Namespaces

Types in MathNet.Numerics.Distributions

Type Stable

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

Continuous Univariate Stable distribution. A random variable is said to be stable (or to have a stable distribution) if it has the property that a linear combination of two independent copies of the variable has the same distribution, up to location and scale parameters. For details about this distribution, see.

Constructors

Static Functions

Methods

Properties

Public Constructors

Stable(double alpha, double beta, double scale, double location, Random randomSource)

Initializes a new instance of the Stable class.
Parameters
double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

Random randomSource

The random number generator which is used to draw random samples.

Stable(double alpha, double beta, double scale, double location)

Initializes a new instance of the Stable class.
Parameters
double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

Public Static Functions

double CDF(double alpha, double beta, double scale, double location, double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
Parameters
double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

double x

The location at which to compute the cumulative distribution function.

Return
double

the cumulative distribution at location x.

bool IsValidParameterSet(double alpha, double beta, double scale, double location)

Tests whether the provided values are valid parameters for this distribution.
Parameters
double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

double PDF(double alpha, double beta, double scale, double location, double x)

Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
Parameters
double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

double x

The location at which to compute the density.

Return
double

the density at x.

double PDFLn(double alpha, double beta, double scale, double location, double x)

Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
Parameters
double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

double x

The location at which to compute the density.

Return
double

the log density at x.

double Sample(Random rnd, double alpha, double beta, double scale, double location)

Generates a sample from the distribution.
Parameters
Random rnd

The random number generator to use.

double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

Return
double

a sample from the distribution.

double Sample(double alpha, double beta, double scale, double location)

Generates a sample from the distribution.
Parameters
double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

Return
double

a sample from the distribution.

void Samples(Double[] values, double alpha, double beta, double scale, double location)

Fills an array with samples generated from the distribution.
Parameters
Double[] values

The array to fill with the samples.

double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

Return
void

a sequence of samples from the distribution.

IEnumerable<double> Samples(Random rnd, double alpha, double beta, double scale, double location)

Generates a sequence of samples from the distribution.
Parameters
Random rnd

The random number generator to use.

double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

Return
IEnumerable<double>

a sequence of samples from the distribution.

void Samples(Random rnd, Double[] values, double alpha, double beta, double scale, double location)

Fills an array with samples generated from the distribution.
Parameters
Random rnd

The random number generator to use.

Double[] values

The array to fill with the samples.

double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

Return
void

a sequence of samples from the distribution.

IEnumerable<double> Samples(double alpha, double beta, double scale, double location)

Generates a sequence of samples from the distribution.
Parameters
double alpha

The stability (α) of the distribution. Range: 2 ≥ α > 0.

double beta

The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double scale

The scale (c) of the distribution. Range: c > 0.

double location

The location (μ) of the distribution.

Return
IEnumerable<double>

a sequence of samples from the distribution.

Public Methods

double CumulativeDistribution(double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
Throws a not supported exception if Alpha != 2 , (Alpha != 1 and Beta !=0) , or (Alpha != 0.5 and Beta != 1)
Parameters
double x

The location at which to compute the cumulative distribution function.

Return
double

the cumulative distribution at location x.

double Density(double x)

Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
Parameters
double x

The location at which to compute the density.

Return
double

the density at x.

double DensityLn(double x)

Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
Parameters
double x

The location at which to compute the log density.

Return
double

the log density at x.

bool Equals(object obj)

int GetHashCode()

Type GetType()

double Sample()

Draws a random sample from the distribution.
Return
double

A random number from this distribution.

IEnumerable<double> Samples()

Generates a sequence of samples from the Stable distribution.
Return
IEnumerable<double>

a sequence of samples from the distribution.

void Samples(Double[] values)

Fills an array with samples generated from the distribution.

string ToString()

A string representation of the distribution.
Return
string

a string representation of the distribution.

Public Properties

double Alpha get;

Gets the stability (α) of the distribution. Range: 2 ≥ α > 0.

double Beta get;

Gets The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.

double Entropy get;

Gets he entropy of the distribution.
Always throws a not supported exception.

double Location get;

Gets the location (μ) of the distribution.

double Maximum get;

Gets the maximum of the distribution.

double Mean get;

Gets the mean of the distribution.

double Median get;

Gets the median of the distribution.
Throws a not supported exception if Beta != 0.

double Minimum get;

Gets the minimum of the distribution.

double Mode get;

Gets the mode of the distribution.
Throws a not supported exception if Beta != 0.

Random RandomSource get; set;

Gets or sets the random number generator which is used to draw random samples.

double Scale get;

Gets the scale (c) of the distribution. Range: c > 0.

double Skewness get;

Gets the skewness of the distribution.
Throws a not supported exception of Alpha != 2.

double StdDev get;

Gets the standard deviation of the distribution.

double Variance get;

Gets the variance of the distribution.