ChiSquaredDistribution Class
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ChiSquaredDistribution Class

Represents a χ2 distribution.
Inheritance Hierarchy

Namespace:  Meta.Numerics.Statistics.Distributions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.0.5.0 (4.0.5.0)
Syntax
public sealed class ChiSquaredDistribution : ContinuousDistribution

The ChiSquaredDistribution type exposes the following members.

Constructors
  NameDescription
Public methodChiSquaredDistribution
Initializes a new χ2 distribution.
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Properties
  NameDescription
Public propertyDegreesOfFreedom
Gets the number of degrees of freedom ν of the distribution.
Public propertyExcessKurtosis
Gets the excess kurtosis of the distribution.
(Overrides UnivariateDistributionExcessKurtosis.)
Public propertyMean
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)
Public propertyMedian
Gets the median of the distribution.
(Overrides ContinuousDistributionMedian.)
Public propertySkewness
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)
Public propertyStandardDeviation
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.)
Public propertySupport
Gets the interval over which the distribution is non-vanishing.
(Overrides ContinuousDistributionSupport.)
Public propertyVariance
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.)
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Methods
  NameDescription
Public methodCentralMoment
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)
Public methodCumulant
Computes a cumulant of the distribution.
(Overrides UnivariateDistributionCumulant(Int32).)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodExpectationValue
Computes the expectation value of the given function.
(Inherited from ContinuousDistribution.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRandomValue
Generates a random variate.
(Inherited from ContinuousDistribution.)
Public methodGetRandomValues
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazard
Computes the hazard function.
(Inherited from ContinuousDistribution.)
Public methodInverseLeftProbability
Returns the point at which the cumulative distribution function attains a given value.
(Overrides ContinuousDistributionInverseLeftProbability(Double).)
Public methodInverseRightProbability
Returns the point at which the right probability function attains the given value.
(Inherited from ContinuousDistribution.)
Public methodLeftProbability
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)
Public methodProbabilityDensity
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)
Public methodRawMoment
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)
Public methodRightProbability
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

A chi squared distribution is an asymmetrical distribution ranging from zero to infinity with a peak near its number of degrees of freedom ν. It is a one-parameter distribution determined entirely by the parameter nu.

The figure above shows the χ2 distribution for ν = 6, as well as the normal distribution with equal mean and variance for reference.

The sum of the squares of ν independent standard-normal distributed variables is distributed as χ2 with ν degrees of freedom.

The χ2 distribution appears in least-squares fitting as the distribution of the sum-of-squared-deviations under the null hypothesis that the model explains the data. For example, the goodness-of-fit statistic returned by the model our model fitting methods (FitToFunction(FuncDouble, T, Double, Double), FitToLinearFunction(FuncT, Double), FitToLine, and others) follows a χ2 distribution.

See Also