NAG Library Function Document
nag_mills_ratio (g01mbc) returns the reciprocal of Mills' Ratio.
||nag_mills_ratio (double x)
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)
Gross A J and Clark V A (1975) Survival Distributions: Reliability Applications in the Biomedical Sciences Wiley
On entry: , the argument of the reciprocal of Mills' Ratio.
Error Indicators and Warnings
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.
Parallelism and Performance
nag_mills_ratio (g01mbc) is not threaded in any implementation.
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
The hazard rate is evaluated at different values of for Normal distributions with different means and variances. The results are then printed.
Program Text (g01mbce.c)
Program Data (g01mbce.d)
Program Results (g01mbce.r)