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# T

Evaluates the Owen's T function.
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Contents

C++

## T

 doublet( double h double a )
This component calculates the T function of Owen with given arguments h and a. This function is useful for computation of the bivariate normal distribution and the distribution of a skewed normal distribution. Although it was originally formulated in terms of the bivariate normal function, the function can be defined more directly as

$\mathrm{T}(h,&space;a)&space;=&space;\frac{1}{2\pi}&space;\int_0^a&space;\frac{e^{-\frac{1+x^2}{2}h^2}}{1+x^2}&space;\mathrm{d}x$

In the following example, the T function is evaluated with the h argument fixed to 1 and the a argument varying in the interval from 1 to 3 with step 0.2.

### Example 1

#include <codecogs/maths/special/t.h>
#include <iostream>
#include <iomanip>

int main()
{
std::cout << std::setprecision(10);
for (double a = 1; a <= 3.1; a += 0.2)
{
std::cout << "T(1, " << a << ") = ";
std::cout << Maths::Special::t(1, a) << std::endl;
}
return 0;
};

### Output

T(1, 1) = 0.06674188217
T(1, 1.2) = 0.071539968
T(1, 1.4) = 0.07464519054
T(1, 1.6) = 0.07659020331
T(1, 1.8) = 0.0777717076
T(1, 2) = 0.07846818696
T(1, 2.2) = 0.07886656741
T(1, 2.4) = 0.07908757312
T(1, 2.6) = 0.07920641123
T(1, 2.8) = 0.07926830709
T(1, 3) = 0.07929951045

### References

John Burkardt's library of statistical C++ routines, http://www.csit.fsu.edu/~burkardt/cpp_src/prob/prob.html

### Parameters

 h the first argument of the T function a the second argument of the T function (upper limit of integration)

### Returns

the value of Owen's T function evaluated with the given arguments

### Authors

Lucian Bentea (September 2005)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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Last Modified: 7 Jul 10 @ 22:03     Page Rendered: 2022-03-14 15:38:42