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

Represents all continuous, univariate probability distribution. More...

+ Inheritance diagram for Meta.Numerics.Statistics.Distributions.Distribution:
+ Collaboration diagram for Meta.Numerics.Statistics.Distributions.Distribution:

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.
Parameters
rThe order of the moment to compute.
Returns
The rth raw moment of the distribution.
See also
Moment
More...
 
override double MomentAboutMean (int r)
 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
More...
 
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...
 
- Public Member Functions inherited from Meta.Numerics.Statistics.Distributions.UnivariateDistribution
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...
 
- Properties inherited from Meta.Numerics.Statistics.Distributions.UnivariateDistribution
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 all continuous, univariate probability distribution.

Member Function Documentation

abstract double Meta.Numerics.Statistics.Distributions.Distribution.ProbabilityDensity ( double  x)
pure virtual

Returns the probability density at the given point.

Parameters
xThe reference point.
Returns
The probability density p(x).

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().

virtual double Meta.Numerics.Statistics.Distributions.Distribution.LeftProbability ( double  x)
inlinevirtual

Returns the cumulative probability to the left of (below) the given point.

Parameters
xThe reference point.
Returns
The integrated probability to obtain a result below 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().

virtual double Meta.Numerics.Statistics.Distributions.Distribution.RightProbability ( double  x)
inlinevirtual

Return the cumulative probability to the right of (above) the given point.

Parameters
xThe reference point.
Returns
The integrated probability 1-P(x1) to obtain a result above 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().

virtual double Meta.Numerics.Statistics.Distributions.Distribution.InverseLeftProbability ( double  P)
inlinevirtual

Returns the point at which the cumulative distribution function attains a given value.

Parameters
PThe left cumulative probability P, which must lie between 0 and 1.
Returns
The value x at which LeftProbability equals P.

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.

Exceptions
ArgumentOutOfRangeExceptionP 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().

override double Meta.Numerics.Statistics.Distributions.Distribution.Moment ( int  r)
inlinevirtual

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

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().

override double Meta.Numerics.Statistics.Distributions.Distribution.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 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().

virtual double Meta.Numerics.Statistics.Distributions.Distribution.ExpectationValue ( Func< double, double >  f)
inlinevirtual

Computes the expectation value of the given function.

Parameters
fThe function.
Returns
The expectation value of the function.

References Meta.Numerics.Analysis.FunctionMath.Integrate().

Referenced by Test.DistributionTest.TransformedBetaMoments().

Property Documentation

virtual double Meta.Numerics.Statistics.Distributions.Distribution.Median
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().


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