Owen's function

Usage

T_Owen(h, a, jmax, cut_point)

Arguments

h a numerical vector. Missing values (NaNs) and Inf are allowed.
a a numerical scalar. Inf is allowed.
jmax an integer scalar value which regulates the accuracy of the result (default is 50). See Details below for explanation.
cut_point a scalar value which regulates the behaviour of the algorithm (default is 6). See Details below for explanation.

Description

Evaluates funtion T(h,a) studied by D.B.Owen

Details

If a>1 and 0<h<=cut_point, a series expansion is used, truncated after jmax terms. If a>1 and h>cut_point, an asymptotic approximation is used. In the other cases, various reflection properties of the function are exploited. See the reference below for more information.

Value

a numerical vector

BACKROUND

The function T(h,a) is useful for the computation of the bivariate normal distribution function and related quantities. See the reference below for more information.

References

Owen, D. B. (1956). Tables for computing bivariate normal probabilities. Ann. Math. Statist. 27, 1075-1090.

See Also

pnorm2, psn

Examples

owen = T_Owen(1:10, 2)


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