Subject: Re: PI series needed
From: "D.J. Wilkinson"
Date: 16 Jan 1997 10:08:25 GMT
Greg Heath (heath@ll.mit.edu) wrote:
> On 13 Jan 1997, Dan Fox wrote:
> > I need the infinite series used to calculate PI. Can anyone help?
> PI = 4 * arctan(1),
> arctan(x) = SUM(k=0,oo){ [(-1)^k] * [x^(2k+1)]/(2k+1) }
> = x - (x^3)/3 + (x^5)/5 - ...
But for x=1, this converges incredibly slowly. However, using the fact
that arctan(1)=arctan(1/2)+arctan(1/3), and evaluating those two series,
gives a series which converges much faster.
--
Dr Darren Wilkinson e-mail
WWW
Subject: CFP: 1997 Fall Technical Conference
From: sasrdt@shewhart.unx.sas.com (Randall D. Tobias)
Date: Thu, 16 Jan 1997 16:06:11 GMT
41st Annual
Fall Technical Conference
1997
Call for Papers
"Mining Data for Quality Improvement"
Omni Inner Harbor Hotel
Baltimore, Maryland
October 16-17, 1997
Co-sponsored by:
American Society for Quality Control
- Chemical and Process Industries Division
- Statistics Division
American Statistical Association
- Section on Physical and Engineering Sciences
Applied and expository papers are needed for parallel sessions in
Statistics, Quality Control, and Tutorial / Case Study.
Detailed submission instructions are available on the Web
http://www.sas.com/ftc97/
or you can request them from one of the following members of the
program committee:
Susan L. Albin
Department of Industrial Engineering
Rutgers University
PO Box 909
Piscataway, NJ 08855-0909
phone: 908-445-2238
email: salbin@rci.rutgers.edu
FAX: 908-445-5467
Sharon Fronheiser (to whom paper correspondance should be addressed)
Eastman Kodak Company
151 Mill Hollow Crossing
Rochester, NY 14626
phone: 716-588-2014
email: sharonf@kodak.com
FAX: 716-722-4415
Randy Tobias (to whom electronic correspondance should be addressed)
SAS Institute Inc.
SAS Campus
Cary, NC 27513-2414
tel: 919-677-8000 x7933
email: sasrdt@unx.sas.com
FAX: 919-677-8123
The submission process will start on August 1, 1996 and conclude on
January 17, 1997. Papers should be strongly justified by application
to a problem in quality control, or the chemical, physical, or
engineering sciences. The mathematical level of papers may range from
none, to that of the Journal of Quality Technology, or that of
Technometrics.
--
Randy Tobias SAS Institute Inc. sasrdt@unx.sas.com
(919) 677-8000 x7933 SAS Campus Dr. us024621@interramp.com
(919) 677-8123 (Fax) Cary, NC 27513-2414
Faith, faith is an island in the setting sun.
But proof, yes: proof is the bottom line for everyone.
-- Paul Simon
Subject: Re: time series analysis, delay coordinate embedding, phase (state) space reconstruction
From: middleto@mcmail.cis.McMaster.CA (Gerard Middleton)
Date: 16 Jan 1997 10:02:50 -0500
The best overall reference for techniques to analyse possibly chaotic
time series is the book by Abarbanel
Henry D.I. Abarbanel, 1996, Analysis of Observed Chaotic Data.
Springer-Verlag, 272 p. ISBN 0-387-94523-7
It will not solve all your problems, though, just add to them!!
--
Gerry Middleton
Department of Geology, McMaster University
Tel: (905) 525-9140 ext 24187 FAX 522-3141
Subject: Re: Iterative proportional fitting, convergence
From: nichols@spss.com (David Nichols)
Date: 16 Jan 1997 18:51:21 GMT
In article <5bgpup$dq@samba.rahul.net>,
Theodore Sternberg wrote:
>Has anyone worked out sufficient conditions for convergence of the
>iterative proportional fitting algorithm? Maybe at least for the special
>case where one starts from a collection of bivariate and univariate
>marginal configurations?
>
>I've turned Bishop, Fienberg et al upside down, and no dice. All they say
>is that Darroch (J Roy S Soc B 1962) worked this out, but I've read
>Darroch and he doesn't offer any such theorem. (The closest he comes is
>something about characterising configurations where ipf will converge in
>one step.)
>
>Necessary conditions are a dime a dozen--familiar adding-up constraints,
>positive-semidefiniteness of the implied correlation matrix, nonnegative
>probabilities--but even all together they don't appear to be sufficient.
>
>Ted Sternberg
>San Jose, California USA
Check page 186 of Agresti's _Categorical Data Analysis_ for discussion
and references.
