calculates the reciprocal of Mills' Ratio, the hazard rate,
, for the standard Normal distribution. It is defined as the ratio of the ordinate to the upper tail area of the standard Normal distribution, that is,
The calculation is based on a Chebyshev expansion as described in s15agc
In the left-hand tail,
the safe range parameter (X02AMC
is returned, which is close to the true value.
The relative accuracy is bounded by the effective machine precision
. See s15agc
for further discussion.
If, before entry,
is not a standard Normal variable, it has to be standardized, and on exit, g01mbc
has to be divided by the standard deviation. That is, if the Normal distribution has mean
, then its hazard rate,
, is given by