Stable |
Represents a symmetric stable distribution in Zolotarev's parametrization.
Inheritance HierarchySystemObject
Altaxo.Calc.ProbabilityDistribution
Altaxo.Calc.ProbabilityContinuousDistribution
Altaxo.Calc.ProbabilityStableDistributionBase
Altaxo.Calc.ProbabilityStableDistributionSymmetric
Altaxo.Calc.ProbabilityDistribution
Altaxo.Calc.ProbabilityContinuousDistribution
Altaxo.Calc.ProbabilityStableDistributionBase
Altaxo.Calc.ProbabilityStableDistributionSymmetric
Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3261.0 (4.8.3261.0)
SyntaxC#
public class StableDistributionSymmetric : StableDistributionBase
The StableDistributionSymmetric type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | StableDistributionSymmetric | Initializes a new instance of the StableDistributionSymmetric class |
Properties| Name | Description | |
|---|---|---|
 | 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) |
| Generator |
Gets or sets a Generator object that can be used as underlying random number generator.
(Inherited from Distribution) |
| Maximum | Gets the maximum possible value of distributed random numbers. (Inherited from StableDistributionBase) |
| Mean | Gets the mean of distributed random numbers. (Inherited from StableDistributionBase) |
| Median | Gets the median of distributed random numbers. (Inherited from StableDistributionBase) |
| Minimum | Gets the minimum possible value of distributed random numbers. (Inherited from StableDistributionBase) |
| Mode | Gets the mode of distributed random numbers. (Inherited from StableDistributionBase) |
| Variance | Gets the variance of distributed random numbers. (Inherited from StableDistributionBase) |
Methods| Name | Description | |
|---|---|---|
 | CCDF(Double, Double) | |
| CCDF(Double, Double, Object, Double) | |
| CDF(Double) | Calculates the cumulative distribution function. (Inherited from ContinuousDistribution) |
| CDF(Double, Double) | |
| CDF(Double, Double, Object, 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) |
| GenerateAsymmetricCaseS1 |
Generates random variates in S1 Parametrization
(Inherited from StableDistributionBase) |
| GenerateAsymmetricCaseS1_AEq1 | (Inherited from StableDistributionBase) |
| GenerateAsymmetricCaseS1_ANe1 | (Inherited from StableDistributionBase) |
| GenerateSymmetricCase | (Inherited from StableDistributionBase) |
| GetAgt1GnParameter | |
| GetAlt1GnParameter | |
| GetAlt1GpParameterByGamma | |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| NextDouble | Returns a distributed floating point random number. (Inherited from StableDistributionBase) |
| PDF(Double) | Calculates the probability density function. (Inherited from ContinuousDistribution) |
| PDF(Double, Double) | |
| PDF(Double, Double, Object, Double) | Calculates the probability density using either series expansion for small or big arguments, or a integration in the intermediate range. |
| PDFAlphaBetween01And02 | 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. |
| PDFAlphaBetween02And099 | 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. |
| PDFAlphaBetween099And101 | Calculation of the PDF if alpha is inbetween 0.99 and 1.01. |
| PDFAlphaBetween101And199999 | 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. |
| PDFAlphaBetween199999And2 | 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. |
| PDFIntegration | |
| PDFSeriesBigX | Imaginary part of the Fourier transformed derivative of the Kohlrausch function for high frequencies. |
| PDFSeriesSmallX | Imaginary part of the Fourier transformed derivative of the Kohlrausch function for low frequencies. |
| PDFSeriesSmallXSmallAlpha | Imaginary part of the Fourier transformed derivative of the Kohlrausch function for low frequencies, and beta<=1/20.. |
| PDFTaylorExpansionAroundAlphaOne | |
| Quantile(Double) | Calculates the quantile of the distribution function. (Inherited from ContinuousDistribution) |
| Quantile(Double, Double) | |
| QuantileCCDF | |
| 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) |
| XZCDF(Double, Double) | |
| XZCDF(Double, Double, Object, Double) |
Fields| Name | Description | |
|---|---|---|
 | _gen_B | Helper variables used for generating the random values. (Inherited from StableDistributionBase) |
| _gen_S | Helper variables used for generating the random values. (Inherited from StableDistributionBase) |
| _gen_Scale | Helper variables used for generating the random values. (Inherited from StableDistributionBase) |
| _gen_t | Helper variables used for generating the random values. (Inherited from StableDistributionBase) |
| generator |
Stores a Generator object that can be used as underlying random number generator.
(Inherited from Distribution) |
RemarksReferences:
[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