Owen's Q-function via repeated integration by parts

This is an implementation of the algorithm given by Owen via repeated integration by parts.

OwensQOwen(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, other values give an error.

b

upper integration limit

Value

Numeric value of Owen’s Q function.

Note

The argument a=0 could be dropped but is retained for sake of completeness.

References

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

Author

D. Labes

Note

This function is mainly for comparative / validation purposes.
The function requireds OwensT function.

See also

OwensQ, OwensT

Examples

# comparison of the results of both implementations
# both should give [1] 0.0731726
OwensQ(2, 2.92, 4.2135, 0, 2.0407)
#> [1] 0.0731726
OwensQOwen(2, 2.92, 4.2135, 0, 2.0407)
#> [1] 0.0731726