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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.


GeneralizedParetoDistributionGeneralized Pareto probability distribution object


Distribution FitterFit probability distributions to data


expand all

Create GeneralizedParetoDistribution Object

makedistCreate probability distribution object
fitdistFit probability distribution object to data

Work with GeneralizedParetoDistribution Object

cdfCumulative distribution function
icdfInverse cumulative distribution function
iqrInterquartile range
meanMean of probability distribution
medianMedian of probability distribution
negloglikNegative loglikelihood of probability distribution
paramciConfidence intervals for probability distribution parameters
pdfProbability density function
proflikProfile likelihood function for probability distribution
randomRandom numbers
stdStandard deviation of probability distribution
truncateTruncate probability distribution object
varVariance of probability distribution

Create paretotails Object

paretotailsPiecewise distribution with Pareto tails

Work with paretotails Object

boundaryPiecewise distribution boundaries
cdfCumulative distribution function
icdfInverse cumulative distribution function
lowerparamsLower Pareto tail parameters
nsegmentsNumber of segments in piecewise distribution
pdfProbability density function
randomRandom numbers
segmentPiecewise distribution segments containing input values
upperparamsUpper Pareto tail parameters
gpcdfGeneralized Pareto cumulative distribution function
gppdfGeneralized Pareto probability density function
gpinvGeneralized Pareto inverse cumulative distribution function
gplikeGeneralized Pareto negative loglikelihood
gpstatGeneralized Pareto mean and variance
gpfitGeneralized Pareto parameter estimates
gprndGeneralized Pareto random numbers
mleMaximum likelihood estimates
mlecovAsymptotic covariance of maximum likelihood estimators
histfitHistogram with a distribution fit
Probability Distribution FunctionInteractive density and distribution plots
probplotProbability plots
qqplotQuantile-quantile plot
randtoolInteractive random number generation


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.