Bang Zeng, NCSU Statistics
Dates: June 13,14
Fee: $160
Module 9
Topic: DNA & Protein Sequence Data
Instructors: Jotun Hein, Aarhus Biology
Jeff Thorne, NCSU Statistics
Dates: June 8,9
Fee: $160
Module 10
Topic: Phylogenetic Methods
Instructors: Paul Lewis, New Mexico Biology
Spencer Muse, Missouri Biology
Jeff Thorne, NCSU Statistics
Dates: June 10,11
Fee: $160
Module 11
Topic: Molecular Evolution
Instructors: Brandon Gaut, Rutgers Biology
Spencer Muse, Columbia Biology
Marta Wayne, NCSU Genetics
Dates: June 12,13
Fee: $160
APPLICATION PROCEDURE
Full details of the Institute, plus a registration form can
be found on the World Wide Web, URL
http://www2.ncsu.edu/ncsu/CIL/stat_genetics/
Alternatively, contact hibbard@stat.ncsu.edu for registration
details, or weir@stat.ncsu.edu for any further information.
Program in Statistical Genetics Phone: (919) 515-3574
Department of Statistics FAX: (919) 515-7315
North Carolina State University email: weir@stat.ncsu.edu
Raleigh NC 27695-8203
URL http://www2.ncsu.edu/ncsu/CIL/stat_genetics/
Subject: exponential-like distribution with mean = alpha*std ???
From: Yves Moreau
Date: Mon, 13 Jan 1997 14:35:00 +0100
Hello,
It is well-known that the negative exponential distribution
(f(x)=exp(-lambda*x) x>=0, 0 else) has the property of having its mean
equal to its standard deviation. I have some data for which I though an
exponential distribution would be appropriate (from looking at the
distribution). However, this does not seem to be such a great model for
my problem; and it would be more appropriate if I had a distribution
that is similar to an exponential distribution, but for which mean =
alpha*std, with alpha between one and two. Can anyone help?
Yves Moreau
Department of Electrical Engineering
Katholieke Universiteit Leuven
Leuven, Belgium
Subject: Cancer-abortion error
From: Califorrniaa E
Date: Tue, 14 Jan 1997 10:50:33 -0800
INTERNET EMBASSY OF THE JURIDIC STATE OF NATURE
http://www.geocities.com/CapitolHill/3067/
1997 Jan 4: Cancer-abortion error
Newsgroup: sci.stat.math
Dear Sirs and Mesdames,
I bring to your attention possible mis-evaluation of the potential
impact of recall bias on a certain study linking breast cancer to
abortions. (1) A basic discussion of the problem may be found among the
papers of this embassy. (2)
Sincerely,
H.E. M. Don Eurica CALIFORRNIAA
Ambassador Extraordinary and Plenipotentiary
Internet Embassy of the Juridic State of Nature
E-mail: califorrniaa@geocities.com
References:
1. Rookus MA, Vanleeuwen FE: Induced abortion and risk for breast
cancer: reporting (recall) bias in a dutch case-control study. Journal
of the National Cancer Institute, 1996 Dec 4, V88 N23: 1759-1764.
Also reported by Recer P: "Recall bias" in cancer-abortion study.
Associated Press: UCLA Daily Bruin, 1996 Dec 5.
2. Califorrniaa E: A case of bad science: using recall bias to explain a
discrepancy in a cancer-abortion study. Juridic State of Nature,
Internet Embassy, 1997 Jan 3, F: newstatistics.html.
Internet location:
http://www.geocities.com/CapitolHill/3067/newstatistics.html
Subject: Statistical Routines for Visual Basic
From: tdierauf@lamar.colostate.edu (Tim Dierauf)
Date: 14 Jan 1997 22:36:48 GMT
Greetings Group,
I am working with a company that is attempting to trend compressor
degradation with software using linear regression and Windows-95. The
application is written in visual basic. I would like to get them to use
some more robust diagnostics such as deleted residuals and/or Cook's
Distances along with an F-test to determine model strength.
I can write these routines for them, but would rather use a commercial
debugged package. Does anybody know if there are any packages available
in DLL or Visual Basic callable forms that provide statistical
distributions such as the Normal, F, and Student-t? Better yet,
regression analysis and diagnostics?
Thanks in advance,
Tim
--
---
Timothy A. Dierauf, PE
Solar Energy Applications Laboratory
Department of Mechanical Engineering
Colorado State University
Subject: Re: exponential-like distribution with mean = alpha*std ???
From: mcohen@cpcug.org (Michael Cohen)
Date: 14 Jan 1997 22:32:13 GMT
Yves Moreau (moreau@esat.kuleuven.ac.be) wrote:
: It is well-known that the negative exponential distribution
: (f(x)=exp(-lambda*x) x>=0, 0 else) has the property of having its mean
: equal to its standard deviation. I have some data for which I though an
: exponential distribution would be appropriate (from looking at the
: distribution). However, this does not seem to be such a great model for
: my problem; and it would be more appropriate if I had a distribution
: that is similar to an exponential distribution, but for which mean =
: alpha*std, with alpha between one and two. Can anyone help?
One possibility to consider is the Gamma distribution. Let lambda be the
shape parameter and beta be the scale parameter. Then the case lambda=1
is the negative exponential distribution (the chi squared is also a
special case). The Gamma has mean lambda*beta and variance lambda*beta^2.
Therefore mean/std=square root of lambda. You want the square root of
lambda to be between 1 and 2, or lambda between 1 and 4.
--
Michael P. Cohen home phone 202-232-4651
1615 Q Street NW #T-1 office phone 202-219-1917
Washington, DC 20009-6310 office fax 202-219-2061
mcohen@cpcug.org
Subject: Re: Multivariate Goodness of fit tests
From: Gaines Harry T
Date: 14 Jan 1997 22:36:59 GMT
Rick Schumeyer wrote:
>Could someone point me to an algorithm for multivariate
>goodness of fit tests? I am familiar with univariate
>tests such as KS and chi-square, but am not sure how to extend
>these to the multivariate case.
>
I'm no expert, but it seems to me that the chi-square test is immediately
applicable. Just set up a 2-d grid, note the observed number of samples
in each cell, calculate the number called for by the proposed 2-d
distribution, then calculate chi-square and look in the table with the
suitable degrees of freedom. My understanding is that the chi-square
test does not rest on any particular assumption about the underlying
distribution, just the multinomial distribution created by setting up the
grid.
Harry
