OwensQ: Owen's Q-function

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

Calculates Owen's Q function.

Usage

1
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 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.

Value

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 (1965)
"A Special Case of a Bivariate Non-central t-Distribution"
Biometrika, 52, 437-446.
doi: 10.2307/2333696

Chou YM (1992)
"A bivariate noncentral T-distibution with applications"
Communications in Statistics - Theory and Methods, 21:12, 3427-3462
doi: 10.1080/03610929208830988

See Also

OwensQOwen

Examples

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# 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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