Stable |
Represents a stable distribution in Nolan's S1 parametrization.
Inheritance HierarchySystemObject
Altaxo.Calc.ProbabilityDistribution
Altaxo.Calc.ProbabilityContinuousDistribution
Altaxo.Calc.ProbabilityStableDistributionBase
Altaxo.Calc.ProbabilityStableDistributionS1
Altaxo.Calc.ProbabilityDistribution
Altaxo.Calc.ProbabilityContinuousDistribution
Altaxo.Calc.ProbabilityStableDistributionBase
Altaxo.Calc.ProbabilityStableDistributionS1
Namespace: Altaxo.Calc.Probability
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3261.0 (4.8.3261.0)
SyntaxC#
public class StableDistributionS1 : StableDistributionBase
The StableDistributionS1 type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | StableDistributionS1 | Creates a new instance of the stable distribution in Nolan's parametrization with default parameters (alpha=1, beta=0) and the default generator. |
| StableDistributionS1(Generator) | Creates a new instance of he stable distribution in Nolan's parametrization with default parameters (alpha=1, beta=0). |
| StableDistributionS1(Double, Double) | Creates a new instance of he stable distribution in Nolan's parametrization with given parameters (alpha, beta) and the default random number generator. |
| StableDistributionS1(Double, Double, Double) | Creates a new instance of he stable distribution in Nolan's parametrization with given parameters (alpha, beta, abe) and the default random number generator. |
| StableDistributionS1(Double, Double, Double, Double) | Creates a new instance of he stable distribution in Nolan's parametrization with given parameters (alpha, beta, scale, location) and the default random number generator. |
| StableDistributionS1(Double, Double, Double, Double, Generator) | Creates a new instance of he stable distribution in Nolan's parametrization with given parameters (alpha, beta, scale, location) and the provided random number generator. |
| StableDistributionS1(Double, Double, Double, Double, Double) | Creates a new instance of the stable distribution in Nolan's parametrization with given parameters (alpha, beta, abe, scale, location) and the default random number generator. |
| StableDistributionS1(Double, Double, Double, Double, Double, Generator) | Creates a new instance of he stable distribution in Nolan's parametrization 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 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. For alpha<=1, it is not defined. For alpha>1, it is the _location parameter. (Overrides StableDistributionBaseMean) |
| Median | Gets the median of distributed random numbers. If beta=0, it is _location. For beta!=0, it is also defined, but not analytically expressable, and is not calcuated here (TODO, please help!). (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. Is finite only for alpha=2. (Overrides StableDistributionBaseVariance) |
Methods| Name | Description | |
|---|---|---|
| CDF(Double) | Calculates the cumulative distribution function. (Overrides ContinuousDistributionCDF(Double)) |
 | CDF(Double, Double, Double) | Calculates the cumulative distribution function of the stable distribution in S1 parametrization. |
| CDF(Double, Double, Double, Double) | Calculates the cumulative distribution function of the stable distribution in S1 parametrization. |
| CDF(Double, Double, Double, Double, Double) | Calculates the cumulative distribution function of the stable distribution in S1 parametrization. |
| CDF(Double, Double, Double, Object, Double) | Calculates the cumulative distribution function of the stable distribution in S1 parametrization. |
| CDF(Double, Double, Double, Double, Double, Double) | Calculates the cumulative distribution function of the stable distribution in S1 parametrization. |
| CDF(Double, Double, Double, Double, Double, Object, Double) | Calculates the cumulative distribution function of the stable distribution in S1 parametrization. |
| CDF(Double, Double, Double, Double, Double, Double, Object, Double) | Calculates the cumulative distribution function of the stable distribution in S1 parametrization. |
| 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 | |
| GetAlt1GpParameter | |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| Initialize | Initializes this instance of the distribution with the distribution parameters. |
| IsValidAlpha | |
| IsValidBeta | |
| IsValidLocation | |
| IsValidScale | |
| 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) | Calculates the probability density function of the stable distribution in S1 parametrization. |
| PDF(Double, Double, Double, Double, Double) | Calculates the probability density function of the stable distribution in S1 parametrization. |
| PDF(Double, Double, Double, Double, Double, Object, Double) | Calculates the probability density function of the stable distribution in S1 parametrization. |
| PDF(Double, Double, Double, Double, Double, Double, Object, Double) | Calculates the probability density function of the stable distribution in S1 parametrization. |
| Quantile(Double) | Calculates the quantile of the distribution function. (Overrides ContinuousDistributionQuantile(Double)) |
| Quantile(Double, Double, Double) | Calculates the quantile of the stable distribution in S1 parametrization. |
| Quantile(Double, Double, Double, Double) | Calculates the quantile of the stable distribution in S1 parametrization. |
| Quantile(Double, Double, Double, Double, Object, Double) | Calculates the quantile of the stable distribution in S1 parametrization. |
| 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 underlying random number generator.
(Inherited from Distribution) |
Remarks
The characteristic function in Nolan's S1 parametrization is:
and
C#
log(phi(t))= -scale^alpha |t|^alpha (1-i beta Sign(t) Tan(pi alpha/2)) + i location t (for alpha not equal to 1)
C#
log(phi(t)) = -scale |t| (1+i beta Sign(t) (2/pi) Log(|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