From: "s.wiesen" <s.wiesen@fz-juelich.de>
Subject: Re: random number generator
Date: Thu, 15 Feb 2001 10:46:47 +0100
Newsgroups: sci.math.num-analysis
Summary: Box-Mueller method to generate normally-distributed random variables 

Puneet Singla wrote:

> Hai,
>
> I need a random number generator with normal distribution(subj to a certain
> mean and variance)......i need a routine in c which would generate this
> number.....the random function in c does not take any input on the nature of
> the distribution or the moments of the probability distribution
> function..........i need something like the "randn" in "matlab".......could
> somebody enlighten me on how to do this in "c"?.......
>
> thanks
> Puneet Singla.

If you got a uniform random generator (like ran2 (numerical recipes)) it is
easy to use the (algebraic) box-mueller method:

float v1,v2,s,ar,r1,r2;
extern float ran2()

do {
    v1=2.0*ran2()-1.0;
    v2=2.0*ran2()-1.0;
    s=v1*v1+v2*v2;
} while(s>1.0);
ar=log(s)
r1=v1*sqrt(-(ar+ar)/s)*sig-mu;
r2=v2*sqrt(-(ar+ar)/s)*sig-mu;

The advantage of the routine is that it generates
two random variables at one time (due to trigonometric
reasons)

further recommendations: Sheldon.M.Ross, "Simulation", 2nd. ed.
or any numerical book

bye

--
Sven Wiesen
Instute for Plasmaphysics, Forschugszentrum Juelich, D-52425 Juelich
phone: +49-2461-615075
==============================================================================

From: George Marsaglia <geo@stat.fsu.edu>
Subject: Re: random number generator
Date: Thu, 15 Feb 2001 07:11:31 -0500
Newsgroups: sci.math.num-analysis

s.wiesen wrote:

[partial quote of previous article trimmed --djr]

> r1=v1*sqrt(-(ar+ar)/s)*sig-mu;
> r2=v2*sqrt(-(ar+ar)/s)*sig-mu;

That a pair of normal variates can be represented by means of
polar coordinates, x=rho*cos(theta), y=rho*sin(theta) is a result
attributed to Box and Meuller, although Gauss attributes it to Laplace.
It is the basis of how most of us learned to evaluate int(exp(-.5x^2))

That a uniform point (v1,v2) in the unit circle has the property that
s=v1^2+v2^2 is uniform in [0,1) and independent of the point (v1,v2)/sqrt(s)
is a result that I used as the basis for a fast and simple way to get a pair
of normal points in the plane,  (v1,v1)*sqrt(-2*log(s)/s).   Although I
used this as early as 1956, I thought it too trivial to push for publication.

George Marsaglia