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 s15agf
In the left-hand tail,
the safe range parameter (x02amf
is returned, which is close to the true value.
The relative accuracy is bounded by the effective machine precision
. See s15agf
for further discussion.
If, before entry,
is not a standard Normal variable, it has to be standardized, and on exit, g01mbf
has to be divided by the standard deviation. That is, if the Normal distribution has mean
, then its hazard rate,
, is given by