C# Class Accord.Math.OwensT

Owen's T function and related functions.

In mathematics, Owen's T function T(h, a), named after statistician Donald Bruce Owen, is defined by

1 a exp{-0.5 h²(1+x²) T(h, a) = ---- ∫ ------------------- dx 2π 0 1 + x²

The function T(h, a) gives the probability of the event (X > h and 0 < Y < aX) where X and Y are independent standard normal random variables. This function can be used to calculate bivariate normal distribution probabilities and, from there, in the calculation of multivariate normal distribution probabilities. It also frequently appears in various integrals involving Gaussian functions.

The code is based on the original FORTRAN77 version by Mike Patefield, David Tandy; and the C version created by John Burkardt. The original code for the C version can be found at http://people.sc.fsu.edu/~jburkardt/c_src/owens/owens.html and is valid under the LGPL.

References: http://people.sc.fsu.edu/~jburkardt/c_src/owens/owens.html Mike Patefield, David Tandy, Fast and Accurate Calculation of Owen's T Function, Journal of Statistical Software, Volume 5, Number 5, 2000, pages 1-25.

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Public Methods

Method	Description
Function ( double h, double a ) : double	Computes Owen's T function for arbitrary H and A.
Function ( double h, double a, double ah ) : double	Owen's T function for a restricted range of parameters.

Method Details

Function() public static method

Computes Owen's T function for arbitrary H and A.

public static Function ( double h, double a ) : double
h	double	Owen's T function argument H.
a	double	Owen's T function argument A.
return	double

Function() public static method

Owen's T function for a restricted range of parameters.

public static Function ( double h, double a, double ah ) : double
h	double	Owen's T function argument H (where 0 <= H).
a	double	Owen's T function argument A (where 0 <= A <= 1).
ah	double	The value of A*H.
return	double