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

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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

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

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

Data Types: double

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

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

Distribution parameter values, specified as a vector of scalar values.

Data Types: single | double

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

Data Types: single | double

Other Object Properties

Probability distribution name, specified as a character vector.

Data Types: char

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

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

Data Types: char

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

Data Types: char

Object Functions

 cdf Cumulative distribution function icdf Inverse cumulative distribution function iqr Interquartile range mean Mean of probability distribution median Median of probability distribution negloglik Negative loglikelihood of probability distribution paramci Confidence intervals for probability distribution parameters pdf Probability density function proflik Profile likelihood function for probability distribution random Random numbers std Standard deviation of probability distribution truncate Truncate probability distribution object var Variance of probability distribution

Examples

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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.