Owens T Function

Computes Owen's T function T(h, a), which gives the probability of the event (X > h and 0 < Y < a*X) where X and Y are independent standard normal random variables.

$$T(h,a)=\frac{1}{2\pi}\int_{0}^{a}\frac{\exp\!\left\{-\tfrac{1}{2}h^{2}(1+x^{2})\right\}}{1+x^{2}}\,dx,\quad (-\infty<h,a<+\infty)$$

Usage

owens_t(h, a)

Arguments

h

The first argument of the Owens T function (boundary parameter)

a

The second argument of the Owens T function (slope parameter)

Value

The value of the Owens T function at (h, a).

See also

Boost Documentation for more details on the mathematical background.

Examples

# Owens T Function
owens_t(1, 0.5)
#> [1] 0.04306469