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

References

Examples

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


[Package dsfa version 1.0.1 Index]