/// <summary>
/// Probability Distribution Function
/// </summary>
/// <see cref="https://en.wikipedia.org/wiki/Probability_density_function"/>
public override double Pdf(double x)
{
if (x < 0)
{
throw new ArgumentOutOfRangeException(nameof(x), "value must be non negative");
}
else if (x == 0)
{
return(Shape <= 1 ? double.PositiveInfinity : 0.0);
}
return(Math.Pow(x, Shape - 1) *
Math.Exp(-x / Scale) /
(GammaFunctions.Gamma(Shape) * Math.Pow(Scale, Shape)));
}
/// <summary>
/// Cumulative Density Function
/// </summary>
/// <see cref="https://en.wikipedia.org/wiki/Cumulative_distribution_function"/>
public override double Cdf(double x)
{
if (x < 0)
{
throw new ArgumentOutOfRangeException(nameof(x), "value must be positive");
}
else if (x == 0)
{
return(0.0);
}
else if (double.IsPositiveInfinity(x))
{
return(1.0);
}
return(GammaFunctions.GammaLow(Shape, x / Scale) / GammaFunctions.Gamma(Shape));
}
/// <summary>
/// Probability Distribution Function
/// </summary>
/// <see cref="https://en.wikipedia.org/wiki/Probability_density_function"/>
public override double Pdf(double x)
{
if (x <= 0)
{
throw new ArgumentOutOfRangeException(nameof(x), "value must be positive");
}
return(Math.Pow(x, DegreeOfFreedom / 2 - 1) * Math.Exp(-x / 2) / (Math.Pow(2, DegreeOfFreedom / 2) * GammaFunctions.Gamma(DegreeOfFreedom / 2)));
}
/// <summary>
/// Probability Distribution Function
/// </summary>
/// <see cref="https://en.wikipedia.org/wiki/Probability_density_function"/>
public override double Pdf(double x)
{
return(GammaFunctions.Gamma((DegreeOfFreedom + 1) / 2) / (Math.Sqrt(DegreeOfFreedom * Math.PI) * GammaFunctions.Gamma(DegreeOfFreedom / 2)) *
Math.Pow(1 + x * x / DegreeOfFreedom, -(DegreeOfFreedom + 1) / 2));
}