IGLib
1.7.2
The IGLib base library EXTENDED - with other lilbraries and applications.
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Represents all continuous, univariate probability distribution. More...
Public Member Functions | |||
abstract double | ProbabilityDensity (double x) | ||
Returns the probability density at the given point. More... | |||
virtual double | LeftProbability (double x) | ||
Returns the cumulative probability to the left of (below) the given point. More... | |||
virtual double | RightProbability (double x) | ||
Return the cumulative probability to the right of (above) the given point. More... | |||
virtual double | InverseLeftProbability (double P) | ||
Returns the point at which the cumulative distribution function attains a given value. More... | |||
virtual double | InverseRightProbability (double Q) | ||
Returns the point at which the right probability function attains the given value. More... | |||
override double | Moment (int r) | ||
Computes a raw moment of the distribution.
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override double | MomentAboutMean (int r) | ||
Computes a central moment of the distribution.
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virtual double | ExpectationValue (Func< double, double > f) | ||
Computes the expectation value of the given function. More... | |||
virtual double | GetRandomValue (Random rng) | ||
Returns a random value. More... | |||
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virtual double | Cumulant (int r) | ||
Computes a cumulant of the distribution. More... | |||
Properties | |
virtual double | Median [get] |
Gets the median of the distribution. More... | |
virtual Interval | Support [get] |
Gets the interval over which the distribution is nonvanishing. More... | |
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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 all continuous, univariate probability distribution.
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pure virtual |
Returns the probability density at the given point.
x | The reference point. |
The probability density function (PDF) gives the relative probability of obtaining different values.
Implemented in Test.TestDistribution, Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.WaldDistribution, Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution, Meta.Numerics.Statistics.Distributions.BetaDistribution, Meta.Numerics.Statistics.Distributions.KuiperDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.TriangularDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, Meta.Numerics.Statistics.Distributions.ChiSquaredDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.StudentDistribution, Meta.Numerics.Statistics.Distributions.UniformDistribution, Meta.Numerics.Statistics.Distributions.PearsonRDistribution, and Meta.Numerics.Statistics.Distributions.KolmogorovDistribution.
Referenced by Test.DistributionTest.DistributionCentralMomentIntegral(), Test.DistributionTest.DistributionMeanIntegral(), Test.DistributionTest.DistributionProbabilityIntegral(), Test.DistributionTest.DistributionProbabilityTestHelper(), Test.DistributionTest.DistributionRawMomentIntegral(), Test.DistributionTest.DistributionVarianceIntegral(), Test.DistributionTest.OutsideDistributionSupport(), and Test.SampleTest.TestMoments().
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inlinevirtual |
Returns the cumulative probability to the left of (below) the given point.
x | The reference point. |
The left probability function is commonly called the cumulative distribution function (CDF).
Reimplemented in Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.WaldDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, Meta.Numerics.Statistics.Distributions.BetaDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.TriangularDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.PearsonRDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.KolmogorovDistribution, Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution, Meta.Numerics.Statistics.Distributions.ChiSquaredDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.StudentDistribution, Meta.Numerics.Statistics.Distributions.UniformDistribution, and Meta.Numerics.Statistics.Distributions.KuiperDistribution.
References Meta.Numerics.Interval.FromEndpoints(), and Meta.Numerics.Analysis.FunctionMath.Integrate().
Referenced by Meta.Numerics.Statistics.Sample.ComputeDStatistics(), Test.DistributionTest.DistributionProbabilityIntegral(), Test.DistributionTest.DistributionProbabilityTestHelper(), Test.DistributionTest.OutsideDistributionSupport(), and FutureTest.FutureTest.TestNormalOrderStatistic().
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inlinevirtual |
Return the cumulative probability to the right of (above) the given point.
x | The reference point. |
In survival analysis, the right probability function is commonly called the survival function, because it gives the fraction of the population remaining after the given time.
Reimplemented in Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, Meta.Numerics.Statistics.Distributions.BetaDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.TriangularDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.KolmogorovDistribution, Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.ChiSquaredDistribution, Meta.Numerics.Statistics.Distributions.StudentDistribution, and Meta.Numerics.Statistics.Distributions.KuiperDistribution.
Referenced by Test.DistributionTest.DistributionProbabilityIntegral(), Test.DistributionTest.DistributionProbabilityTestHelper(), Test.DistributionTest.OutsideDistributionSupport(), and FutureTest.FutureTest.TestNormalOrderStatistic().
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inlinevirtual |
Returns the point at which the cumulative distribution function attains a given value.
P | The left cumulative probability P, which must lie between 0 and 1. |
The inverse left probability is commonly called the quantile function. Given a quantile, it tells which variable value is the lower border of that quantile.
ArgumentOutOfRangeException | P lies outside [0,1]. |
Reimplemented in Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.BetaDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, Meta.Numerics.Statistics.Distributions.TriangularDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.ChiSquaredDistribution, Meta.Numerics.Statistics.Distributions.StudentDistribution, and Meta.Numerics.Statistics.Distributions.UniformDistribution.
References Meta.Numerics.Analysis.FunctionMath.FindZero().
