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
Thetype exposes the following members.
Gets the number of degrees of freedom ν of the distribution.
Gets the excess kurtosis of the distribution.(Overrides UnivariateDistributionExcessKurtosis.)
Gets the mean of the distribution.(Overrides UnivariateDistributionMean.)
Gets the median of the distribution.(Overrides ContinuousDistributionMedian.)
Gets the skewness of the distribution.(Overrides UnivariateDistributionSkewness.)
Gets the standard deviation of the distribution.(Inherited from UnivariateDistribution.)
Gets the interval over which the distribution is non-vanishing.(Overrides ContinuousDistributionSupport.)
Gets the variance of the distribution.(Overrides UnivariateDistributionVariance.)
Computes a central moment of the distribution.(Overrides ContinuousDistributionCentralMoment(Int32).)
Computes a cumulant of the distribution.(Overrides UnivariateDistributionCumulant(Int32).)
Determines whether the specified object is equal to the current object.(Inherited from Object.)
Computes the expectation value of the given function.(Inherited from ContinuousDistribution.)
Serves as the default hash function.(Inherited from Object.)
Generates a random variate.(Inherited from ContinuousDistribution.)
Generates the given number of random variates.(Inherited from ContinuousDistribution.)
Gets the Type of the current instance.(Inherited from Object.)
Computes the hazard function.(Inherited from ContinuousDistribution.)
Returns the point at which the cumulative distribution function attains a given value.(Overrides ContinuousDistributionInverseLeftProbability(Double).)
Returns the point at which the right probability function attains the given value.(Inherited from ContinuousDistribution.)
Returns the cumulative probability to the left of (below) the given point.(Overrides ContinuousDistributionLeftProbability(Double).)
Returns the probability density at the given point.(Overrides ContinuousDistributionProbabilityDensity(Double).)
Computes a raw moment of the distribution.(Overrides ContinuousDistributionRawMoment(Int32).)
Returns the cumulative probability to the right of (above) the given point.(Overrides ContinuousDistributionRightProbability(Double).)
Returns a string that represents the current object.(Inherited from Object.)
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.