Calculates Owen's Q function.

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`nu` |
degree of Owen's Q |

`t` |
parameter t |

`delta` |
parameter delta |

`a` |
lower integration limit, only a=0 implemented |

`b` |
upper integration limit |

Uses the relationship to non-central t-distribution (see Chou YM)

OwensQ = pt(t, df=nu, ncp=delta) - Integal_b_Inf(Q_integrand)

The definite integral is numerically evaluated using `integrate()`

from
package `stats`

after a variables transformation resulting in the
integration range from 0 to 1 instead of the semi-infinite original range.
This may result in higher precision and better numerical stability.

The arguments to the function must be scalars. No vectors allowed.

Numeric value of Owen's Q-function at given input arguments.

This function is intended for internal use in the power calculations.

But may be useful for others.

D. Labes

Owen DB.

*A special case of a bivariate non-central t-distribution*

Biometrika. 1965;52(3/4):437–46. doi: 10.2307/2333696

Chou YM.

*A bivariate noncentral T-distibution with applications*

Commun Stat Theory Methods. 1992;21(12):3427–62. doi: 10.1080/03610929208830988

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