ChiSquareDistribution Class

Generates central chi-square distributed random numbers.

Inheritance Hierarchy

SystemObject
  Altaxo.Calc.ProbabilityDistribution
    Altaxo.Calc.ProbabilityContinuousDistribution
      Altaxo.Calc.ProbabilityChiSquareDistribution

Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)

Syntax

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public class ChiSquareDistribution : ContinuousDistribution

The ChiSquareDistribution type exposes the following members.

Constructors

	Name	Description
	ChiSquareDistribution	Initializes a new instance of the ChiSquareDistribution class using the default generator.
	ChiSquareDistribution(Double)	Initializes a new instance of the ChiSquareDistribution class using the specified degrees of freedom and the default generator.
	ChiSquareDistribution(Generator)	Initializes a new instance of the ChiSquareDistribution class using the specified random number generator.
	ChiSquareDistribution(Double, Generator)	Initializes a new instance of the ChiSquareDistribution class using the specified degrees of freedom and random number generator.

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Properties

	Name	Description
	Alpha	Gets or sets the parameter alpha which is used for generation of chi-square distributed random numbers.
	CanReset	Gets a value indicating whether the random number distribution can be reset so that it produces the same random number sequence again. (Inherited from Distribution)
	Freedom	Gets the degrees of freedom of the distribution.
	Generator	Gets or sets a Generator object that can be used as the underlying random number generator. (Inherited from Distribution)
	Maximum	Gets the maximum possible value of distributed random numbers. (Overrides DistributionMaximum)
	Mean	Gets the mean of distributed random numbers. (Overrides DistributionMean)
	Median	Gets the median of distributed random numbers. (Overrides DistributionMedian)
	Minimum	Gets the minimum possible value of distributed random numbers. (Overrides DistributionMinimum)
	Mode	Gets the mode of distributed random numbers. (Overrides DistributionMode)
	Variance	Gets the variance of distributed random numbers. (Overrides DistributionVariance)

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Methods

	Name	Description
	CDF(Double)	Calculates the cumulative distribution function. (Overrides ContinuousDistributionCDF(Double))
	CDF(Double, Double)	Calculates the cumulative distribution function for the specified degrees of freedom.
	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)
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	Initialize	Initializes this instance with the specified degrees of freedom.
	IsValidAlpha	Determines whether the specified value is valid for parameter Alpha.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	NextDouble	Returns a distributed floating-point random number. (Overrides DistributionNextDouble)
	PDF(Double)	Calculates the probability density function. (Overrides ContinuousDistributionPDF(Double))
	PDF(Double, Double)	Calculates the probability density function for the specified degrees of freedom.
	Quantile(Double)	Calculates the quantile of the distribution function. (Overrides ContinuousDistributionQuantile(Double))
	Quantile(Double, Double)	Calculates the quantile function for the specified degrees of freedom.
	Reset	Resets the random number distribution so that it produces the same random number sequence again. (Inherited from Distribution)
	ToString	Returns a string that represents the current object. (Inherited from Object)

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Fields

	Name	Description
	F	Gets the degrees of freedom.
	gamma	Stores the underlying GammaDistribution used for number generation.
	generator	Stores a Generator object that can be used as the underlying random number generator. (Inherited from Distribution)

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Remarks

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Generates random deviates from a central chi-square distribution with
f degrees of freedom. f must be positive.
The density of this distribution is:


               -f/2   f/2-1  -x/2
              2      x      e
 p (x) dx =  --------------------- dx  for x > 0
  f               Gamma(f/2)

          =  0                         otherwise

The calculation uses the relation between the chi-square and gamma distributions:

 ChiSquare(f) = GammaDistribution(f/2, 1/2)

References:
   K. Behnen, G. Neuhaus, "Grundkurs Stochastik", Teubner Studienbuecher
   Mathematik, Teubner Verlag, Stuttgart, 1984.

Reference

Altaxo.Calc.Probability Namespace