NAG Library Routine Document
g01mbf returns the reciprocal of Mills' Ratio, via the routine name.
|Real (Kind=nag_wp)||:: ||g01mbf|
|Real (Kind=nag_wp), Intent (In)||:: ||x|C Header Interface
g01mbf_ (const 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 s15agf
Gross A J and Clark V A (1975) Survival Distributions: Reliability Applications in the Biomedical Sciences Wiley
- 1: – Real (Kind=nag_wp)Input
On entry: , the argument of the reciprocal of Mills' Ratio.
Error Indicators and Warnings
In the left-hand tail,
the safe range argument (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.
Parallelism and Performance
g01mbf is not threaded in any implementation.
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
The hazard rate is evaluated at different values of for Normal distributions with different means and variances. The results are then printed.
Program Text (g01mbfe.f90)
Program Data (g01mbfe.d)
Program Results (g01mbfe.r)