nag_mills_ratio (g01mbc) 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 nag_erfcx (s15agc)
In the left-hand tail,
the safe range argument (nag_real_safe_small_number (X02AMC)
is returned, which is close to the true value.
The relative accuracy is bounded by the effective machine precision
. See nag_erfcx (s15agc)
for further discussion.
If, before entry,
is not a standard Normal variable, it has to be standardized, and on exit, nag_mills_ratio (g01mbc) has to be divided by the standard deviation. That is, if the Normal distribution has mean
, then its hazard rate,
, is given by