HDTenEightyP/NetNews huggingface dataset:
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Bell's _Men of Mathematics_ (was: Great and Inspirational ?)
    <1992Aug13.193848.5184@ariel.ec.usf.edu> <5105@tuegate.tue.nl>
Date: Wed, 19 Aug 1992 14:17:59 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

In article <5105@tuegate.tue.nl> wsadjw@urc.tue.nl writes:
>In article <1992Aug13.193848.5184@ariel.ec.usf.edu> mccolm@darwin.math.usf.edu. (Gregory McColm) writes:

[discussion of math history books and their shortcomings]

The book I found most exciting as a high-schooler was my
CRC handbook of math.  Was I not properly politicized?

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu
Newsgroups: sci.math
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: Primes
Date: Mon, 17 Aug 1992 14:21:44 GMT
Reply-To: victor@watson.ibm.com
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM, T.J. Watson Research Center

>>>>> On Mon, 17 Aug 1992 11:02:34 GMT, bs@faron.mitre.org (Robert D. Silverman) said:
Bob> Nntp-Posting-Host: faron.mitre.org

Bob> In article <1992Aug17.160252.10145@waikato.ac.nz> bill@waikato.ac.nz writes:
Bob> :How many primes are there less than 2 to the power of p?
Bob> :
Bob> 2^p/(p log 2)   [approximately]

Bob> :Is there a way of calculating this, or does anyone know of where I can get my
Bob>  
Bob> How big is p? If p isn't too large it can be calculated exactly using
Bob> methods developed by Lagarias, Odlyzko, and Coppersmith. These are

Make that Lagarias, Odlyzko and Miller (not Coppersmith!).

Bob> improvements on the Meisel-Lehmer method.

Bob> :hands on a list of primes so I can find out how many primes there are
Bob> :less than 2^16 or 2^32 for example?
Bob>  
Bob> For p THIS small you can do it directly by sieving. 2^16 will take
Bob> milliseconds. How long 2^32 will take is memory dependent, but should
Bob> only be a few hours at most.

Bob> :Is there some way of determining (or estimating) the expected magnitude of the
Bob> :nth prime? Or of the growth of the difference between the nth and (n+1)th
Bob>  
Bob> the n'th prime is approximately n log n.

Bob> the growth of the difference is not well understood. studying it involves
Bob> some deep methods in analytic number theory. For example, if one has
Bob> a 'random' sequence of integers going to infinity, whose normal order
Bob> difference is log n, then one has lim sup (n-->infinity) p_n/log n = 2,
Bob> whereas for primes, the lim sup is infinite. Further, Rankin has shown
Bob> that the difference is

Bob> C log n  loglog n  loglogloglog n
Bob> ---------------------------------

Bob> 	logloglog n ^2

Bob> infinitely often.

Bob> I suggest you start by reading a book on number theory. Start with
Bob> Hardy & Wright.
Bob> --
Bob> Bob Silverman
Bob> These are my opinions and not MITRE's.
Bob> Mitre Corporation, Bedford, MA 01730
Bob> "You can lead a horse's ass to knowledge, but you can't make him think"
--
			Victor S. Miller
			Vnet and Bitnet:  VICTOR at WATSON
			Internet: victor@watson.ibm.com
			IBM, TJ Watson Research Center
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Is Card(R)=Card(R^2)?
Date: 14 Aug 1992 07:58:28 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

>>>I believe that there is even an everywhere-continuous 
>>>bijective mapping from the unit line to the unit square.
>>
>>No, there is not.  The interval and the square are not homeomorphic.
>>Such a continuous bijective map would be a homeomorphism,
>>since the two spaces are compact Hausdorff spaces.
>>
>
>How about the unit line minus the end points, and the interior of
>the unit square?

A continuous bijection from the open interval onto the open square
is also not possible.  The reason for it is a bit harder, this time.
But still not beyond a first course in point-set topology.


-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
From: torkel@sics.se (Torkel Franzen)
Newsgroups: sci.math
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Date: 16 Aug 92 17:26:42 GMT
	<1992Jul29.173257.5041@ariel.ec.usf.edu> <1992Aug4.174928.1071@sics.se>
	<1992Aug11.190119.23518@ariel.ec.usf.edu>
Organization: Swedish Institute of Computer Science, Kista

In article <1992Aug11.190119.23518@ariel.ec.usf.edu> mccolm@darwin.math.usf.
edu. (Gregory McColm) writes:

   >From there, we get more problems.  Suppose that you 
   >believe that the model of the integers exist.  Is PA 
   >true on this model?

