Gamma Class

Continuous Univariate Gamma distribution. For details about this distribution, see Wikipedia - Gamma distribution.

Inheritance Hierarchy

SystemObject
Altaxo.Calc.DistributionsGamma

Namespace: Altaxo.Calc.Distributions
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)

Syntax

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public class Gamma : IContinuousDistribution, IUnivariateDistribution, 
	IDistribution

The Gamma type exposes the following members.

Constructors

	Name	Description
	Gamma(Double, Double)	Initializes a new instance of the Gamma class.
	Gamma(Double, Double, Random)	Initializes a new instance of the Gamma class.

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Properties

	Name	Description
	Entropy	Gets the entropy of the Gamma distribution.
	Maximum	Gets the maximum of the Gamma distribution.
	Mean	Gets the mean of the Gamma distribution.
	Median	Gets the median of the Gamma distribution.
	Minimum	Gets the minimum of the Gamma distribution.
	Mode	Gets the mode of the Gamma distribution.
	RandomSource	Gets or sets the random number generator which is used to draw random samples.
	Rate	Gets or sets the rate or inverse scale (β) of the Gamma distribution. Range: β ≥ 0.
	Scale	Gets or sets the scale (θ) of the Gamma distribution.
	Shape	Gets or sets the shape (k, α) of the Gamma distribution. Range: α ≥ 0.
	Skewness	Gets the skewness of the Gamma distribution.
	StdDev	Gets the standard deviation of the Gamma distribution.
	Variance	Gets the variance of the Gamma distribution.

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Methods

	Name	Description
	CDF	Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
	CumulativeDistribution	Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
	Density	Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
	DensityLn	Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	InvCDF	Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function.
	InverseCumulativeDistribution	Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function.
	IsValidParameterSet	Tests whether the provided values are valid parameters for this distribution.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	PDF	Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
	PDFLn	Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
	Sample	Generates a sample from the Gamma distribution.
	Sample(Double, Double)	Generates a sample from the Gamma distribution.
	Sample(Random, Double, Double)	Generates a sample from the Gamma distribution.
	Samples	Generates a sequence of samples from the Gamma distribution.
	Samples(Double)	Fills an array with samples generated from the distribution.
	Samples(Double, Double)	Generates a sequence of samples from the Gamma distribution.
	Samples(Double, Double, Double)	Fills an array with samples generated from the distribution.
	Samples(Random, Double, Double)	Generates a sequence of samples from the Gamma distribution.
	Samples(Random, Double, Double, Double)	Fills an array with samples generated from the distribution.
	ToString	A string representation of the distribution. (Overrides ObjectToString)
	WithShapeRate	Constructs a Gamma distribution from a shape and inverse scale parameter. The distribution will be initialized with the default random number generator.
	WithShapeScale	Constructs a Gamma distribution from a shape and scale parameter. The distribution will be initialized with the default random number generator.

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Remarks

The Gamma distribution is parametrized by a shape and inverse scale parameter. When we want to specify a Gamma distribution which is a point distribution we set the shape parameter to be the location of the point distribution and the inverse scale as positive infinity. The distribution with shape and inverse scale both zero is undefined. Random number generation for the Gamma distribution is based on the algorithm in: "A Simple Method for Generating Gamma Variables" - Marsaglia & Tsang ACM Transactions on Mathematical Software, Vol. 26, No. 3, September 2000, Pages 363–372.

Reference

Altaxo.Calc.Distributions Namespace