T.Owen {sn}

Owen's function

Description

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

Usage

T.Owen(h, a, jmax=50, cut.point=8)

Arguments

h

a numeric vector. Missing values (NAs) and Inf are allowed.

a

a numeric value. Inf is allowed.

jmax

an integer scalar value which regulates the accuracy of the result. See Section ‘Details’ below for explanation.

cut.point

a scalar value which regulates the behaviour of the algorithm, as explained in Section ‘Details’ below (default value: 8).

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 numeric vector.

Background

The function T(h,a) studied by Owen (1956) is useful for the computation of the bivariate normal distribution function and related quantities, including the distribution function of a skew-normal variate; see psn. See the reference below for more information on function T(h,a).

Author(s)

Adelchi Azzalini and Francesca Furlan

References

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

See Also

psn

Examples

 owen <- T.Owen(1:10, 2)