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OwensT Class

Owen's T function and related functions.
Inheritance Hierarchy

Namespace:  Accord.Math
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
public static class OwensT
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Public methodStatic memberFunction(Double, Double)
Computes Owen's T function for arbitrary H and A.
Public methodStatic memberFunction(Double, Double, Double)
Owen's T function for a restricted range of parameters.

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 and is valid under the LGPL.


  • 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.

// Computes Owens' T function
double t = OwensT.Function(h: 2, a: 42); // 0.011375065974089608
See Also