IGLib
1.7.2
The IGLib base library EXTENDED - with other lilbraries and applications.
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Represents a probability distribution over a single variable. More...
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... | |
Represents a probability distribution over a single variable.
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pure virtual |
Computes a raw moment of the distribution.
r | The order of the moment to compute. |
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().
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inlinevirtual |
Computes a central moment of the distribution.
r | The order of the moment to compute. |
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().
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inlinevirtual |
Computes a cumulant of the distribution.
r | The index of the cumulant to compute. |
Reimplemented in Meta.Numerics.Statistics.Distributions.PoissonDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.UniformDistribution, Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.ChiSquaredDistribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, and Meta.Numerics.Statistics.Distributions.WaldDistribution.
References Meta.Numerics.Statistics.Distributions.MomentMath.CentralToCumulant().
Referenced by Test.UnivariateDistributionTest.CumulantToCentralAndRaw(), FutureTest.FutureTest.TestCumulant2(), Test.DistributionTest.TimeOperations(), Test.UnivariateDistributionTest.UnivariantDistributionCumulantSpecialCases(), and Test.UnivariateDistributionTest.UnivariateDistributionExcessKurtosis().
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get |
Gets the mean of the distribution.
Referenced by Test.BivariateSampleTest.BivariateLinearRegressionGoodnessOfFitDistribution(), Test.BugTests.Bug7788(), Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DistributionTest.DistributionBase(), Test.DistributionTest.DistributionCentralInequality(), Test.DistributionTest.DistributionCentralMomentIntegral(), Test.DistributionTest.DistributionMeanIntegral(), Test.DistributionTest.DistributionMomentTranslations(), Test.DistributionTest.DistributionVarianceIntegral(), Test.NullDistributionTests.KendallNullDistributionTest(), Test.NullDistributionTests.KolmogorovNullDistributionTest(), Test.NullDistributionTests.KuiperNullDistributionTest(), Test.SampleTest.NormalFit(), Test.SampleTest.SampleKolmogorovSmirnovTest(), Test.SampleTest.SampleKuiperTest(), Test.SampleTest.SampleMoments(), Test.NullDistributionTests.SpearmanNullDistributionTest(), Test.DistributionTest.StudentTest(), Test.SampleTest.TestMoments(), Test.SampleTest.TTestDistribution(), Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest(), Test.UnivariateDistributionTest.UnivariantDistributionCumulantSpecialCases(), Test.UnivariateDistributionTest.UnivariateDistributionCentralMomentSpecialCases(), Test.UnivariateDistributionTest.UnivariateDistributionRawMomentSpecialCases(), and Test.SampleTest.ZTestDistribution().
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get |
Gets the variance of the distribution.
Referenced by Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DiscreteDistributionTest.DiscreteDistributionBase(), Test.DiscreteDistributionTest.DiscreteDistributionVariance(), Test.DistributionTest.DistributionVarianceIntegral(), Test.NullDistributionTests.KendallNullDistributionTest(), Test.NullDistributionTests.KolmogorovNullDistributionTest(), Test.NullDistributionTests.KuiperNullDistributionTest(), Test.NullDistributionTests.SpearmanNullDistributionTest(), Test.UnivariateDistributionTest.UnivariantDistributionCumulantSpecialCases(), and Test.UnivariateDistributionTest.UnivariateDistributionCentralMomentSpecialCases().
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get |
Gets the standard deviation of the distribution.
Referenced by Test.BugTests.Bug7788(), Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DiscreteDistributionTest.DiscreteDistributionRandomValues(), Test.DistributionTest.DistributionBase(), Test.DistributionTest.DistributionCentralInequality(), Test.DistributionTest.DistributionVarianceIntegral(), Test.SampleTest.NormalFit(), Test.SampleTest.SampleKolmogorovSmirnovTest(), Test.SampleTest.SampleKuiperTest(), Test.SampleTest.SampleMoments(), Test.SampleTest.SignTestDistribution(), Test.SampleTest.TestMoments(), Test.SampleTest.TTestDistribution(), Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest(), and Test.SampleTest.ZTestDistribution().
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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().
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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().