ChiSquaredDistribution Class

public sealed class ChiSquaredDistribution : ContinuousDistribution

Public NotInheritable Class ChiSquaredDistribution
	Inherits ContinuousDistribution

public ref class ChiSquaredDistribution sealed : public ContinuousDistribution

[<SealedAttribute>]
type ChiSquaredDistribution = 
    class
        inherit ContinuousDistribution
    end

Inheritance

Object    UnivariateDistribution    ContinuousDistribution    ChiSquaredDistribution

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 ν.

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.

Reference

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