/// <inheritdoc />
public override double ProbabilityDensity(double x)
{
if (x < 0.0)
{
return(0.0);
}
else
{
double z = x / s;
// use Gamma(a) or Ln(Gamma(a)) form depending on size of a
if (ga > 0.0)
{
return(Math.Pow(z, a - 1.0) * Math.Exp(-z) / ga / s);
}
else
{
// The standard Gamma distribution p(\alpha, x) is the same as the
// Poisson distribution P(\lambda, k) with k \leftarrow \alpha - 1
// and \lambda \leftarrow x. Use this fact plus our Poisson
// machinery to accurately compute probabilities for large \alpha.
return(Stirling.PoissonProbability(z, a - 1.0) / s);
//return (Math.Exp((a - 1.0) * Math.Log(z) - z + ga) / s);
}
}
}
/// <inheritdoc />
public override double ProbabilityMass(int k)
{
if (k < 0)
{
return(0.0);
}
else
{
// These are the same expression, but the form for small arguments is faster,
// while the form for large arguments avoids overflow and cancellation errors.
if (k < 16)
{
return(Math.Exp(-mu) * MoreMath.Pow(mu, k) / AdvancedIntegerMath.Factorial(k));
}
else
{
return(Stirling.PoissonProbability(mu, k));
}
}
}