Documentation

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

Functions

expand all

Create GeneralizedParetoDistribution Object

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

Work with GeneralizedParetoDistribution Object

 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

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
 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
 mle Maximum likelihood estimates mlecov Asymptotic covariance of maximum likelihood estimators
 histfit Histogram with a distribution fit Probability Distribution Function Interactive density and distribution plots probplot Probability plots 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.