IGLib  1.7.2
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Meta.Numerics.Statistics.Distributions.UnivariateDistribution Class Referenceabstract

Represents a probability distribution over a single variable. More...

+ Inheritance diagram for Meta.Numerics.Statistics.Distributions.UnivariateDistribution:

Public Member Functions

abstract double Moment (int r)
 Computes a raw moment of the distribution. More...
 
virtual double MomentAboutMean (int r)
 Computes a central moment of the distribution. More...
 
virtual double Cumulant (int r)
 Computes a cumulant of the distribution. More...
 

Properties

virtual double Mean [get]
 Gets the mean of the distribution. More...
 
virtual double Variance [get]
 Gets the variance of the distribution. More...
 
virtual double StandardDeviation [get]
 Gets the standard deviation of the distribution. More...
 
virtual double Skewness [get]
 Gets the skewness of the distribution. More...
 
virtual double ExcessKurtosis [get]
 Gets the excess kurtosis of the distribution. More...
 

Detailed Description

Represents a probability distribution over a single variable.

Member Function Documentation

abstract double Meta.Numerics.Statistics.Distributions.UnivariateDistribution.Moment ( int  r)
pure virtual

Computes a raw moment of the distribution.

Parameters
rThe order of the moment to compute.
Returns
The rth raw moment of the distribution.
See also
Moment

Implemented in Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.TriangularDistribution, Meta.Numerics.Statistics.Distributions.KuiperDistribution, Meta.Numerics.Statistics.Distributions.PoissonDistribution, Meta.Numerics.Statistics.Distributions.KolmogorovDistribution, Meta.Numerics.Statistics.Distributions.BetaDistribution, Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.DiscreteDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.GeometricDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution, Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.StudentDistribution, Meta.Numerics.Statistics.Distributions.BinomialDistribution, Meta.Numerics.Statistics.Distributions.BernoulliDistribution, Meta.Numerics.Statistics.Distributions.Distribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.ChiSquaredDistribution, Meta.Numerics.Statistics.Distributions.PearsonRDistribution, Meta.Numerics.Statistics.Distributions.UniformDistribution, and Meta.Numerics.Statistics.Distributions.WaldDistribution.

Referenced by Test.UnivariateDistributionTest.CumulantToCentralAndRaw(), Test.UnivariateDistributionTest.UnivariateDistributionMomentSums(), and Test.UnivariateDistributionTest.UnivariateDistributionRawMomentSpecialCases().

virtual double Meta.Numerics.Statistics.Distributions.UnivariateDistribution.MomentAboutMean ( int  r)
inlinevirtual

Computes a central moment of the distribution.

Parameters
rThe order of the moment to compute.
Returns
The rth central moment of the distribution.
See also
Moment

Reimplemented in Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.TriangularDistribution, Meta.Numerics.Statistics.Distributions.PoissonDistribution, Meta.Numerics.Statistics.Distributions.KuiperDistribution, Meta.Numerics.Statistics.Distributions.BetaDistribution, Meta.Numerics.Statistics.Distributions.KolmogorovDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.DiscreteDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.UniformDistribution, Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.StudentDistribution, Meta.Numerics.Statistics.Distributions.BinomialDistribution, Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution, Meta.Numerics.Statistics.Distributions.BernoulliDistribution, Meta.Numerics.Statistics.Distributions.Distribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, Meta.Numerics.Statistics.Distributions.ChiSquaredDistribution, Meta.Numerics.Statistics.Distributions.WaldDistribution, and Meta.Numerics.Statistics.Distributions.PearsonRDistribution.

References Meta.Numerics.Statistics.Distributions.MomentMath.RawToCentral().

Referenced by Test.UnivariateDistributionTest.CumulantToCentralAndRaw(), Test.UnivariateDistributionTest.UnivariateDistributionCentralMomentSpecialCases(), and Test.UnivariateDistributionTest.UnivariateDistributionMomentSums().

Property Documentation

virtual double Meta.Numerics.Statistics.Distributions.UnivariateDistribution.Skewness
get

Gets the skewness of the distribution.

The skewness of a distribution is a measurement of its asymmetry about its mean. It is the third moment about the mean, measured in units of the cubed standard deviation.

Referenced by Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DiscreteDistributionTest.DiscreteDistributionSkewness(), Test.DistributionTest.DistributionBase(), and Test.DistributionTest.DistributionSkewness().

virtual double Meta.Numerics.Statistics.Distributions.UnivariateDistribution.ExcessKurtosis
get

Gets the excess kurtosis of the distribution.

The excess kurtosis of a distribution is a measurement of the fatness of its tails relative to the normal distribution.

Referenced by Test.UnivariateDistributionTest.UnivariateDistributionExcessKurtosis().


The documentation for this class was generated from the following file: