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From: winston@cubsvax.UUCP (Ken Winston)
Newsgroups: net.math
Subject: Series for normal distribution function
Message-ID: <443@cubsvax.UUCP>
Date: Sat, 1-Mar-86 20:17:04 EST
Article-I.D.: cubsvax.443
Posted: Sat Mar  1 20:17:04 1986
Date-Received: Mon, 3-Mar-86 01:32:27 EST
Organization: Columbia Univ. Bio. CG Fac., NY
Lines: 22


Here is a question for numerical analysis types:

The standard normal distribution function is

	N(t) = 1/sqrt(2*pi) * integral(-infinity to t) [exp(-z^2/2)]*dz.

I have seen the following approximation a few different times now as a way
of finding N(t) on a computer. It seems to be accurate in the usual range, for
t<=0:

    N(t) ~= x*exp(-t^2/2)*(.436184 - .120167*x + .937298*x^2)/sqrt(2*pi),
	where x = 1/(1+.3327*|t|)

For t>0 use N(t) = 1-N(-t).

My ignorance of numerical analysis is vast (not just half-vast). Does anybody
know where this comes from? What is the general method that gives rise to this
series?

Ken Winston
...{cmcl2,rna,cubsvax}!wealth!ken