  What is PA? My explanation of the integers is simple: the integers
are 0, s(0), s(s(0)) and so on. Any obscurity or ambiguity that you
find in this explanation carries over to any explanation of what is
meant by "PA".
From: jerry@nutmeg.hnrc.tufts.edu (Jerry Dallal)
Newsgroups: sci.math.stat
Subject: Stochastic curtailment -- software wanted
Date: 13 Aug 92 13:59:46 GMT
Organization: USDA HNRC at Tufts University

Does anyone have/know of PC software for dealing with calculations related to
stochastic curtailment?

Thanks.
Newsgroups: su.macintosh,sci.math.stat
From: vijay@jessica.Stanford.EDU (vijay mehrotra)
Subject: Simulation Software for the Mac
Reply-To: vijay@jessica.Stanford.EDU (vijay mehrotra)
Organization: Stanford University
Distribution: na
Date: Wed, 12 Aug 92 20:31:51 GMT

I am interested in finding an icon-based discrete event simulation
package for the Macintosh, or one which runs under Windows (PC) or
X-Windows (UNIX) instead.  I would appreciate any suggestions at all
about a package which fits this general description.

Please send mail to this account (vijay@jessica.stanford.edu)
or give me a call at (415) 723-1900.  I will be happy to post
a summary of whatever information I receive.

Thanks in advance,

Vijay
===============================================================================
|| Vijay Mehrotra         L&IR Math/Stat Consultant      Stanford University ||
|| Ph.D. Student in Operations Research    email: vijay@jessica.stanford.edu || 
||---------------------------------------------------------------------------||
|| 	"Well, it wasn't no way to carry on/ It wasn't no way to live/       ||
||	 But he could put up with it for a little while/                     ||
||	 He was working on something big."                                   ||
||			TOM PETTY AND THE HEARTBREAKERS                      ||
===============================================================================
From: strgh@warwick.ac.uk (J E H Shaw)
Newsgroups: sci.math.stat
Subject: Re: 1) Bootstrap  2) Standard deviation
Date: 17 Aug 92 17:27:31 GMT
Organization: Computing Services, Warwick University, UK

1) Most statistical methods attempt to generalise from a set of data
   by making assumptions about the underlying population (e.g. `Normal
   with unknown mean & variance'), estimating the unknown parameters
   (here mean & variance) and using the properties of the fitted
   distribution (here Normal) to, for example, predict future data.

   `Bootstrapping' goes straight for the jugular (bypassing the brain
   almost entirely :-) and uses the observed data distribution as an
   estimate of the population distribution (i.e. probability mass 1/N
   at each of the N data points).  Properties of the assumed underlying
   population are inferred from the corresponding data properties.
   (And if it's too hard to do analytically, simulate by generating
   further `bootstrap samples' from the data distribution).

   Bootstrapping is the ultimate in maximum likelihood estimation
   (attempts to produce a Bayesian analogue are, IMHO, weird).

2) Biasedness of the SD is hardly mentioned because it's too hard.
   (And in almost any practical analysis, biasedness is the least
   of my worries anyway).

                -- Ewart Shaw
-- 
J.E.H.Shaw,  Department of Statistics,  |  JANET:  strgh@uk.ac.warwick.cu
             University of Warwick,     |  BITNET: strgh%uk.ac.warwick.cu@UKACRL
             Coventry  CV4 7AL,  U.K.   |  PHONE:  +44 203 523069
yacc - the piece of code that understandeth all parsing
Newsgroups: sci.math.stat
From: katholi@cisa.cis.uab.edu (C.R. Katholi)
Subject: mixtures of normal density functions
Originator: katholi@cisa
Organization: University of Alabama at Birmingham
Date: Tue, 18 Aug 1992 15:38:53 GMT

    I am posting this for a friend. He wants to know if there is any
readily available software for fitting a mixture of two normal
density functions to data by Maximum Likelihood. Any help would
be appreciated...he does not want to have to write his own :-).

Send responses to katholi@cis.uab.edu. 

