Gamma Structure

Infer.NET Documentation

Microsoft Research, Cambridge

A Gamma distribution on positive reals.

Namespace:�MicrosoftResearch.Infer.Distributions
Assembly:�Infer.Runtime (in Infer.Runtime.dll) Version: 2.5.30417.0 (2.5.30417.0)

Syntax

C++

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[SerializableAttribute]
[Quality(QualityBand.Mature)]
public�struct�Gamma : IDistribution<double>, ICloneable, 
	HasPoint<double>, CanGetLogProb<double>, SettableTo<Gamma>, 
	SettableToProduct<Gamma>, SettableToProduct<Gamma, Gamma>, 
	Diffable, SettableToUniform, SettableToRatio<Gamma>, SettableToRatio<Gamma, Gamma>, 
	SettableToPower<Gamma>, SettableToWeightedSum<Gamma>, Sampleable<double>, 
	CanGetMean<double>, CanGetVariance<double>, CanGetMeanAndVarianceOut<double, double>, 
	CanSetMeanAndVariance<double, double>, CanGetLogAverageOf<Gamma>, CanGetLogAverageOfPower<Gamma>, 
	CanGetAverageLog<Gamma>, CanGetLogNormalizer

[SerializableAttribute]
[Quality(QualityBand.Mature)]
public�struct�Gamma : IDistribution<double>, ICloneable, 
	HasPoint<double>, CanGetLogProb<double>, SettableTo<Gamma>, 
	SettableToProduct<Gamma>, SettableToProduct<Gamma, Gamma>, 
	Diffable, SettableToUniform, SettableToRatio<Gamma>, SettableToRatio<Gamma, Gamma>, 
	SettableToPower<Gamma>, SettableToWeightedSum<Gamma>, Sampleable<double>, 
	CanGetMean<double>, CanGetVariance<double>, CanGetMeanAndVarianceOut<double, double>, 
	CanSetMeanAndVariance<double, double>, CanGetLogAverageOf<Gamma>, CanGetLogAverageOfPower<Gamma>, 
	CanGetAverageLog<Gamma>, CanGetLogNormalizer

[<SealedAttribute>]
[<SerializableAttribute>]
[<Quality(QualityBand.Mature)>]
type�Gamma =  
    struct�
��������interface�IDistribution<float>
        interface�ICloneable�
��������interface�HasPoint<float>
        interface�CanGetLogProb<float>
        interface�SettableTo<Gamma>
        interface�SettableToProduct<Gamma>
        interface�SettableToProduct<Gamma, Gamma>
        interface�Diffable�
��������interface�SettableToUniform�
��������interface�SettableToRatio<Gamma>
        interface�SettableToRatio<Gamma, Gamma>
        interface�SettableToPower<Gamma>
        interface�SettableToWeightedSum<Gamma>
        interface�Sampleable<float>
        interface�CanGetMean<float>
        interface�CanGetVariance<float>
        interface�CanGetMeanAndVarianceOut<float, float>
        interface�CanSetMeanAndVariance<float, float>
        interface�CanGetLogAverageOf<Gamma>
        interface�CanGetLogAverageOfPower<Gamma>
        interface�CanGetAverageLog<Gamma>
        interface�CanGetLogNormalizer�
����end

[<SealedAttribute>]
[<SerializableAttribute>]
[<Quality(QualityBand.Mature)>]
type�Gamma =  
    struct�
��������interface�IDistribution<float>
        interface�ICloneable�
��������interface�HasPoint<float>
        interface�CanGetLogProb<float>
        interface�SettableTo<Gamma>
        interface�SettableToProduct<Gamma>
        interface�SettableToProduct<Gamma, Gamma>
        interface�Diffable�
��������interface�SettableToUniform�
��������interface�SettableToRatio<Gamma>
        interface�SettableToRatio<Gamma, Gamma>
        interface�SettableToPower<Gamma>
        interface�SettableToWeightedSum<Gamma>
        interface�Sampleable<float>
        interface�CanGetMean<float>
        interface�CanGetVariance<float>
        interface�CanGetMeanAndVarianceOut<float, float>
        interface�CanSetMeanAndVariance<float, float>
        interface�CanGetLogAverageOf<Gamma>
        interface�CanGetLogAverageOfPower<Gamma>
        interface�CanGetAverageLog<Gamma>
        interface�CanGetLogNormalizer�
����end

