# ExtremeValueDistribution

Extreme value probability distribution object

## Description

An ExtremeValueDistribution object consists of parameters, a model description, and sample data for an extreme value probability distribution.

The extreme value distribution is appropriate for modeling the smallest value from a distribution whose tails decay exponentially fast, for example, the normal distribution. It can also model the largest value from a distribution, such as the normal or exponential distributions, by using the negative of the original values.

The extreme value distribution uses the following parameters.

ParameterDescriptionSupport
muLocation parameter$-\infty <\mu <\infty$
sigmaScale parameter$\sigma \ge 0$

## Creation

There are several ways to create a ExtremeValueDistribution 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

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

Data Types: single | double

Scale parameter of the extreme value distribution, specified as a nonnegative 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 gather Gather properties of Statistics and Machine Learning Toolbox object from GPU icdf Inverse cumulative distribution function iqr Interquartile range of probability distribution 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 plot Plot probability distribution object 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 an extreme value distribution object using the default parameter values.

pd = makedist('ExtremeValue')
pd =
ExtremeValueDistribution

Extreme Value distribution
mu = 0
sigma = 1

Create an extreme value distribution object by specifying the parameter values.

pd = makedist('ExtremeValue','mu',-1,'sigma',2)
pd =
ExtremeValueDistribution

Extreme Value distribution
mu = -1
sigma =  2

Compute the standard deviation for the distribution.

s = std(pd)
s = 2.5651

## Version History

Introduced in R2013a