/// <summary>
/// Chi-squared probability density function.
/// </summary>
/// <param name="x">The value at which the PDF is evaluated.</param>
/// <param name="k">Degress of freedom, or number independent standard normal distributions.</param>
/// <returns></returns>
public static double ChiSquaredProbabilityDensityFunction(double x, int k)
{
double g = MMath.GammaFunction(0.5 * k);
double a = 1.0 / (Math.Pow(2, 0.5 * k) * g);
return(a * Math.Pow(x, 0.5 * k - 1.0) * Math.Exp(-0.5 * x));
}
/// <summary>
/// Returns the PDF of Student's t distribution.
/// </summary>
/// <param name="x">Value at which the distribution is evaluated.</param>
/// <param name="k">Degrees of freedom.</param>
public static double StudentsTProbabilityDensityFunction(double x, double k)
{
double a = MMath.GammaFunction(0.5 * k + 0.5);
double b = Math.Pow(1.0 + (x * x) / k, -0.5 * k - 0.5);
double c = Math.Sqrt(k * Math.PI) * MMath.GammaFunction(0.5 * k);
return(a * b / c);
}
