naginterfaces.library.stat.mills_​ratio

naginterfaces.library.stat.mills_ratio(x)[source]

mills_ratio returns the reciprocal of Mills’ Ratio.

For full information please refer to the NAG Library document for g01mb

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01mbf.html

Parameters
xfloat

, the argument of the reciprocal of Mills’ Ratio.

Returns
rmrfloat

The reciprocal of Mills’ Ratio.

Notes

mills_ratio 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 specfun.erfcx_real.

References

Gross, A J and Clark, V A, 1975, Survival Distributions: Reliability Applications in the Biomedical Sciences, Wiley