Calculates Owen's Q function.
degree of Owen's Q
lower integration limit
upper integration limit
integrate() from package stats to perform the numerical evaluation
of the definite integral in Owen's Q function.
See ../doc/BE_power_sample_size_excerpt.pdf in the package sub-directory /doc for the definition of Owen's Q and implmentation details.
In case of high delta and/or high upper integration limit b where the implementation via R's function
integrate() may fail the function
OwensQOwen() is used.
The arguments to the function must be scalars. No vectors allowed.
Numeric value of Owen's Q-function at given input arguments.
Since for really large values of nu and the upper integration limit b the integrand is a function which is zero over nearly all its range, the
integrate() function may fail (see
OwensQ() then returns erroneously 0.
The function now tries to return a value via non-central t-approximation in such cases. This approximation is up to 6 decimals correct as far as tested.
OwensQ() issues a warning if the nct-approximation is used.
This function is intended for internal use in the power calculations.
But may be useful for others.
Owen, D. B. (1965)
"A Special Case of a Bivariate Non-central t-Distribution"
Biometrika, 52, 437-446.
1 2 3 4 5