OwenT {dsfa}

R Documentation

OwenT

Description

Evaluates the Owen T-function

Usage

OwenT(x, a, jmax = 50, cut.point = 8, deriv = 0)

OwenT_vec(x, a, jmax = 50, cut.point = 8)

Arguments

x	numeric vector of quantiles. Missing values (NAs) and Inf are allowed.
a	numeric vector. Inf is allowed.
jmax	an integer scalar value which regulates the accuracy of the result.
cut.point	a scalar value which regulates the behaviour of the algorithm.
deriv	derivative of order deriv of the T.Owen function. Available are 0 and 2.

Details

The OwenT function is defined as

T(x,a)=\frac{1}{2 \pi} \int_0^{a} \frac{\exp\{-x^2 (1+t^2)/2 \}}{1+t^2} d t

. If a>1 and 0<x<=cut.point, a series expansion is used, truncated after jmax terms. If a>1 and x>cut.point, an asymptotic approximation is used. In the other cases, various reflection properties of the function are exploited. For deriv=0, the function is a clone of T.Owen.

Value

OwenT evaluates the OwenT function with given parameters x and a. If the derivatives are calculated these are provided as the attributes gradient, hessian.

Functions

• OwenT_vec(): Vectorized OwenT function without derivatives.

References

• Owen DB (1956). “Tables for Computing Bivariate Normal Probabilities.” Annals of Mathematical Statistics, 27, 1075-1090.

Examples

OwenT(x=1, a=1, jmax = 50, cut.point = 8, deriv=2)

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