GammaDistribution Class

Generates Gamma distributed random numbers.

Inheritance Hierarchy

SystemObject
  Altaxo.Calc.ProbabilityDistribution
    Altaxo.Calc.ProbabilityContinuousDistribution
      Altaxo.Calc.ProbabilityGammaDistribution

Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)

Syntax

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public class GammaDistribution : ContinuousDistribution

The GammaDistribution type exposes the following members.

Constructors

	Name	Description
	GammaDistribution	Initializes a new instance of the GammaDistribution class, using a StandardGenerator as underlying random number generator.
	GammaDistribution(Generator)	Initializes a new instance of the GammaDistribution class, using the specified Generator as underlying random number generator.
	GammaDistribution(Double, Double)	Initializes a new instance of the GammaDistribution class.
	GammaDistribution(Double, Double, Generator)	Initializes a new instance of the GammaDistribution class.

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Properties

	Name	Description
	Alpha	Gets or sets the parameter alpha which is used for generation of Gamma distributed random numbers.
	CanReset	Gets a value indicating whether the random number distribution can be reset so that it produces the same random number sequence again. (Inherited from Distribution)
	Generator	Gets or sets a Generator object that can be used as the underlying random number generator. (Inherited from Distribution)
	Location	Gets or sets the location parameter.
	Maximum	Gets the maximum possible value of distributed random numbers. (Overrides DistributionMaximum)
	Mean	Gets the mean of distributed random numbers. (Overrides DistributionMean)
	Median	Gets the median of distributed random numbers. (Overrides DistributionMedian)
	Minimum	Gets the minimum possible value of distributed random numbers. (Overrides DistributionMinimum)
	Mode	Gets the mode of distributed random numbers. (Overrides DistributionMode)
	Order	Gets the order (shape) parameter of the distribution.
	Theta	Gets or sets the parameter theta which is used for generation of Gamma distributed random numbers.
	Variance	Gets the variance of distributed random numbers. (Overrides DistributionVariance)

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Methods

	Name	Description
	CDF(Double)	Calculates the cumulative distribution function. (Overrides ContinuousDistributionCDF(Double))
	CDF(Double, Double, Double)	Computes the cumulative distribution function (CDF) for a Gamma distribution with the given parameters.
	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)
	Initialize	Initializes this instance with the specified distribution parameters.
	IsValidAlpha	Determines whether the specified value is valid for parameter Alpha.
	IsValidTheta	Determines whether the specified value is valid for parameter Theta.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	NextDouble	Returns a distributed floating-point random number. (Overrides DistributionNextDouble)
	PDF(Double)	Calculates the probability density function. (Overrides ContinuousDistributionPDF(Double))
	PDF(Double, Double, Double)	Computes the probability density function (PDF) for a Gamma distribution with the given parameters.
	Quantile(Double)	Calculates the quantile of the distribution function. (Overrides ContinuousDistributionQuantile(Double))
	Quantile(Double, Double, Double)	Computes the quantile (inverse CDF) for a Gamma distribution with the given parameters.
	Reset	Resets the random number distribution so that it produces the same random number sequence again. (Inherited from Distribution)
	ToString	Returns a string that represents the current object. (Inherited from Object)

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Fields

	Name	Description
	_invTheta
	algorithmGD
	alpha
	b
	c
	d
	exponentialDistribution
	generator	Stores a Generator object that can be used as the underlying random number generator. (Inherited from Distribution)
	normalDistribution
	q0
	r
	s
	s2
	scale
	si
	theta

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Remarks

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Return Gamma distributed random deviates according to:

                     a-1  -bx
               b (bx)    e
 p   (x) dx = ---------------- dx   for x > 0
  a,b             Gamma(a)

            =  0                    otherwise
                            // 
The arguments must satisfy the conditions:
a > 0   (positive)
b != 0  (non-zero)

References:

For parameter a >= 1 corresponds to algorithm GD in:
J. H. Ahrens and U. Dieter, Generating Gamma Variates by a
Modified Rejection Technique, Comm. ACM, 25, 1, 47-54 (1982).
For parameter 0 < a < 1 corresponds to algorithm GS in:
J. H. Ahrens and U. Dieter, Computer Methods for Sampling
from Gamma, Beta, Poisson and Binomial Distributions,
Computing, 12, 223-246 (1974).

Reference

Altaxo.Calc.Probability Namespace