OwensQ | R Documentation |

Calculates Owen’s Q function.

OwensQ(nu, t, delta, a=0, b)

`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)

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

The definite integral is numerically evaluated using `integrate`

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

`OwensQOwen`

# This function is mainly intended for internal use. OwensQ(10, 2.5, 5, 0, 2) #should give [1] 9.388137e-06 OwensQ(10, -2.5, -5, 0, 2) #should give [1] 0.05264363

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