Hope this isn't a FAQ...if it is I am sorry.
From: rons@hardy.u.washington.edu (Ronald Schoenberg)
Newsgroups: sci.math.stat
Subject: Re: Gauss-to-Matlab translator?
Date: 21 Aug 92 22:26:08 GMT
Organization: University of Washington, Seattle

In article <morrison.714425903@cunews> morrison@isaac.carleton.ca (Greg Morrison) writes:
>We have a user here who would like some Gauss programs translated into
>Matlab programs (Pro-Matlab for Sun workstations, to be specific).
>Would it be feasible to write a translator program, perhaps in awk or
>perl, to do this?  I'm not a user of either package myself, but I'd
>imagine that the two languages are reasonably similar.  Are there
>non-obvious (or even obvious!) pitfalls involved?  Does anybody
>already have such a translator??
>
>Thanks,
>
>Greg Morrison                           |  morrison@ccs.carleton.ca
>Computing and Communications Services   |  phone: (613) 788-2600 ext. 2507
>Carleton University                     |  fax:   (613) 788-4448
>Ottawa, Ontario, Canada K1S 5B6         |  
>

Aptech Systems will have a version of GAUSS running a Sun workstation
sometime in the next few months, if you're able to wait.  For latest
info call them at (206) 432-7855.
From: nichols@spss.com (David Nichols)
Newsgroups: sci.math.stat
Subject: 1) Bootstrap  2) Standard deviation
Date: 14 Aug 92 19:32:27 GMT
Article-I.D.: spss.1992Aug14.193227.9029
Organization: SPSS Inc.

Bootstrapping refers to a methodology in which error estimates are
produced by resampling with replacement from a finite set of data,
in order to produce unbiased or less biased estimates of standard
errors. This may be a simplistic defintion that can be improved
upon by the more mathematically oriented, but it's the jist of it.

The reason that n-1 is used in the denominator when calculating
standard deviations of samples is that the squared standard deviation,
the variance, is estimated in an unbiased manner by using n-1 instead
of n. You've estimated a parameter (the mean) in calcuating the sum
of squared deviations about the mean, so you have one less degree of
freedom than when you started. Incidentally, either divisor produces
a biased estimate of the population standard deviation.
--
 David Nichols           Statistical Support Specialist            SPSS, Inc.
 Phone: (312) 329-3684     Internet: nichols@spss.com     Fax: (312) 329-3657
*******************************************************************************
 Any correlation between my views and those of SPSS is strictly due to chance.
Newsgroups: sci.math.stat
From: jerry@nutmeg.hnrc.tufts.edu (Jerry Dallal)
Newsgroups: sci.math.stat
Subject: Re: Powell's Min. w/ Brent's mod. wanted
Date: 13 Aug 92 14:02:25 GMT
Organization: USDA HNRC at Tufts University

In article <11545.2a890722@cpva.saic.com>, inlowm@cpva.saic.com writes:
> See "Numerical Recipes" by Press (? -- three other authors).
> There is a fortran version and a c version.  


New editions of C and FORTRAN will be published in October.  Don't go out now
and buy the first edition!
Newsgroups: sci.math.stat
From: morrison@isaac.carleton.ca (Greg Morrison)
Subject: Gauss-to-Matlab translator?
Organization: Carleton University
Date: Fri, 21 Aug 1992 19:38:23 GMT

We have a user here who would like some Gauss programs translated into
Matlab programs (Pro-Matlab for Sun workstations, to be specific).
Would it be feasible to write a translator program, perhaps in awk or
perl, to do this?  I'm not a user of either package myself, but I'd
imagine that the two languages are reasonably similar.  Are there
non-obvious (or even obvious!) pitfalls involved?  Does anybody
already have such a translator??

