/// <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(0.0);
}
return(Math.Pow(Rate, x) * Math.Exp(-Rate) / GammaFunctions.Factorial(x));
}
/// <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.GammaHigh(x + 1, Rate) / GammaFunctions.Factorial(x));
}