OwensQ function

Owen's Q-function

Calculates Owen’s Q function. utf-8

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

Arguments

• nu: degree of Owen’s Q
• t: parameter t
• delta: parameter delta
• a: lower integration limit, only a=0 implemented
• b: upper integration limit

Details

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.

Returns

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

Note

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

But may be useful for others.

Author(s)

D. Labes

References

Owen DB. A special case of a bivariate non-central t-distribution. Biometrika. 1965;52(3/4):437--46. tools:::Rd_expr_doi("10.2307/2333696")

Chou YM. A bivariate noncentral T-distibution with applications. Commun Stat Theory Methods. 1992;21(12):3427--62. tools:::Rd_expr_doi("10.1080/03610929208830988")

See Also

OwensQOwen

Examples

# 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