Stable |
public class StableDistributionS1 : StableDistributionBase
The StableDistributionS1 type exposes the following members.
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. |
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) |
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) |
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) |
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)
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.