/// <summary>
/// This function return the cummulative distribution function (CDF)
/// for Student's t distribution less than t and number degree of
/// freedom k.
/// </summary>
/// <param name="t">double. t</param>
/// <param name="k">int. k is number degree of freedom</param>
/// <returns>
/// The value of cummulative distribution function (CDF)
/// for Student's t distribution less than t and number degree of
/// freedom k.
/// </returns>
public static double CDF(double t, int k)
{
// number degree of freedom must be mor than 0
if (k <= 0) return double.NaN;
if (t == 0) return 0.5;
StudentFunction function = new StudentFunction(k);
if (t < 0)
return 0.5 - Integrator.GaussLegendre(function, t, 0, 1.0e-6);
else
return 0.5 + Integrator.GaussLegendre(function, 0, t, 1.0e-6);
}
/// <summary>
/// This function return the probability density function (PDF)
/// for Student's t distribution with T=t and number degree
/// of freedom k.
/// </summary>
/// <param name="t">double. t</param>
/// <param name="k">int. k is number degree of freedom</param>
/// <returns>
/// The value of probability density function (PDF)
/// for Student's t distribution with T=t and number degree
/// of freedom k.
/// </returns>
private static double PDF(double t, int k)
{
StudentFunction function = new StudentFunction(k);
return function.Value(t);
}