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StableDistributionS0 Class

Represents a stable distribution in Nolan's S0 parametrization.
Inheritance Hierarchy

Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
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public class StableDistributionS0 : StableDistributionBase

The StableDistributionS0 type exposes the following members.

Constructors
 NameDescription
Public methodStableDistributionS0 Creates a new instance of this distribution with default parameters (alpha=1, beta=0) and the default generator.
Public methodStableDistributionS0(Generator) Creates a new instance of this distribution with default parameters (alpha=1, beta=0).
Public methodStableDistributionS0(Double, Double) Creates a new instance of this distribution with given parameters (alpha, beta) and the default random number generator.
Public methodStableDistributionS0(Double, Double, Double) Creates a new instance of this distribution with given parameters (alpha, beta, abe) and the default random number generator.
Public methodStableDistributionS0(Double, Double, Double, Double) Creates a new instance of this distribution with given parameters (alpha, beta, scale, location) and the default random number generator.
Public methodStableDistributionS0(Double, Double, Double, Double, Generator) Creates a new instance of this distribution with given parameters (alpha, beta, scale, location) and the provided random number generator.
Public methodStableDistributionS0(Double, Double, Double, Double, Double) Creates a new instance of this distribution with given parameters (alpha, beta, abe, scale, location) and the default random number generator.
Public methodStableDistributionS0(Double, Double, Double, Double, Double, Generator) Creates a new instance of this distribution with given parameters (alpha, beta, abe, scale, location) and the provided random number generator.
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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 propertyMaximum
(Overrides StableDistributionBaseMaximum)
Public propertyMean
(Overrides StableDistributionBaseMean)
Public propertyMedian
(Overrides StableDistributionBaseMedian)
Public propertyMinimum
(Overrides StableDistributionBaseMinimum)
Public propertyMode
(Overrides StableDistributionBaseMode)
Public propertyVariance
(Overrides StableDistributionBaseVariance)
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Methods
 NameDescription
Public methodCDF(Double)
(Overrides ContinuousDistributionCDF(Double))
Public methodStatic memberCDF(Double, Double, Double) 
Public methodStatic memberCDF(Double, Double, Double, Double) 
Public methodStatic memberCDF(Double, Double, Double, Double, Double) 
Public methodStatic memberCDF(Double, Double, Double, Object, Double) 
Public methodStatic memberCDF(Double, Double, Double, Double, Double, Double) 
Public methodStatic memberCDF(Double, Double, Double, Double, Double, Object, Double) 
Public methodStatic memberCDF(Double, Double, Double, Double, Double, Double, Object, Double) 
Public methodStatic memberCDFMethodAlphaOne 
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 memberGetAgt1GpParameter 
Public methodStatic memberGetAlt1GnParameter 
Public methodStatic memberGetAlt1GpParameter 
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Public methodInitialize Updates the helper variables that store intermediate results for generation of exponential distributed random numbers.
Public methodStatic memberIsValidAlpha 
Public methodStatic memberIsValidBeta 
Public methodStatic memberIsValidMu 
Public methodStatic memberIsValidSigma 
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodNextDouble
(Overrides StableDistributionBaseNextDouble)
Public methodPDF(Double)
(Overrides ContinuousDistributionPDF(Double))
Public methodStatic memberPDF(Double, Double, Double) 
Public methodStatic memberPDF(Double, Double, Double, Double, Double) 
Public methodStatic memberPDF(Double, Double, Double, Object, Double) 
Public methodStatic memberPDF(Double, Double, Double, Double, Object, Double) 
Public methodStatic memberPDF(Double, Double, Double, Double, Double, Object, Double) 
Public methodStatic memberPDF(Double, Double, Double, Double, Double, Double, Object, Double) 
Public methodStatic memberPDFMethodAlphaOne 
Public methodQuantile(Double)
(Overrides ContinuousDistributionQuantile(Double))
Public methodStatic memberQuantile(Double, Double, Double) 
Public methodStatic memberQuantile(Double, Double, Double, Double) 
Public methodStatic memberQuantile(Double, Double, Double, Double, Object, Double) 
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)
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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
The characteristic function in Nolan's S0 parametrization is:
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log(phi(t))= -scale^alpha |t|^alpha (1+i beta Sign(t) Tan(pi alpha/2) (|scale t|^(1-alpha)-1)) + i location t              (for alpha not equal to 1)
and
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log(phi(t)) = -scale |t| (1+i beta Sign(t) (2/pi) Log(scale |t|)) + i location t  (for alpha equal to 1)

Reference: J.P.Nolan, Numerical calculation of stable densities and distribution functions. Communication is statistics - Stochastic models, 13, 759-774, 1999

Reference: S.Borak, W.Härdle, R.Weron, Stable distributions. SFB 649 Discussion paper 2005-2008, http://sfb649.wiwi.hu-berlin.de, ISSN 1860-5664

If you are interested in accurate calculations when beta is close to 1 or -1, you should use those functions which allow you to provide the parameter abe. This helps specifying beta with higher accuracy close to +1 or -1. For instance, by using abe=1E-30 and beta=1, it is possible to specify beta=1-1E-30, which is impossible otherwise since with the 64-bit representation of numbers.

See Also