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From: BARTHO@CGEUGE54.BITNET (PAUL BARTHOLDI)
Newsgroups: comp.lang.forth
Subject: mathematical routines (realy random numbers)
Message-ID: <9003161408.AA25741@jade.berkeley.edu>
Date: 16 Mar 90 09:34:00 GMT
Sender: daemon@ucbvax.BERKELEY.EDU
Reply-To: PAUL BARTHOLDI <BARTHO%CGEUGE54.bitnet@jade.berkeley.edu>
Organization: The Internet
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>Category 3,  Topic 10
>Message 37        Wed Mar 14, 1990
>HARV                         at 03:27 MST
>
>  Subject:  Random Number Generators
> I am currently working on Monter Carlo simulation program. The literatue
> sources I have available stat that a linear and Gaussian random number
> generators are required.  I have a shuffling random number generator alreay
>and think that it is a linear one.  Any clarification of this matter would
> be greatly appreciated.  I am especially interested if there is some way I
> can modify my existing random number generator to produce Gaussian random
>numbers.

Two solutions :

I assume that all your numbers are between 0 and 1.  Then

1.  sum 12 uniform random numbers, and substract 6.  You get a ~gaussian
    number, with mean=0.0  and variance=1.0 .  If you need gaussian with
    mean m  and variance v,  then multiply previous gaussian by v  and
    add m .  For realy most applications, this is a good gaussian generator.
    Only limitation :  you will never get number above ou below 6 sigma !

2.  take 2 uniform random numbers x1 and x2, then calculate :
          n1 = sqrt( -2*log(x1) ) * cos( 2 * pi * x2)
          n2 = sqrt( -2*log(x1) ) * sin( 2 * pi * x2)
    then n1 and n2 are two independant gaussian random numbers,
    with  mean=0  variance=1.  See above for other means or variances.

Ref: any book on Monte Carlo Methods,
for example :  J. M. Hammersley and D. C. Handscomb
               Monte Carlo Methods
               Methuen's Monographs on Applied Probability and statistics
               John Wiley and Sons Inc, London - New York 1964