--
-----------------------------------------------------------------------------
David Nichols Senior Support Statistician SPSS, Inc.
Phone: (312) 329-3684 Internet: nichols@spss.com Fax: (312) 329-3668
-----------------------------------------------------------------------------
Subject: Question about Confidence intervals
From: Charles H Ouyang
Date: Thu, 16 Jan 1997 17:34:10 -0500
Hi,
I am writing a program to calculate Critical Area by sampling.
Info about data:
1. Assume normal distribution.
2. The total population is known.
3. The samples are equally weighted and have a min value of 0
and a known max value.
The idea is that total population (Pt) is large, and is too expensive
to extract all, so I only want to extract n samples.
I have an equation which uses the info 1 above and can calculate the
confidence interval to get a range in which actual mean is located
using sample mean and sample variance.
Equation:
(X - z * s / sqrt(n), X - z * s / sqrt(n))
where: X - calcualted sample mean
z - a table value assigned based on the desired confidence
level.
s - calculated sample variance
Question:
Is there any way I can use info 2 and 3 to further narrow my
inteerval?
Thanks,
Charles O.
Subject: Re: Question about repeated measures study
From: mcohen@cpcug.org (Michael Cohen)
Date: 16 Jan 1997 23:38:31 GMT
Dick Adams (rdadams@access2.digex.net) wrote:
:
: > Since the two groups differ on age, sex, and rural/urban residence,
: > we would like to adjust for these factors in the analysis.
:
: Rather than "adjusting" (whatever that means), I would test to
: see if there is an effect at each measurement for age, gender,
: or residence. (BTW: Gender = Female/Male; Sex = Yes/No)
:
Originally, it was Sex=Female/Male; Gender=Feminine/Masculine. In the
U.S. Federal Government, Sex is still the accepted term (Office of
Management and Budget rules) for the Female/Male question. In journals
that use APA style, gender is now the required term.
At any rate, I would be inclined to include these variables in the
analysis as independent variables.
--
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: PI series needed
From: jpc@a.cs.okstate.edu (John Chandler)
Date: 17 Jan 1997 04:27:24 GMT
In article <5bkump$nij@whitbeck.ncl.ac.uk>,
D.J. Wilkinson wrote:
>Greg Heath (heath@ll.mit.edu) wrote:
>> On 13 Jan 1997, Dan Fox wrote:
>
>> > I need the infinite series used to calculate PI. Can anyone help?
>
>> PI = 4 * arctan(1),
>> arctan(x) = SUM(k=0,oo){ [(-1)^k] * [x^(2k+1)]/(2k+1) }
>> = x - (x^3)/3 + (x^5)/5 - ...
>
>But for x=1, this converges incredibly slowly. However, using the fact
>that arctan(1)=arctan(1/2)+arctan(1/3), and evaluating those two series,
>gives a series which converges much faster.
It's true that (1 - 1/3 + 1/5 - 1/7 + ...) converges slowly,
but you can speed up the convergence greatly using either Euler's
averaging transformation with Mark Townsend's two-thirds rule,
repeated Aitken delta-squared extrapolation,
or Wynn's epsilon algorithm, to mention only three
of the simplest acceleration algorithms.
Using only twenty terms in the series, the accelerated
approximations to the limit are accurate to more than
ten decimal digits, as I recall.
There are better ways to compute pi than this, it's true,
but pessimistic pronouncements such as Knopp's statement that
the series above converges too slowly to be of any practical
use are quite incorrect. Apparently Knopp never met Aitken.
Acceleration methods also yield useful results when applied
to many, and perhaps most, divergent series.
(x - x^2/2 + x^3/3 - x^4/4 + ...) only converges to ln(1+x)
for abs(x)<1, but the diagonals of the epsilon algorithm
tableau converge for all x>-1 and provide very accurate values
of ln(1+x) for x=2 or x=10 or x=100 or...
--
John Chandler
jpc@a.cs.okstate.edu
Subject: Re: The Fuzzy Debate
From: "D.J. Wilkinson"
Date: 17 Jan 1997 09:19:22 GMT
Dogmat (dogmat@aol.com) wrote:
> I build chemical plants, and we talk about WAGs and SWAGs. A WAG is
> a wild-ass-guess. A SWAG is a scientific-wild-ass-guess. (Reassuring isn't
> it?) That is my reality folks.
And the formalism you require is subjective probability. YOUR probabilty
for an event is the proportion of a dollar YOU think is a fair price for
the bet which pays a dollar if the event occurs, and nothing otherwise.
> Very often,. I have little to no
> information, I'm extrapolating an empirical model beyond its known region,
> I get one shot at it, I cannot trust the information I do have, and I
> still have to guarantee that the chemical plant will operate
> satisfactorily and safely.
