From: "John A. Major" <jmajor@cwixmail.com>
Subject: Re: Correlated random numbers?
Date: Mon, 03 May 1999 18:36:26 GMT
Newsgroups: alt.sci.math.probability,sci.math.num-analysis
Keywords: Generating random variables with a given correlation

Shillelagh wrote:
> 
> Is there an algorithm which provides two random numbers, 'a' and 'b',
> whose correlation is 'r'?
> 
> I have searched for this on netlib, acm, and cern, the result being
> broken links or no matches.
> 
> Thanks in advance!
> --
> Shillelagh

There are a number of ways to do this.  The easiest assumes that you are
talking about random normal deviates with mean zero and variance 1. 
Take b=r*a+((1-r^2)^0.5)*c where c is also a unit normal, independent of
a.  Then b is unit normal and corr(a,b)=r.

If you have other distributions in mind, it gets trickier....

_____________________________________________________________

John A. Major, ASA             7 Old County Highway
Senior Vice President          East Granby, CT, USA 06026
GC Instrat                     (860) 658-4129
Guy Carpenter & Company, Inc.  John.Major@guycarp.com
           http://www.guycarp.com/major.html
_____________________________________________________________