Calculates Owen's Q function.
1 |
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 (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
OwensQOwen
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