Stable |
Represents a stable distribution in Nolan's S0 parametrization.
Inheritance HierarchySystemObject
Altaxo.Calc.ProbabilityDistribution
Altaxo.Calc.ProbabilityContinuousDistribution
Altaxo.Calc.ProbabilityStableDistributionBase
Altaxo.Calc.ProbabilityStableDistributionS0
Altaxo.Calc.ProbabilityDistribution
Altaxo.Calc.ProbabilityContinuousDistribution
Altaxo.Calc.ProbabilityStableDistributionBase
Altaxo.Calc.ProbabilityStableDistributionS0
Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)
SyntaxC#
public class StableDistributionS0 : StableDistributionBase
The StableDistributionS0 type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | StableDistributionS0 | Creates a new instance of this distribution with default parameters (alpha=1, beta=0) and the default generator. |
| StableDistributionS0(Generator) | Creates a new instance of this distribution with default parameters (alpha=1, beta=0). |
| StableDistributionS0(Double, Double) | Creates a new instance of this distribution with given parameters (alpha, beta) and the default random number generator. |
| StableDistributionS0(Double, Double, Double) | Creates a new instance of this distribution with given parameters (alpha, beta, abe) and the default random number generator. |
| StableDistributionS0(Double, Double, Double, Double) | Creates a new instance of this distribution with given parameters (alpha, beta, scale, location) and the default random number generator. |
| StableDistributionS0(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. |
| StableDistributionS0(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. |
| StableDistributionS0(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. |
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. (Overrides StableDistributionBaseMaximum) |
| Mean | Gets the mean of distributed random numbers. (Overrides StableDistributionBaseMean) |
| Median | Gets the median of distributed random numbers. (Overrides StableDistributionBaseMedian) |
| Minimum | Gets the minimum possible value of distributed random numbers. (Overrides StableDistributionBaseMinimum) |
| Mode | Gets the mode of distributed random numbers. (Overrides StableDistributionBaseMode) |
| Variance | Gets the variance of distributed random numbers. (Overrides StableDistributionBaseVariance) |
Methods| Name | Description | |
|---|---|---|
| CDF(Double) | Calculates the cumulative distribution function. (Overrides ContinuousDistributionCDF(Double)) |
 | CDF(Double, Double, Double) | Gets the cumulative distribution function (CDF) of the standardized S0 stable distribution. |
| CDF(Double, Double, Double, Double) | Gets the cumulative distribution function (CDF) of the standardized S0 stable distribution. |
| CDF(Double, Double, Double, Double, Double) | Gets the cumulative distribution function (CDF) for the specified scale and location. |
| CDF(Double, Double, Double, Object, Double) | Gets the cumulative distribution function (CDF) of the standardized S0 stable distribution. |
| CDF(Double, Double, Double, Double, Double, Double) | Gets the cumulative distribution function (CDF) for the specified scale and location. |
| CDF(Double, Double, Double, Double, Double, Object, Double) | Gets the cumulative distribution function (CDF) for the specified scale and location. |
| CDF(Double, Double, Double, Double, Double, Double, Object, Double) | Gets the cumulative distribution function (CDF) for the specified S0 parameters, scale, and location. |
| CDFMethodAlphaOne | Calculates the CDF for the special case alpha = 1. |
| 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). |
| GetAgt1GpParameter | Computes parameters used for the direct integration approach for alpha > 1 (Gp variant). |
| GetAlt1GnParameter | Computes parameters used for the direct integration approach for alpha < 1 (Gn variant). |
| GetAlt1GpParameter | Computes parameters used for the direct integration approach for alpha < 1 (Gp variant). |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| Initialize | Initializes this distribution instance with the given parameters. |
| IsValidAlpha | Checks whether alpha is valid for a stable distribution. |
| IsValidBeta | Checks whether beta is valid for a stable distribution. |
| IsValidMu | Checks whether mu is a valid location parameter. |
| IsValidSigma | Checks whether sigma is a valid scale parameter. |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| NextDouble | Returns a distributed floating point random number. (Overrides StableDistributionBaseNextDouble) |
| PDF(Double) | Calculates the probability density function. (Overrides ContinuousDistributionPDF(Double)) |
| PDF(Double, Double, Double) | Gets the probability density function (PDF) of the (standardized) S0 stable distribution. |
| PDF(Double, Double, Double, Double, Double) | Gets the probability density function (PDF) for the specified scale and location. |
| PDF(Double, Double, Double, Object, Double) | Gets the probability density function (PDF) of the standardized S0 stable distribution. |
| PDF(Double, Double, Double, Double, Object, Double) | Gets the probability density function (PDF) of the standardized S0 stable distribution. |
| PDF(Double, Double, Double, Double, Double, Object, Double) | Gets the probability density function (PDF) for the specified scale and location. |
| PDF(Double, Double, Double, Double, Double, Double, Object, Double) | Gets the probability density function (PDF) for the specified S0 parameters, scale, and location. |
| PDFMethodAlphaOne | Calculates the PDF for the special case alpha = 1. |
| Quantile(Double) | Calculates the quantile of the distribution function. (Overrides ContinuousDistributionQuantile(Double)) |
| Quantile(Double, Double, Double) | Gets the quantile (inverse CDF) for the standardized S0 stable distribution. |
| Quantile(Double, Double, Double, Double) | Gets the quantile (inverse CDF) for the standardized S0 stable distribution. |
| Quantile(Double, Double, Double, Double, Object, Double) | Gets the quantile (inverse CDF) for the standardized S0 stable distribution. |
| 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) |
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) |
Remarks
The characteristic function in Nolan's S0 parametrization is:
and
C#
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)
C#
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. Communications in 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 specify 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 otherwise impossible with the 64-bit floating-point representation.
See Also