Thanks,

Greg Morrison                           |  morrison@ccs.carleton.ca
Computing and Communications Services   |  phone: (613) 788-2600 ext. 2507
Carleton University                     |  fax:   (613) 788-4448
Ottawa, Ontario, Canada K1S 5B6         |  

Newsgroups: sci.math.stat
From: regeorge@magnus.acs.ohio-state.edu (Robert E George)
Subject: Re: Fwd: Standard Deviation.
Organization: The Ohio State University
Date: Mon, 17 Aug 1992 12:53:06 GMT

In article <1992Aug16.212245.27577@mailhost.ocs.mq.edu.au> wskelly@laurel.ocs.m
q.edu.au (William Skelly) writes:
[deletions]
>
>This and other posting indicate that there is a relationship between
>sample size and and estimated variance (of the population) which is
>positive and always an underestimate.  What is the limit, or point
>at which an increasing sample size no longer improve the estimate
>of populations variance?
                      ___  _         _
(1) the statistic T=  \   | X - Xbar  | 2                              __  2
                      /__ |_         _|         has expectation (n-1) O
       __ 2
where O    denotes the population variance  *for any value of n*. Therefore,
    T                                   __ 2
------------    is always unbiased for O     and    T
   n - 1                                         -------
                                                    n

                         __ 2
will always have bias - O             regardless of the value of n.
                      _____
                        n

Expectation is a linear operator. Note that the bias --> 0 as n gets large,
but T/n is biased for all finite n.

(2) The variance of the unbiased estimator T/(n-1) is O(1/n), so taking
a large sample will be beneficial in the sense of leading to an estimator
with smaller variance.

>Can this be tested by taking samples of sample (the later sample
>being elevated to the status of population)?

(3) I'm not clear what your mean here, this sounds something like
bootstrapping / jackknifing (well-known words for well-known techniques
which are not well-understood. . . )

Robert George
(speaking only for myself)
Newsgroups: sci.math.stat
From: wskelly@laurel.ocs.mq.edu.au (William Skelly)
Subject: Re: Fwd: Standard Deviation.
Organization: Macquarie University, Australia.
Date: Sun, 16 Aug 1992 21:22:45 GMT

In article <1992Aug14.231916.23479@magnus.acs.ohio-state.edu> regeorge@magnus.acs.ohio-state.edu (Robert E George) writes:
>
>More intuitively, if we take a very sample, we are less likely to get
>extreme values and so our notion of what the population variance is (note
>that I am not proposing some particular estimator) will be unrealistic.
>For instance, I give an exam to two students. Their scores are 67 and
>71. I think, "Gee, there's not a lot of variability in these scores."
>But then 8 more students take the exam:
>     60 78  100 38  50 88  99 39
>

I have a further question with regard to the negative biasness of
the sample variance estimate.

This and other posting indicate that there is a relationship between
sample size and and estimated variance (of the population) which is
positive and always an underestimate.  What is the limit, or point
at which an increasing sample size no longer improve the estimate
of populations variance?

Can this be tested by taking samples of sample (the later sample
being elevated to the status of population)?

cheers,
chris
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math.stat
Subject: Re: sample size and invdference (was: Maximulikelihood  estimates in LISREL)
Date: 19 Aug 92 13:58:43 GMT
Organization: Purdue University Statistics Department

In article <1992Aug18.152355.16237@news.cs.brandeis.edu> mokaba@binah.cc.brandeis.edu writes:
>could somebody explain in English what the true effect of sample size
>is on maximulikelihood estimates.  I have been playing around with 
>LISREL and have a little problem conceptualizing the effect of sample
>size on the estimates I get using maximumlikelihood estimators.  Are the
>effects comming in becuase of the effect of sample size on the standard
>error of estimates or is there something I am too dense to see. 
>I have also learn that the problem with large sample in LISREL is that they
>lead to even small effect being significant... or something like that..
>Furthermore, is a sample of 103 good enough for a full model estimation.
>i.e running the Mesurement equations at the same time as the Structural 
>model.  
In English, a larger sample is very likely to have a more concentrated
likelihood function.  Among other things, this reduces the "standard error"
of estimates.

As for statistical significance, neither I nor anyone else has been able
to come up with any good reason to use it; it is a leftover from the time
when it was misinterpreted.  

As for a sample of 103 being good enough for ..., in some cases samples
of 10 are quite adequate for purposes, and in some cases samples larger
than the entire world population are inadequate.

This is not an attempt at obfuscation, but the proper use of statistics
is not that simple; see a good mathematical statistician.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math.stat
Subject: Re: Generating a set of random bits
Date: 19 Aug 92 14:44:11 GMT
Organization: Purdue University Statistics Department

In article <36984@sdcc12.ucsd.edu> whart@cs.ucsd.edu (Bill Hart) writes:
>I have an application for which I need to generate a random 'vector' of 
>bits of length N.  I have looked at stuff in Numerical Recipies for
>generating a random sequence of bits, but it remains unclear whether
>such a generator would be appropriate for generating a random
>vector of bits.

