/// <summary>
/// Cumulative Density Function
/// </summary>
/// <see cref="https://en.wikipedia.org/wiki/Cumulative_distribution_function"/>
/// <seealso cref="https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function"/>
public override double Cdf(double x)
{
if (x < 0 || x > 1.0)
{
throw new ArgumentOutOfRangeException(nameof(x), "value must be in [0..1] range");
}
return(GammaFunctions.BetaIncompleteRegular(x, Alpha, Beta));
}
/// <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 not be negative");
}
return(1.0 - GammaFunctions.BetaIncompleteRegular(DegreeOfFreedom / (x * x + DegreeOfFreedom), DegreeOfFreedom / 2, 0.5) / 2);
}
/// <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");
}
return(GammaFunctions.BetaIncompleteRegular(DegreeOfFreedom1 * x / (DegreeOfFreedom1 * x + DegreeOfFreedom2),
DegreeOfFreedom1 / 2,
DegreeOfFreedom2 / 2));
}