Generalized Pareto Distribution

Fit, evaluate, and generate random samples from generalized Pareto distribution

To model extreme events from a distribution, use the generalized Pareto distribution (GPD). Statistics and Machine Learning Toolbox™ offers several ways to work with the GPD.

Create a probability distribution object GeneralizedParetoDistribution by fitting a probability distribution to sample data or by specifying parameter values. Then, use the object functions to evaluate the distribution, generate random numbers, and so on.
Work with the GPD interactively by using the Distribution Fitter app. You can export an object from the app and use the object functions.
Use distribution-specific functions with specified distribution parameters. The distribution-specific functions can accept parameters of multiple GPDs.
Use generic distribution functions (cdf, icdf, pdf, random) with a specified distribution name ('Generalized Pareto') and parameters.
Create a paretotails object to model the tails of a distribution by using the GPDs, with another distribution for the center. A paretotails object is a piecewise distribution that consists of one or two GPDs in the tails and another distribution in the center. You can specify the distribution type for the center by using the cdffun argument of paretotails when you create the object. Valid values of cdffun are 'ecdf' (interpolated empirical cumulative distribution), 'kernel' (interpolated kernel smoothing estimator), and a function handle. After creating an object, you can use the object functions to evaluate the distribution and generate random numbers.

To learn about the generalized Pareto distribution, see Generalized Pareto Distribution.

Objects

GeneralizedParetoDistribution Generalized Pareto probability distribution object

Apps

Distribution Fitter	Fit probability distributions to data
Probability Distribution Function	Interactive density and distribution plots

Functions

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`GeneralizedParetoDistribution` Object Functions

Create `GeneralizedParetoDistribution` Object

`makedist`	Create probability distribution object
`fitdist`	Fit probability distribution object to data

Work with `GeneralizedParetoDistribution` Object

`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

`paretotails` Object Functions

Create `paretotails` Object

paretotails Piecewise distribution with Pareto tails

Work with `paretotails` Object

`boundary`	Piecewise distribution boundaries
`cdf`	Cumulative distribution function
`icdf`	Inverse cumulative distribution function
`lowerparams`	Lower Pareto tail parameters
`nsegments`	Number of segments in piecewise distribution
`pdf`	Probability density function
`random`	Random numbers
`segment`	Piecewise distribution segments containing input values
`upperparams`	Upper Pareto tail parameters

Distribution-Specific Functions

`gpcdf`	Generalized Pareto cumulative distribution function
`gppdf`	Generalized Pareto probability density function
`gpinv`	Generalized Pareto inverse cumulative distribution function
`gplike`	Generalized Pareto negative loglikelihood
`gpstat`	Generalized Pareto mean and variance
`gpfit`	Generalized Pareto parameter estimates
`gprnd`	Generalized Pareto random numbers

Maximum Likelihood Estimation

`mle`	Maximum likelihood estimates
`mlecov`	Asymptotic covariance of maximum likelihood estimators

Distribution Plots

`histfit`	Histogram with a distribution fit
`probplot`	Probability plots
`plot`	Plot probability distribution object
`qqplot`	Quantile-quantile plot
`randtool`	Interactive random number generation

Topics

Generalized Pareto Distribution
Learn about the generalized Pareto distribution used to model extreme events from a distribution.
Nonparametric and Empirical Probability Distributions
Estimate a probability density function or a cumulative distribution function from sample data.
Fit a Nonparametric Distribution with Pareto Tails
Fit a nonparametric probability distribution to sample data using Pareto tails to smooth the distribution in the tails.
Nonparametric Estimates of Cumulative Distribution Functions and Their Inverses
Estimate the cumulative distribution function (cdf) from data in a nonparametric or semiparametric way.
Modelling Tail Data with the Generalized Pareto Distribution
This example shows how to fit tail data to the Generalized Pareto distribution by maximum likelihood estimation.