T — Special | CodeCogs

Evaluates the Owen's T function.

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Interface

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

using namespace Maths::Special;

double t(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

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

(1)

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

Parameters

the first argument of the T function

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

Interactive Calculator

Result –