Numeric value of Owen's Q-function at given input arguments.
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.
References
Owen DB.
A special case of a bivariate non-central t-distribution
Biometrika. 1965;52(3/4):437--46. 10.2307/2333696
Chou YM.
A bivariate noncentral T-distibution with applications
Commun Stat Theory Methods. 1992;21(12):3427--62. 10.1080/03610929208830988
# NOT RUN {# 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 # }