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From: rms@hpfcpf.HP.COM
Newsgroups: sci.math
Subject: Re: Need formula for Normal Distribution Simulation
Message-ID: <5270001@hpfcpf.HP.COM>
Date: Tue, 28-Oct-86 11:00:27 EST
Article-I.D.: hpfcpf.5270001
Posted: Tue Oct 28 11:00:27 1986
Date-Received: Wed, 29-Oct-86 22:40:15 EST
References: <146@helm.UUCP>
Organization: Hewlett-Packard
Lines: 23

The following is called the Box-Muller algorithm, and does a very
good job of generating normal random deviates:

   1. Generate two uniform random numbers, U1 and U2.

   2. Let V1 = 2 * U1 - 1, and V2 = 2 * U2 - 1.

   3. Let S = V1^2 + V2^2.

   4. If S >= 1, go back to step 1.

   5. Else, let T = SQRT(-2 * LN(S)/S).

   6. Let X1 = V1 * T, and X2 = V2 * T.

Now X1 and X2 are from a normal distribution having mean 0 and standard
deviation 1.  To get mean A and standard deviation S, multiply both
by S and add A.

Rick Scherer
Statistician
Hewlett-Packard Co.
Ft. Collins, CO