ChiSquaredDistribution Class 
Namespace: Meta.Numerics.Statistics.Distributions
The ChiSquaredDistribution type exposes the following members.
Name  Description  

ChiSquaredDistribution 
Initializes a new χ^{2} distribution.

Name  Description  

DegreesOfFreedom 
Gets the number of degrees of freedom ν of the distribution.
 
ExcessKurtosis 
Gets the excess kurtosis of the distribution.
(Overrides UnivariateDistributionExcessKurtosis.)  
Mean 
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)  
Median 
Gets the median of the distribution.
(Overrides ContinuousDistributionMedian.)  
Skewness 
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)  
StandardDeviation 
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.)  
Support 
Gets the interval over which the distribution is nonvanishing.
(Overrides ContinuousDistributionSupport.)  
Variance 
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.) 
Name  Description  

CentralMoment 
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)  
Cumulant 
Computes a cumulant of the distribution.
(Overrides UnivariateDistributionCumulant(Int32).)  
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
ExpectationValue 
Computes the expectation value of the given function.
(Inherited from ContinuousDistribution.)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetRandomValue 
Generates a random variate.
(Inherited from ContinuousDistribution.)  
GetRandomValues 
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
Hazard 
Computes the hazard function.
(Inherited from ContinuousDistribution.)  
InverseLeftProbability 
Returns the point at which the cumulative distribution function attains a given value.
(Overrides ContinuousDistributionInverseLeftProbability(Double).)  
InverseRightProbability 
Returns the point at which the right probability function attains the given value.
(Inherited from ContinuousDistribution.)  
LeftProbability 
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)  
ProbabilityDensity 
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)  
RawMoment 
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)  
RightProbability 
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)  
ToString  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 oneparameter distribution determined entirely by the parameter ν.
The figure above shows the χ^{2} 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 standardnormal distributed variables is distributed as χ^{2} with ν degrees of freedom.
The χ^{2} distribution appears in leastsquares fitting as the distribution of the sumofsquareddeviations under the null hypothesis that the model explains the data. For example, the goodnessoffit statistic returned by the model our model fitting methods (FitToFunction(FuncDouble, T, Double, Double), FitToLinearFunction(FuncT, Double), FitToLine, and others) follows a χ^{2} distribution.