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From: cedman@lynx.ps.uci.edu (Carl Edman)
Newsgroups: comp.graphics,sci.math
Subject: Re: question regarding random numbers
Message-ID: <CEDMAN.90Oct29210857@lynx.ps.uci.edu>
Date: 30 Oct 90 05:08:53 GMT
References: <29358@pasteur.Berkeley.EDU>
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In-reply-to: ph@miro.Berkeley.EDU's message of 30 Oct 90 04:42:35 GMT

In article <29358@pasteur.Berkeley.EDU> ph@miro.Berkeley.EDU (Paul Heckbert) writes:
   I'm looking for good references on techniques for generating random numbers
   with arbitrary density functions.  For example, to generate a gaussian
   random number from uniform random numbers:

	   r = sqrt(-2*log(U));
	   t = 2*pi*U;
	   x = r*sin(t);
	   y = r*cos(t);
	   where U is a random number between 0 and 1, different every time

   x and y will then be gaussian-distributed between -inf and inf.

   Similarly, you can generate a point uniformly distributed inside a circle with:

	   r = radius*sqrt(U);
	   theta = 2*pi*U;

   I assume the method is well known in probability and statistics.
   What are good references for such techniques of distribution shaping?

There is one general method of getting random variables given an arbitrary
distribution. It is known under the handy name of Metropolis-Rosenbluth-
-Rosenbluth-Teller-Teller-algorithm.

As such random numbers are very important for the numerical integration
of high-dimensional integrals (High meaning something of the order of 10^23 
dimensions) using Monte-Carlo methods, this algorithm should be described
in any text-book on numerical methods. I am having "Computational Physics"
by Steven E.Koonin here at hand. The algorithm is quite simple, really,
so if there is demand I can describe it to the net.

	Carl Edman


Theorectial Physicist,N.:A physicist whose   | Send mail
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