Evaluates the Owen's T function.

Contents

Interface Function Documentation Page Comments

Interface

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

using namespace Maths::Special;

	double	t (double h, double a) Evaluates the Owen's T function.
	Real	cc_t (Real h, Real a) This function is available as a Microsoft Excel add-in.

Function Documentation

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

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:

#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

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

References:

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

Authors:

Lucian Bentea (September 2005)