[SerializableAttribute]
[Quality(QualityBand::Mature)]
public�value class�Gamma : IDistribution<double>, 
	ICloneable, HasPoint<double>, CanGetLogProb<double>, SettableTo<Gamma>, 
	SettableToProduct<Gamma>, SettableToProduct<Gamma, Gamma>, 
	Diffable, SettableToUniform, SettableToRatio<Gamma>, SettableToRatio<Gamma, Gamma>, 
	SettableToPower<Gamma>, SettableToWeightedSum<Gamma>, Sampleable<double>, 
	CanGetMean<double>, CanGetVariance<double>, CanGetMeanAndVarianceOut<double, double>, 
	CanSetMeanAndVariance<double, double>, CanGetLogAverageOf<Gamma>, CanGetLogAverageOfPower<Gamma>, 
	CanGetAverageLog<Gamma>, CanGetLogNormalizer

[SerializableAttribute]
[Quality(QualityBand::Mature)]
public�value class�Gamma : IDistribution<double>, 
	ICloneable, HasPoint<double>, CanGetLogProb<double>, SettableTo<Gamma>, 
	SettableToProduct<Gamma>, SettableToProduct<Gamma, Gamma>, 
	Diffable, SettableToUniform, SettableToRatio<Gamma>, SettableToRatio<Gamma, Gamma>, 
	SettableToPower<Gamma>, SettableToWeightedSum<Gamma>, Sampleable<double>, 
	CanGetMean<double>, CanGetVariance<double>, CanGetMeanAndVarianceOut<double, double>, 
	CanSetMeanAndVariance<double, double>, CanGetLogAverageOf<Gamma>, CanGetLogAverageOfPower<Gamma>, 
	CanGetAverageLog<Gamma>, CanGetLogNormalizer

<SerializableAttribute> _
<Quality(QualityBand.Mature)> _
Public�Structure�Gamma _
	Implements�IDistribution(Of�Double), ICloneable,  _
	HasPoint(Of�Double), CanGetLogProb(Of�Double), SettableTo(Of�Gamma),  _
	SettableToProduct(Of�Gamma), SettableToProduct(Of�Gamma, Gamma),  _
	Diffable, SettableToUniform, SettableToRatio(Of�Gamma), SettableToRatio(Of�Gamma, Gamma),  _
	SettableToPower(Of�Gamma), SettableToWeightedSum(Of�Gamma), Sampleable(Of�Double),  _
	CanGetMean(Of�Double), CanGetVariance(Of�Double), CanGetMeanAndVarianceOut(Of�Double, Double),  _
	CanSetMeanAndVariance(Of�Double, Double), CanGetLogAverageOf(Of�Gamma),  _
	CanGetLogAverageOfPower(Of�Gamma), CanGetAverageLog(Of�Gamma), CanGetLogNormalizer

<SerializableAttribute> _
<Quality(QualityBand.Mature)> _
Public�Structure�Gamma _
	Implements�IDistribution(Of�Double), ICloneable,  _
	HasPoint(Of�Double), CanGetLogProb(Of�Double), SettableTo(Of�Gamma),  _
	SettableToProduct(Of�Gamma), SettableToProduct(Of�Gamma, Gamma),  _
	Diffable, SettableToUniform, SettableToRatio(Of�Gamma), SettableToRatio(Of�Gamma, Gamma),  _
	SettableToPower(Of�Gamma), SettableToWeightedSum(Of�Gamma), Sampleable(Of�Double),  _
	CanGetMean(Of�Double), CanGetVariance(Of�Double), CanGetMeanAndVarianceOut(Of�Double, Double),  _
	CanSetMeanAndVariance(Of�Double, Double), CanGetLogAverageOf(Of�Gamma),  _
	CanGetLogAverageOfPower(Of�Gamma), CanGetAverageLog(Of�Gamma), CanGetLogNormalizer

Remarks

The distribution is p(x) = x^(a-1)*exp(-x*b)*b^a/Gamma(a). In this code, the a parameter is called the "Shape" and the b parameter is called the "Rate". The distribution is sometimes also parameterized by (shape,scale) where scale = 1/rate. The mean of the distribution is shape/rate and the variance is shape/rate^2.

Special cases: When the shape is 1 and rate is 0, the distribution is uniform. When the shape is infinity, the distribution is a point mass and the density is delta(x-Point) where the Point property gives the mean. When a <= 0 or b <= 0 the b^a/Gamma(a) term is dropped.