ChiSquareDistribution Class

Generates central chi-square distributed random numbers.

Inheritance Hierarchy

SystemObject
  Altaxo.Calc.Probability.OldProbabilityDistribution
    Altaxo.Calc.Probability.OldGammaDistribution
      Altaxo.Calc.Probability.OldChiSquareDistribution

Namespace: Altaxo.Calc.Probability.Old
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3572.0 (4.8.3572.0)

Syntax

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public class ChiSquareDistribution : GammaDistribution

The ChiSquareDistribution type exposes the following members.

Constructors

	Name	Description
	ChiSquareDistribution(Double)	Initializes a new instance of the ChiSquareDistribution class.
	ChiSquareDistribution(Double, RandomGenerator)	Initializes a new instance of the ChiSquareDistribution class.

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Properties

	Name	Description
	Freedom	Gets the degrees of freedom.
	Generator	Returns the random generator used by the distribution to generate the random values. (Inherited from ProbabilityDistribution)
	Location	Gets the inverse scale parameter of the distribution. (Inherited from GammaDistribution)
	Order	Gets the shape parameter of the distribution. (Inherited from GammaDistribution)

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Methods

	Name	Description
	CDF	Gives the cumulative probability at x. (Overrides GammaDistributionCDF(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)
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	Initialize	Initializes the parameters for the gamma distribution. (Inherited from GammaDistribution)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	NextDouble	Generates the next chi-square distributed random value.
	PDF	Gives the probability density at x. (Overrides GammaDistributionPDF(Double))
	Quantile	Gives the pth quantile of the distribution. (Overrides GammaDistributionQuantile(Double))
	ToString	Returns a string that represents the current object. (Inherited from Object)

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Fields

	Name	Description
	_invTheta	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	algorithmGD	Cached flag indicating whether algorithm GD is used. (Inherited from GammaDistribution)
	alpha	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	b	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	c	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	d	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	exponentialDistribution	Cached exponential helper distribution used by the gamma distribution implementation. (Inherited from GammaDistribution)
	F	Cached degrees of freedom.
	generator	Pointer to generator. (Inherited from ProbabilityDistribution)
	normalDistribution	Cached helper distributions used by the gamma distribution implementation. (Inherited from GammaDistribution)
	q0	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	r	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	s	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	s2	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	scale	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)
	si	Cached coefficients used by the gamma distribution implementation. (Inherited from GammaDistribution)

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Remarks


             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 chi-square and gamma distribution:
            
              ChiSquare(f) = GammaDistribution(f/2,1/2)
            
             References:
                K. Behnen, G. Neuhaus, "Grundkurs Stochastik", Teubner Studienbücher
                Mathematik, Teubner Verlag, Stuttgart, 1984.

Reference

Altaxo.Calc.Probability.Old Namespace