GammaDistribution Class

public sealed class GammaDistribution : ContinuousDistribution

Public NotInheritable Class GammaDistribution
	Inherits ContinuousDistribution

public ref class GammaDistribution sealed : public ContinuousDistribution

[<SealedAttribute>]
type GammaDistribution = 
    class
        inherit ContinuousDistribution
    end

Inheritance

Object    UnivariateDistribution    ContinuousDistribution    GammaDistribution

The sum of n exponentially distributed variates is a Gamma distributed variate with shape parameter n.

When the shape parameter is an integer, the Gamma distribution is also called the Erlang distribution. When the shape parameter is one, the Gamma distribution reduces to the exponential distribution.

With large shape parameters, the Gamma distribution becomes approximately Gaussian.

With shape parameters less than one, the Gamma distribution becomes ever more strongly peaked near zero.

With very small shape parameters, say below about 0.01, the distribution becomes peaked so strongly near zero that a non-negligible fraction consists of unrepresentatably small numbers that round to zero. For a shape parameter of 0.001, for example, almost half the area under the curve corresponds to number smaller than 10^-324. This can cause problems if the distinction between zero and such small values is relevent to your application. For example, if you do a KolmogorovSmirnovTest(IReadOnlyListDouble, ContinuousDistribution) on deviates generated from this distribution, you will get D ~ 0.47 and may conclude that the sample is nonreprestative. But this happened only because 47% of the values rounded to zero, making the KS test compute P(0) = 0 for the 47th percentile value. Without rouding the 47th percentile value would have been P(~1.0E-324) ~ 0.47 resulting in an unremarkable D value.

Reference

Other Resources