# Owen's Q-function via repeated integration by parts

### Description

This is an implementation of the algorithm given in Owen's original paper (Biometrica 1965) via repeated integration by parts.

### Usage

1 | ```
OwensQOwen(nu, t, delta, a=0, b)
``` |

### Arguments

`nu` |
degree of Owen's Q |

`t` |
parameter t |

`delta` |
parameter delta |

`a` |
lower integration limit. |

`b` |
upper integration limit |

### Value

numeric value of Owen's Q function.

### Note

The argument `a=0`

could be dropped but is retained for sake of completeness.

### Note

This function is mainly for comparative / validation purposes.

It is used in `OwensQ()`

in case of high nu and/or high upper integration
limit where the implementation via R's function `integrate()`

may fail.
The implementation needs `OwensT()`

function.

### Author(s)

D. Labes

### References

Owen, D.B. (1965)

"A Special Case of a Bivariate Non-central t-Distribution"

Biometrika Vol. 52, p437-446.

### See Also

`OwensQ`

, `OwensT`

### Examples

1 2 3 4 | ```
# comparison of the results of both implementations
# both should give [1] 0.0731726
OwensQ(2, 2.92, 4.2135, 0, 2.0407)
OwensQOwen(2, 2.92, 4.2135, 0, 2.0407)
``` |