So you are making one-off decisions based on uncertain information.
Utility theory can help here.....
> The probability statistics I know doesn't have
> a chance in hell of modelling my situation -- my real-world violates every
> classical assumption in the book. So what do I do? Learn how to SWAG very
> well,and add a little safety margin (actually a lot; although the exact
> number is unknown, generally each new plant is about 20%-25%
> overdesigned.)
I'm glad you add a margin of safety, you stickler, you! :-)
> I have never heard a
> satisfactory explanation of what 30% possibility really means, but I know
> I can provide that value.
I have never heard a satisfactory answer either, but the definition of
subjective _probability_ I give above does give real meaning to
statements of uncertainty.
> Here is a question (not original) for the probability zealots. Say I
> "know" that a value (x) is between 10 and 20. But that is ALL I know. Show
> me a probability distribution that models that (and no more) and I will
> never look at possibilities again.
There is no probabilistic representation of only that information.
However, constraint propagation is easy - it is discussed in many books
on computer programming. The trouble is, you are wanting to make
probabilistic inferences based on constraint statements - you can't. Make
probabilistic statements if you want probabilistic inferences. In fact,
in most practical situations, you wouldn't know _for_sure_ that the
variable is constrained between 10 and 20. You would simply know that it
rarely ever strays outside that range. You could therefore make a
statement like E(X)=15, Var(X)=(10/6)^2. It is possible to make
inferences based on limited specifications such as those (Bayes linear
methods, http://fourier.dur.ac.uk:8000/stats/bayeslin/).
See - "fuzzy logic" is not only the most aptly named subject I know, but
it isn't needed or helpful, anyway.... :-)
--
Dr Darren Wilkinson e-mail
WWW
Subject: Re: Air Pollution
From: wpilib+@pitt.edu (Richard F Ulrich)
Date: 17 Jan 1997 17:01:28 GMT
joew (joew@bda-inc.com) wrote:
: Air pollution standards are uasually given in ppm or ug/m^3 along with a
: time value (such as annual arithmetic mean or maximum 24 hr concentration
: etc.) I am looking for these, generally speaking, in tons of pollutant
: per year.
The "ambient concentration", which is what is measured and regulated in
ppm, depends on how much is emitted, divided by how broadly it is
dispersed, and how rapidly it is filtered out or settles out or converts
to some other form (for example, SO2 gas becoming sulfates in small
particles).
So, regulations for the human environment - either the city street, or
the factory workfloor - are in different terms from the regulations
at the smokestack, or what pours from the mouth of a sewage pipe, where
it is proper and necessary to look at the total tonnage that is
released.
: This was the question as it was posed to me. Make any
: assumptions.
: Specifically for:
: SO2 - 60 ug/m^3 annual arithmetic mean
: PM10 50 ug/m^3 annual arithmetic mean
: NOx - 100 ug/m^3 annual arithmetic mean (comprised mainly of NO & NO2)
I think that the kind of assumptions that you have to make are like
this: total emissions are measured (say) for the Ohio River valley,
and areas up to the Rocky Mountains; average ambient level is
what is measured in the central part of the state of New York. Then
the historical relationship gives you a translation-factor, where
you could argue about the relevant geography of the sources and the area
where you are measuring ambient levels.
But there is no automatic way to convert emissions to ambient levels,
or vice-versa.
Rich Ulrich, biostatistician wpilib+@pitt.edu
http://www.pitt.edu/~wpilib/index.html Univ. of Pittsburgh
Subject: Re: What is "mode" in stats?
From: "M.GASPARINI"
Date: Thu, 16 Jan 1997 07:52:43 GMT
Justin wrote:
> for example, a survey was taken to see how many eggs were made from
> chickens in a 1 year period. The chickens were numbered 1,2,3, and 4 for
> easy identification.
>
> the results were as follows:...
>
> Chicken No. of eggs
> 1 50
> 2 73
> 3 90
> 4 100
>
> The mode here is 100.
Nope, the mode here is 4.
Mauro.
Subject: Hitting time probability of Brownian motion through deterministic nonlinear barrier
From: "Pedro Santa-Clara"
Date: 17 Jan 1997 19:36:52 GMT
Hi everybody,
I want to know the probability that a Brownian motion, $W$, will hit the
barrier
\[ B(t) = ae^{b(T-t)} + ct + d \]
in the interval $[0,T]$. $W$ starts at zero in time $0$ and $a$, $b$,
$c$ and $d$ are constants such that, at $0$, the barrier is negative,
$B(0)<0$.
My hope would be that this probability could be written as a one
dimensional integral with respect to time.
Pedro Santa-Clara
The Anderson School at UCLA
psantacl@anderson.ucla.edu
