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ExtremeValueDistribution

Extreme value probability distribution object

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Description

AnExtremeValueDistributionobject 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.

Parameter Description 金宝app
mu Location parameter − ∞ < μ < ∞
sigma Scale parameter σ ≥ 0

Creation

There are several ways to create aExtremeValueDistributionprobability distribution object.

  • Create a distribution with specified parameter values usingmakedist.

  • Fit a distribution to data usingfitdist.

  • Interactively fit a distribution to data using theDistribution Fitter应用程序。

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

This property is read-only.

Logical flag for truncated distribution, specified as a logical value. IfIsTruncatedequals0, the distribution is not truncated. IfIsTruncatedequals1, 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 ap-by-pmatrix, wherepis the number of parameters in the distribution. The (i,j) element is the covariance between the estimates of theith parameter and thejth parameter. The (i,i) element is the estimated variance of theith parameter. If parameteriis 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. If0, the corresponding parameter in theParameterNamesarray is not fixed. If1, the corresponding parameter in theParameterNamesarray is fixed.

Data Types:logical

This property is read-only.

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

Data Types:single|double

This property is read-only.

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

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

cdf Cumulative distribution function
gather Gather properties ofStatistics and Machine Learning Toolboxobject from GPU
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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Open Live Script

Create an extreme value distribution object using the default parameter values.

pd = makedist('ExtremeValue')
pd = ExtremeValueDistribution Extreme Value distribution mu = 0 sigma = 1
Open Live Script

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

Extended Capabilities

See Also

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Topics

Introduced in R2013a

统计和机器学习的工具箱Documentation

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Mastering Machine Learning: A Step-by-Step Guide with MATLAB

Mastering Machine Learning: A Step-by-Step Guide with MATLAB

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