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From: norman@lasspvax.UUCP (Norman Ramsey)
Newsgroups: net.math
Subject: Re: deviates from various distr
Message-ID: <433@lasspvax.UUCP>
Date: Mon, 5-Aug-85 15:15:53 EDT
Article-I.D.: lasspvax.433
Posted: Mon Aug  5 15:15:53 1985
Date-Received: Mon, 12-Aug-85 01:47:29 EDT
References: <2238@utcsstat.UUCP>
Reply-To: norman@lasspvax.UUCP (Norman Ramsey)
Organization: LASSP, Cornell University
Lines: 23
Keywords: random numbers

In article <2238@utcsstat.UUCP> anthony@utcsstat.UUCP (Anthony Ayiomamitis) writes:
>
>	I am looking for references to papers describing how one may generate
>random deviates from various distributions (for example, normal, Poisson)
>using a uniform random number generator. As many of you may know, micro-
>computers have built-in random number generators. However, these only
>produce deviates which are uniform and in the range [0,1]. Thus, one must
>use some "trick" to get deviates from other distributions.

This is real easy. I assume you have a probability density function on
[-infinity, infinity] that you want to duplicate. What you do is integrate
this up to yield an integral probability distribution P(x). This is a
monotonic function of x and is zero at - infinity and one at infinity. You
can think of it as the probability of a random variable's being less than x.
Anyway you have this beautiful monotonic thing with a range of [0,1], so you
just invert it, and voila! you have your uniform-to-whatever conversion
function. It's a theorem.
-- 
Norman Ramsey
ARPA: norman@lasspvax  -- or --  norman%lasspvax@cu-arpa.cs.cornell.edu
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