>I need/want to have the distribution of vectors remain 'random'.  Right
>now I'm generating a random float in [0,1> and testing to see
>if it is less than 0.5 or not.  This works, but I'm sure there is
>a better way of doing this.

>Any ideas or pointers?


I would suggest using a long-gap shift-register procedure, using
XOR or + (if full word integer addition is possible).  By long-gap,
I mean something like using the n-406 and the n-607 words to get
the n-th word.  If the appropriate length seed (here 607 words) is
something like physically generated (or even the noise from usenet
news), the individual bits should be fairly good, at least after a
few runs to hand initial bias.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
Newsgroups: sci.math.stat
From: news@massey.ac.nz (USENET News System)
Subject: Re: Fwd: Standard Deviation.
Organization: Massey University
Date: Sun, 16 Aug 92 22:59:26 GMT

In article <1992Aug16.212245.27577@mailhost.ocs.mq.edu.au>, wskelly@laurel.ocs.mq.edu.au (William Skelly) writes:
> 
> This and other posting indicate that there is a relationship between
> sample size and and estimated variance (of the population) which is
> positive and always an underestimate.  What is the limit, or point
> at which an increasing sample size no longer improve the estimate
> of populations variance?
> 
When the sample size is equal to the population size (never for an
infinite population).

> Can this be tested by taking samples of sample 

Yes but we can work out the theory so it isn't necessary.

> (the later sample
> being elevated to the status of population)?
> 
???
From: martin@biostat.washington.edu (Don Martin)
Newsgroups: sci.math.stat
Subject: Re: Standard Deviation.
Summary: Fun with n+1,n,n-1,n-2
Keywords: (n) versus (n-1)
Date: 17 Aug 92 21:27:02 GMT
Article-I.D.: u.1992Aug17.212702.21327
Organization: Biostatistics, School of Public Health, Univ. of Wash.

This is off the top of my head but I think that it is
reasonably accurate.

Personal opinion: There are a lot of bad stat books out there.

Main topic: Why divide by n-1 instead of n etc. Here are
a few proposals:

n+1  This has a smaller mean square error for s.
n    ML estimator
n-1  unbiased variance but not standard deviation
n-2  2 works better for 95% confidence intervals.


In fact, the varince/standard deviation estimates tend to
be pretty poor, depending on the distribution, for the
range where the divisor makes a difference.

Does anyone have an argument for n+2 or n-3 ?

Don Martin
From: inlowm@cpva.saic.com
Newsgroups: sci.math.stat
Subject: <None>
Date: 12 Aug 92 20:37:05 GMT
Organization: Science Applications Int'l Corp./San Diego

See the book "Numerical Recipes" by (? -- don't have it handy but there
are four authors one of which is Press -- hopefully this is enough to
help pin down the book).  You should be able to find it in any good
technical bookstore.  Be careful as there are versions containing
C programs and fortran programs -- make sure you get/order the correct
one.

Mark Inlow
SAIC
(619) 546-6978
inlowm@jupiter.saic.com
From: jerry@ginger.hnrc.tufts.edu (Jerry Dallal)
Newsgroups: sci.math.stat
Subject: Inference
Date: 19 Aug 92 17:47:12 GMT
Organization: USDA HNRC at Tufts University

In article <1992Aug18.214711.6657@mailhost.ocs.mq.edu.au>, wskelly@laurel.ocs.mq.edu.au (William Skelly) writes:
> I am not sure I follow you.  From my applications I only want to test
> some null-hypothesis (perhaps a narrow application...but very useful!).
> Generally I want to know if two samples are from the same population.
> Isn't this just asking whether or not the two sample means are close?
> 

Heck, *NO*!!!

Suppose you have two safety devices.  Both are inexpensve to manufacture,
install, and replace, compared to the consequences of their failure.  
One has failure times that follow a
normal distribution with a mean of 10 years and a standard deviation of 1 day.
The other has failure times that follow a
normal distribution with a mean of 10 years and a standard deviation of 
3 years.  I hope you wouldn't be indifferent in choosing a 
device to use when your test of significance fails to reject the null
hypothesis of equal population means.
Newsgroups: sci.math.stat