Normal density and cdf approximations

[Roger W. Johnson]

In response to the article on polynomial and rational approximations
for the normal density function and the normal cummulative distribution
function see the "Handbook of Mathematical Functions with formulas
graphs, and mathematical tables", by Abramowitz & Stegun or the
references contained therein - ifically C. Hastings, Jr
Approximations for digital computers, Princeton Univ Press, Princeton,
N,J. (1955).

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

Reply to: wjoh...@cod.UUCP

[Gary Perlman]

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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