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From: wjohnson@cod.UUCP (Roger W. Johnson)
Newsgroups: sci.math
Subject: Re: Need formula for Normal Distribution Simulation
Message-ID: <197@cod.UUCP>
Date: Thu, 30-Oct-86 12:12:04 EST
Article-I.D.: cod.197
Posted: Thu Oct 30 12:12:04 1986
Date-Received: Sat, 1-Nov-86 04:37:15 EST
References: <146@helm.UUCP> <5270001@hpfcpf.HP.COM>
Reply-To: wjohnson@cod.UUCP (Roger W. Johnson)
Organization: Naval Ocean Systems Center, San Diego
Lines: 37

In article <5270001@hpfcpf.HP.COM> rms@hpfcpf.HP.COM writes:
>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

The variables X1 and X2 are also independent (if U1 and U2 are independ-
ent).  The above "polar method for normal variates" is discussed on pg 117
of 'The Art of Computer Programming:  Seminumerical Algorithms', (vol 2),
2nd ed by Donald Knuth.  Other ways of generating normal variates are 
discussed in this text.


-- 
Roger Johnson/Naval Ocean Systems Center/Code 421/San Diego, Ca 92152
             /2150 Pacific Beach Drive/Apt 207/San Diego, Ca 92109

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