StableDistribution

Stable probability distribution object

Description

StableDistribution is an object consisting of parameters, a model description, and sample data for a stable probability distribution.

The stable distribution uses the following parameters.

ParameterDescriptionSupport
alphaFirst shape parameter0 < α ≤ 2
betaSecond shape parameter-1 ≤ β ≤ 1
gamScale parameter0 < γ < ∞
deltaLocation parameter-∞ < δ < ∞

Creation

There are several ways to create a StableDistribution probability distribution object.

  • Create a distribution with specified parameter values using makedist.

  • Fit a distribution to data using fitdist.

  • Interactively fit a distribution to data using the Distribution Fitter app.

Properties

expand all

Distribution Parameters

First shape parameter of the stable distribution, specified as a scalar value in the range (0,2].

Data Types: single | double

Second shape parameter of the stable distribution, specified as a scalar value in the range [-1,1].

Data Types: single | double

Scale parameter of the stable distribution, specified as a scalar value in the range (0,∞).

Data Types: single | double

Location parameter of the stable distribution, specified as a scalar value.

Data Types: single | double

Distribution Characteristics

This property is read-only.

Logical flag for truncated distribution, specified as a logical value. If IsTruncated equals 0, the distribution is not truncated. If IsTruncated equals 1, the distribution is truncated.

Data Types: logical

This property is read-only.

Number of parameters for the probability distribution, specified as a positive integer value.

Data Types: double

This property is read-only.

Covariance matrix of the parameter estimates, specified as a p-by-p matrix, where p is the number of parameters in the distribution. The (i,j) element is the covariance between the estimates of the ith parameter and the jth parameter. The (i,i) element is the estimated variance of the ith parameter. If parameter i is fixed rather than estimated by fitting the distribution to data, then the (i,i) elements of the covariance matrix are 0.

Data Types: double

This property is read-only.

Logical flag for fixed parameters, specified as an array of logical values. If 0, the corresponding parameter in the ParameterNames array is not fixed. If 1, the corresponding parameter in the ParameterNames array is fixed.

Data Types: logical

This property is read-only.

Distribution parameter values, specified as a vector.

Data Types: single | double

This property is read-only.

Truncation interval for the probability distribution, specified as a vector containing the lower and upper truncation boundaries.

Data Types: single | double

Other Object Properties

This property is read-only.

Probability distribution name, specified as a character vector.

Data Types: char

This property is read-only.

Data used for distribution fitting, specified as a structure containing the following:

  • data: Data vector used for distribution fitting.

  • cens: Censoring vector, or empty if none.

  • freq: Frequency vector, or empty if none.

Data Types: struct

This property is read-only.

Distribution parameter descriptions, specified as a cell array of character vectors. Each cell contains a short description of one distribution parameter.

Data Types: char

This property is read-only.

Distribution parameter names, specified as a cell array of character vectors.

Data Types: char

Object Functions

cdfCumulative distribution function
icdfInverse cumulative distribution function
iqrInterquartile range
meanMean of probability distribution
medianMedian of probability distribution
negloglikNegative loglikelihood of probability distribution
paramciConfidence intervals for probability distribution parameters
pdfProbability density function
proflikProfile likelihood function for probability distribution
randomRandom numbers
stdStandard deviation of probability distribution
truncateTruncate probability distribution object
varVariance of probability distribution

Examples

collapse all

Create a stable distribution object using the default parameter values.

pd = makedist('Stable')
pd = 
  StableDistribution

  Stable distribution
    alpha = 2
     beta = 0
      gam = 1
    delta = 0

Create a stable distribution object by specifying the parameter values alpha = 0.5, beta = 0, gam = 1, and delta = 0.

pd = makedist('Stable','alpha',0.5,'beta',0,'gam',1,'delta',0);

Calculate the mean of the distribution.

m = mean(pd)
m = NaN

The mean of the stable distribution is undefined for values of alpha less than or equal to 1.

Introduced in R2016a