NonCentralChiSquareDistribution Class

[SerializableAttribute]
public class NonCentralChiSquareDistribution : ContinuousDistribution

<SerializableAttribute>
Public Class NonCentralChiSquareDistribution
	Inherits ContinuousDistribution

[SerializableAttribute]
public ref class NonCentralChiSquareDistribution : public ContinuousDistribution

[<SerializableAttribute>]
type NonCentralChiSquareDistribution =  
    class
        inherit ContinuousDistribution
    end

The NonCentralChiSquareDistribution type exposes the following members.

	Name	Description
	NonCentralChiSquareDistribution	Constructs a new Chi Squared distribution.

	Name	Description
	DegreesOfFreedom	Gets the degrees of freedom for this chi-square distribution.
	Entropy	Gets the entropy of the distribution. (Inherited from Distribution.)
	InterQuartileRange	Returns the inter-quartile range of this distribution. (Inherited from ContinuousDistribution.)
	IsSymmetrical	Gets whether the distribution is known to be symmetrical around the mean. (Inherited from ContinuousDistribution.)
	IsUnimodal	Gets whether the distribution has one or more modes. (Inherited from ContinuousDistribution.)
	Kurtosis	Gets the kurtosis of the distribution. (Overrides DistributionKurtosis.)
	Mean	Gets the mean or expectation value of the distribution. (Overrides DistributionMean.)
	Median	Gets the median of the distribution. (Inherited from ContinuousDistribution.)
	Mode	Gets the mode of the distribution. (Inherited from ContinuousDistribution.)
	NonCentralityParameter	Gets the non-centrality parameter.
	NumberOfModes	Gets the number of modes of the distribution. (Inherited from ContinuousDistribution.)
	Skewness	Gets the skewness of the distribution. (Overrides DistributionSkewness.)
	StandardDeviation	Gets the standard deviation of the distribution. (Inherited from Distribution.)
	StatisticSymbol	Gets the common symbol to describe a statistic from the distribution. (Overrides DistributionStatisticSymbol.)
	Support	Gets the support of the distribution. (Overrides ContinuousDistributionSupport.)
	Variance	Gets the variance of the distribution. (Overrides DistributionVariance.)

	Name	Description
	Cdf	Evaluates the cumulative distribution function (CDF) of this distribution for the specified value. (Inherited from ContinuousDistribution.)
	DistributionFunction	Returns the value of the cumulative probability distribution function. (Overrides ContinuousDistributionDistributionFunction(Double).)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetAllModes	Returns an array that contains all the modes of the distribution. (Inherited from ContinuousDistribution.)
	GetExpectationValue(FuncDouble, Double)	Returns the expectation value of a function. (Inherited from ContinuousDistribution.)
	GetExpectationValue(FuncDouble, Double, Double, Double)	Returns the un-normalized expectation value of a function over the specified interval. (Inherited from ContinuousDistribution.)
	GetExpectedHistogram(Double, Double)	Gets a vector containing a histogram of the expected number of samples for a given total number of samples. (Inherited from ContinuousDistribution.)
	GetExpectedHistogram(IntervalIndexDouble, Double)	Gets a vector containing a histogram of the expected number of samples for a given total number of samples. (Inherited from ContinuousDistribution.)
	GetExpectedHistogram(Double, Double, Int32, Double)	Gets a vector whose bins contain the expected number of samples for a given total number of samples. (Inherited from ContinuousDistribution.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRandomSequence	Returns a sequence of random samples from the distribution. (Inherited from ContinuousDistribution.)
	GetRandomSequence(Random)	Returns a sequence of random samples from the distribution. (Inherited from ContinuousDistribution.)
	GetRandomSequence(Random, Int32)	Returns a sequence of random samples of the specified length from the distribution. (Inherited from ContinuousDistribution.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	HazardFunction	Returns the probability of failure at the specified value. (Inherited from ContinuousDistribution.)
	InverseCdf	Returns the inverse of the DistributionFunction(Double). (Inherited from ContinuousDistribution.)
	InverseDistributionFunction	Returns the inverse of the DistributionFunction(Double). (Overrides ContinuousDistributionInverseDistributionFunction(Double).)
	LeftTailProbability	Returns the probability that a sample from the distribution is less than the specified value. (Inherited from ContinuousDistribution.)
	LogProbabilityDensityFunction	Returns the logarithm of the probability density function (PDF) of this distribution for the specified value. (Inherited from ContinuousDistribution.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	MomentFunction	Returns the value of the moment function of the specified order. (Inherited from ContinuousDistribution.)
	Pdf	Returns the value of the probability density function (PDF) of this distribution for the specified value. (Inherited from ContinuousDistribution.)
	Probability	Returns the probability that a sample taken from the distribution lies inside the specified interval. (Inherited from ContinuousDistribution.)
	ProbabilityDensityFunction	Returns the value of the probability density function (PDF) of this distribution for the specified value. (Overrides ContinuousDistributionProbabilityDensityFunction(Double).)
	RightTailProbability	Returns the probability that a sample from the distribution is larger than the specified value. (Inherited from ContinuousDistribution.)
	Sample	Returns a random sample from the distribution. (Inherited from ContinuousDistribution.)
	Sample(Int32)	Returns a vector of random samples from the distribution. (Inherited from ContinuousDistribution.)
	Sample(Random)	Returns a random sample from the distribution. (Inherited from ContinuousDistribution.)
	Sample(Int32, Random)	Returns a vector of random samples from the distribution. (Inherited from ContinuousDistribution.)
	SampleInto(Random, IListDouble)	Fills a list with random numbers from the distribution. (Inherited from ContinuousDistribution.)
	SampleInto(Random, IListDouble, Int32, Int32)	Fills part of a list with random numbers from the distribution. (Inherited from ContinuousDistribution.)
	SurvivorDistributionFunction	Evaluates the survivor distribution function (SDF) of this distribution for the specified value. (Overrides ContinuousDistributionSurvivorDistributionFunction(Double).)
	ToString	Returns a string that represents the current object. (Overrides ObjectToString.)
	TwoTailedProbability	Returns the probability that a sample from the distribution deviates from the mean more than the specified value. (Inherited from ContinuousDistribution.)

The sum of the squares of n indepemdent normal variables with zero mean and unit variance has a chi-squared distribution with n degrees of freedom. This means it also describes the Variance of samples taken from a normal distribution.

From this last property, we can see the usefulness of the chi-squared distribution as a test of statistical significance. We can determine the likelihood of obtaining a sample that deviates from the expected value by a specified amount.

The sum of two or more variables that have a chi-squared distribution also has a chi-squared distribution. The number of degrees of freedom of the new distribution equals the sum of the degrees of freedom of the original distributions.

Reference