Referenced by Test.MultivariateSampleTest.CreateMultivariateNormalSample(), Test.DistributionTest.DistributionInvalidProbabilityInput(), Test.DistributionTest.DistributionMedian(), Test.DistributionTest.DistributionMonotonicity(), Test.DistributionTest.FisherTest(), Test.MultivariateSampleTest.MultivariateLinearRegressionTest(), Test.SampleTest.SampleComparisonTest(), Test.DistributionTest.StudentTest(), Test.DistributionTest.StudentTest2(), Test.RandomTest.TimeGammaGenerators(), and Test.RandomTest.TimeNormalGenerators().
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inlinevirtual |
Returns the point at which the right probability function attains the given value.
Q | The right cumulative probability, which must lie between 0 and 1. |
Reimplemented in Meta.Numerics.Statistics.Distributions.BetaDistribution, Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, and Meta.Numerics.Statistics.Distributions.UniformDistribution.
References Meta.Numerics.Analysis.FunctionMath.FindZero().
Referenced by FutureTest.FutureTest.TestInverseKS().
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inlinevirtual |
Computes a raw moment of the distribution.
r | The order of the moment to compute. |
Implements Meta.Numerics.Statistics.Distributions.UnivariateDistribution.
Reimplemented in Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.TriangularDistribution, Meta.Numerics.Statistics.Distributions.KuiperDistribution, Meta.Numerics.Statistics.Distributions.KolmogorovDistribution, Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.StudentDistribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.PearsonRDistribution, Meta.Numerics.Statistics.Distributions.UniformDistribution, and Meta.Numerics.Statistics.Distributions.WaldDistribution.
References Meta.Numerics.MoreMath.Pow().
Referenced by FutureTest.FutureTest.CumulantTest(), Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DistributionTest.DistributionMomentTranslations(), Test.DistributionTest.DistributionRawMomentIntegral(), Test.SampleTest.SampleMoments(), and Test.SampleTest.TestMoments().
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inlinevirtual |
Computes a central moment of the distribution.
r | The order of the moment to compute. |
Reimplemented from Meta.Numerics.Statistics.Distributions.UnivariateDistribution.
Reimplemented in Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.TriangularDistribution, Meta.Numerics.Statistics.Distributions.KuiperDistribution, Meta.Numerics.Statistics.Distributions.KolmogorovDistribution, Meta.Numerics.Statistics.Distributions.FisherDistribution, Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.WeibullDistribution, Meta.Numerics.Statistics.Distributions.LogisticDistribution, Meta.Numerics.Statistics.Distributions.UniformDistribution, Meta.Numerics.Statistics.Distributions.GumbelDistribution, Meta.Numerics.Statistics.Distributions.ParetoDistribution, Meta.Numerics.Statistics.Distributions.StudentDistribution, Meta.Numerics.Statistics.Distributions.ExponentialDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.WaldDistribution, and Meta.Numerics.Statistics.Distributions.PearsonRDistribution.
References Meta.Numerics.MoreMath.Pow().
Referenced by FutureTest.FutureTest.CumulantTest(), Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DistributionTest.DistributionCentralMomentIntegral(), Test.DistributionTest.DistributionMomentTranslations(), Test.DistributionTest.DistributionSkewness(), Test.SampleTest.SampleMoments(), Test.SampleTest.TestMoments(), and Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest().
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inlinevirtual |
Computes the expectation value of the given function.
f | The function. |
References Meta.Numerics.Analysis.FunctionMath.Integrate().
Referenced by Test.DistributionTest.TransformedBetaMoments().
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inlinevirtual |
Returns a random value.
rng | A random number generator. |
Note that the random number generator rng will be advanced by this method. The next call to its generator methods will not give the same value as it would had it not been passed to this method.
Reimplemented in Meta.Numerics.Statistics.Distributions.GammaDistribution, Meta.Numerics.Statistics.Distributions.BetaDistribution, Meta.Numerics.Statistics.Distributions.NormalDistribution, Meta.Numerics.Statistics.Distributions.LognormalDistribution, Meta.Numerics.Statistics.Distributions.CauchyDistribution, and Meta.Numerics.Statistics.Distributions.StudentDistribution.
Referenced by Test.SampleTest.AnovaDistribution(), Test.BivariateSampleTest.BivariateLinearRegression(), Test.BivariateSampleTest.BivariatePolynomialRegression(), Test.BugTests.Bug7788(), Test.SampleTest.CreateSample(), Test.DistributionTest.FisherInversion(), Test.DistributionTest.InverseGaussianSummation(), Test.MultivariateSampleTest.MultivariateMoments(), Test.SampleTest.SignTestDistribution(), Test.SampleTest.TTestDistribution(), Test.DistributionTest.UniformOrderStatistics(), Test.SampleTest.WaldFitUncertainties(), and Test.SampleTest.ZTestDistribution().
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get |
Gets the median of the distribution.
The median is the point with equal integrated probability above and below, i.e. with P(x1) = 0.5.
Referenced by Test.BugTests.Bug7788(), Test.DistributionTest.DistributionBase(), Test.DistributionTest.DistributionCentralInequality(), Test.DistributionTest.DistributionMedian(), and Test.SampleTest.SignTestDistribution().
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get |
Gets the interval over which the distribution is nonvanishing.
Referenced by Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DistributionTest.DistributionCentralMomentIntegral(), Test.DistributionTest.DistributionMeanIntegral(), Test.DistributionTest.DistributionProbabilityIntegral(), Test.DistributionTest.DistributionRawMomentIntegral(), Test.DistributionTest.DistributionVarianceIntegral(), Test.DistributionTest.OutsideDistributionSupport(), and Test.SampleTest.TestMoments().