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From: perlman@wanginst.UUCP (Gary Perlman)
Newsgroups: net.math.stat
Subject: Re: Normal density and cdf approximations
Message-ID: <1722@wanginst.UUCP>
Date: Mon, 10-Mar-86 23:13:55 EST
Article-I.D.: wanginst.1722
Posted: Mon Mar 10 23:13:55 1986
Date-Received: Wed, 12-Mar-86 22:04:56 EST
References: <240@noscvax.UUCP>
Reply-To: perlman@wanginst.UUCP (Gary Perlman)
Organization: Wang Institute, Tyngsboro, MA 01879 USA
Lines: 24
Summary: 

Algorithms for computing normal probabilities can be found in the
Collected Algorithms of the CACM in most technical library reference
sections.  Many of these originally appeared in the CACM.

The algorithm used in my stat package is based on a polynomial
approximation in:
	Ibbetson, D. Algorithm 209.  CACM, 1963, p. 616.
It is accurate to six decimal places (standard normal scores up
to an absolute value of 6).

The discussion in the Collected Algorithms covers other algorithms
for the same purpose.  There is a cross reference to a different
algorithm that will compute cumulative normal probabilities to
the accuracy of the machine in use.  The tradeoff, in one Remarks
section, is that Algorithm 209 is very fast and reasonably accurate,
while the other (whose number escapes me), is reasonably fast and
very accurate.

The Collected algorithms include ones for F ratios, t,
and chi-square probabilities.  The algorithms are in Algol,
and so are easy to translate to other high level languages.
-- 
Gary Perlman  Wang Institute  Tyngsboro, MA 01879  (617) 649-9731
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