# Documentation

### This is machine translation

Translated by
Mouse over text to see original. Click the button below to return to the English verison of the page.

# prob.ExtremeValueDistribution class

Package: prob
Superclasses: prob.ToolboxFittableParametricDistribution

Extreme value probability distribution object

## Description

prob.ExtremeValueDistribution is an object consisting of parameters, a model description, and sample data for an extreme value probability distribution.

Create a probability distribution object with specified parameter values using makedist. Alternatively, fit a distribution to data using fitdist or the Distribution Fitting app.

## Construction

pd = makedist('ExtremeValue') creates an extreme value probability distribution object using the default parameter values.

pd = makedist('ExtremeValue','mu',mu,'sigma',sigma) creates an extreme value probability distribution object using the specified parameter values.

### Input Arguments

expand all

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

## Properties

expand all

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

Data Types: single | double

Scale parameter of the extreme value distribution, stored as a nonnegative scalar value.

Data Types: single | double

Probability distribution name, stored as a character vector. This property is read-only.

Data Types: char

Data used for distribution fitting, stored 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

Logical flag for truncated distribution, stored as a logical value. If IsTruncated equals 0, the distribution is not truncated. If IsTruncated equals 1, the distribution is truncated. This property is read-only.

Data Types: logical

Number of parameters for the probability distribution, stored as a positive integer value. This property is read-only.

Data Types: single | double

Covariance matrix of the parameter estimates, stored 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. This property is read-only.

Data Types: single | double

Distribution parameter descriptions, stored as a cell array of character vectors. Each cell contains a short description of one distribution parameter. This property is read-only.

Data Types: char

Logical flag for fixed parameters, stored 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. This property is read-only.

Data Types: logical

Distribution parameter names, stored as a cell array of character vectors. This property is read-only.

Data Types: char

Distribution parameter values, stored as a vector. This property is read-only.

Data Types: single | double

Truncation interval for the probability distribution, stored as a vector containing the lower and upper truncation boundaries. This property is read-only.

Data Types: single | double

## Methods

### Inherited Methods

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

## Definitions

### Extreme Value 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$\sigma \ge 0$

The probability density function (pdf) is

$f\left(x|\mu ,\sigma \right)={\sigma }^{-1}\mathrm{exp}\left(\frac{x-\mu }{\sigma }\right)\mathrm{exp}\left(-\mathrm{exp}\left(\frac{x-\mu }{\sigma }\right)\right)\text{ };\text{ }-\infty

This form of the probability density function is suitable for modeling the minimum value. To model the maximum value, use the negative of the original values.

## Examples

expand all

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