R: Owen's function

T.Owen {sn} | R Documentation

## 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 (`NA`s) 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)

[Package sn version 1.5-0 Index]