"Jason H. Stover" <jstover at gcsu.edu> writes:
> In the R source, nmath/pnorm.c contains the
> code for a rational function approximation
> for the normal cdf. These constants are listed:
>
> const double a[5] = {
> 2.2352520354606839287,
> 161.02823106855587881,
> 1067.6894854603709582,
> 18154.981253343561249,
> 0.065682337918207449113
> };
>
> The source file cites a paper by Cody (1969)
> and states that these constants are derived from
> Cody's paper. I've checked the paper, and
> the constants do not agree, so I assume someone
> else derived slightly different constants. The source
> also contains a reference to 1993 paper by Cody,
> but this paper describes software itself, not the
> derivation of the approximation used.
>
> Does anyone know of another reference for these
> and other constants used in pnorm.c? Is there a
> general reference detailing how to derive such
> approximations?
>
> Thank-you,
> Jason
pnorm.c is based on ANORM from http://www.netlib.org/toms/715, which
has the same constants and is by Cody himself. The exacts words there
are:
C The main computation evaluates near-minimax approximations
C derived from those in "Rational Chebyshev approximations for
C the error function" by W. J. Cody, Math. Comp., 1969, 631-637.
Notice "derived from". My guess would be that he applied the same
methods but to give optimal approximations over different intervals
from the 1969 paper.
--
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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