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: 4.8.3448.0 (4.8.3448.0)
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 the 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) | Gets the complementary cumulative distribution function (CCDF) value. |
| CCDF(Double, Double, Object, Double) | Gets the complementary cumulative distribution function (CCDF) value. |
| CDF(Double) | Calculates the cumulative distribution function. (Inherited from ContinuousDistribution) |
| CDF(Double, Double) | Gets the cumulative distribution function (CDF) value. |
| CDF(Double, Double, Object, Double) | Gets the cumulative distribution function (CDF) value. |
| 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 for asymmetric cases.
(Inherited from StableDistributionBase) |
| GenerateAsymmetricCaseS1_AEq1 |
Generates random variates for the asymmetric S1 case when alpha equals 1.
(Inherited from StableDistributionBase) |
| GenerateAsymmetricCaseS1_ANe1 |
Generates random variates for the asymmetric S1 case when alpha is not equal to 1.
(Inherited from StableDistributionBase) |
| GenerateSymmetricCase |
Generates a symmetric stable variate for the provided characteristic exponent.
(Inherited from StableDistributionBase) |
| GetAgt1GnParameter | Computes parameters used for the direct integration approach for alpha > 1 (Gn variant). |
| GetAlt1GnParameter | Computes parameters used for the direct integration approach for alpha < 1 (Gn variant). |
| GetAlt1GpParameterByGamma | Computes parameters used for the direct integration approach for alpha < 1 (Gp variant), parameterized by gamma. |
| 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) | Gets the probability density function (PDF) of the symmetric stable distribution. |
| PDF(Double, Double, Object, Double) | Calculates the probability density using either a series expansion for small or large arguments, or an integration in the intermediate range. |
| PDFAlphaBetween01And02 | Calculates the PDF for alpha in the interval [0.1, 0.2]. |
| PDFAlphaBetween02And099 | Calculates the PDF for alpha in the interval (0.2, 0.99]. |
| PDFAlphaBetween099And101 | Calculates the PDF for alpha in the interval [0.99, 1.01]. |
| PDFAlphaBetween101And199999 | Calculates the PDF for alpha in the interval (1.01, 1.99995]. |
| PDFAlphaBetween199999And2 | Calculates the PDF for alpha in the interval [1.99999, 2]. |
| PDFIntegration | Calculates the PDF by direct numerical integration. |
| PDFSeriesBigX | Series expansion of the PDF for large z. |
| PDFSeriesSmallX | Series expansion of the PDF for small z. |
| PDFSeriesSmallXSmallAlpha | Series expansion of the PDF for small z and small alpha, using logarithmic evaluation for improved numerical stability. |
| PDFTaylorExpansionAroundAlphaOne | Calculates the PDF by a Taylor expansion around alpha = 1. |
| Quantile(Double) | Calculates the quantile of the distribution function. (Inherited from ContinuousDistribution) |
| Quantile(Double, Double) | Gets the quantile (inverse CDF) for the given probability p. |
| QuantileCCDF | Gets the quantile (inverse CCDF) for the given complementary probability q. |
| 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) | Gets the CDF relative to 0, i.e. CDF(x) - 0.5, preserving the sign of x. |
| XZCDF(Double, Double, Object, Double) | Gets the CDF relative to 0, i.e. CDF(x) - 0.5, preserving the sign of x. |
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 the 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, Tokyo, August 2004
See Also