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StableDistributionSymmetric Class

Represents a symmetric stable distribution in Zolotarev's parametrization.
Inheritance Hierarchy

Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
public class StableDistributionSymmetric : StableDistributionBase

The StableDistributionSymmetric type exposes the following members.

Constructors
 NameDescription
Public methodStableDistributionSymmetricInitializes a new instance of the StableDistributionSymmetric class
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Properties
 NameDescription
Public propertyCanReset 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)
Public propertyGenerator Gets or sets a Generator object that can be used as underlying random number generator.
(Inherited from Distribution)
Public propertyMaximumGets the maximum possible value of distributed random numbers.
(Inherited from StableDistributionBase)
Public propertyMeanGets the mean of distributed random numbers.
(Inherited from StableDistributionBase)
Public propertyMedianGets the median of distributed random numbers.
(Inherited from StableDistributionBase)
Public propertyMinimumGets the minimum possible value of distributed random numbers.
(Inherited from StableDistributionBase)
Public propertyModeGets the mode of distributed random numbers.
(Inherited from StableDistributionBase)
Public propertyVarianceGets the variance of distributed random numbers.
(Inherited from StableDistributionBase)
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Methods
 NameDescription
Public methodStatic memberCCDF(Double, Double) 
Public methodStatic memberCCDF(Double, Double, Object, Double) 
Public methodCDF(Double)Calculates the cumulative distribution function.
(Inherited from ContinuousDistribution)
Public methodStatic memberCDF(Double, Double) 
Public methodStatic memberCDF(Double, Double, Object, Double) 
Public methodEqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Protected methodGenerateAsymmetricCaseS1 Generates random variates in S1 Parametrization
(Inherited from StableDistributionBase)
Protected methodGenerateAsymmetricCaseS1_AEq1
(Inherited from StableDistributionBase)
Protected methodGenerateAsymmetricCaseS1_ANe1
(Inherited from StableDistributionBase)
Protected methodGenerateSymmetricCase
(Inherited from StableDistributionBase)
Public methodStatic memberGetAgt1GnParameter 
Public methodStatic memberGetAlt1GnParameter 
Public methodStatic memberGetAlt1GpParameterByGamma 
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodNextDoubleReturns a distributed floating point random number.
(Inherited from StableDistributionBase)
Public methodPDF(Double)Calculates the probability density function.
(Inherited from ContinuousDistribution)
Public methodStatic memberPDF(Double, Double) 
Public methodStatic memberPDF(Double, Double, Object, Double) Calculates the probability density using either series expansion for small or big arguments, or a integration in the intermediate range.
Public methodStatic memberPDFAlphaBetween01And02 Calculation of the PDF if alpha is inbetween 0.1 and 0.2. For small x (1E-16), the accuracy at alpha=0.1 is only 1E-7.
Public methodStatic memberPDFAlphaBetween02And099 Calculation of the PDF if alpha is inbetween 0.2 and 0.99. For small x (1E-8), the accuracy at alpha=0.2 is only 1E-7.
Public methodStatic memberPDFAlphaBetween099And101 Calculation of the PDF if alpha is inbetween 0.99 and 1.01.
Public methodStatic memberPDFAlphaBetween101And199999 Calculation of the PDF if alpha is inbetween 0.2 and 0.99. For small x (1E-8), the accuracy at alpha=0.2 is only 1E-7.
Public methodStatic memberPDFAlphaBetween199999And2 Calculation of the PDF if alpha is inbetween 1.99999 and 2. For small x ( max 7), the asymptotic expansion is used. For big x, the maximum value resulting from direct integration and series expansion w.r.t. alpha is used.
Public methodStatic memberPDFIntegration 
Public methodStatic memberPDFSeriesBigX Imaginary part of the Fourier transformed derivative of the Kohlrausch function for high frequencies.
Public methodStatic memberPDFSeriesSmallX Imaginary part of the Fourier transformed derivative of the Kohlrausch function for low frequencies.
Public methodStatic memberPDFSeriesSmallXSmallAlpha Imaginary part of the Fourier transformed derivative of the Kohlrausch function for low frequencies, and beta<=1/20..
Public methodStatic memberPDFTaylorExpansionAroundAlphaOne 
Public methodQuantile(Double)Calculates the quantile of the distribution function.
(Inherited from ContinuousDistribution)
Public methodStatic memberQuantile(Double, Double) 
Public methodStatic memberQuantileCCDF 
Public methodReset Resets the random number distribution, so that it produces the same random number sequence again.
(Inherited from Distribution)
Public methodToStringReturns a string that represents the current object.
(Inherited from Object)
Public methodStatic memberXZCDF(Double, Double) 
Public methodStatic memberXZCDF(Double, Double, Object, Double) 
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Fields
 NameDescription
Protected field_gen_BHelper variables used for generating the random values.
(Inherited from StableDistributionBase)
Protected field_gen_SHelper variables used for generating the random values.
(Inherited from StableDistributionBase)
Protected field_gen_ScaleHelper variables used for generating the random values.
(Inherited from StableDistributionBase)
Protected field_gen_tHelper variables used for generating the random values.
(Inherited from StableDistributionBase)
Protected fieldgenerator Stores a Generator object that can be used as underlying random number generator.
(Inherited from Distribution)
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Remarks

References:

[1] Matsui M., Takemura A.: "Some Improvements in Numerical Evaluation of Symmetric Stable Densities and its Derivatives", Discussion Paper, CIRJE-F-292, Tokio, August 2004

See Also