Mill's ratio is expressed as a convergent series in orthogonal polynomials. Truncation of the series provides an approximation for the complemented normal distribution function $Q(x)$, with its maximum error at a finite value of $x$. The analogous approximation for $xQ(x)$ is used to obtain a new method of calculating the bivariate normal probability function.
Publié le : 1979-07-14
Classification:
Univariate normal probability,
bivariate normal probability,
polynomial approximation,
orthogonal polynomials,
60E05,
41A10
@article{1176344739,
author = {Divgi, D. R.},
title = {Calculation of Univariate and Bivariate Normal Probability Functions},
journal = {Ann. Statist.},
volume = {7},
number = {1},
year = {1979},
pages = { 903-910},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344739}
}
Divgi, D. R. Calculation of Univariate and Bivariate Normal Probability Functions. Ann. Statist., Tome 7 (1979) no. 1, pp. 903-910. http://gdmltest.u-ga.fr/item/1176344739/