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.
GeneralizedParetoDistribution | Generalized Pareto probability distribution object |
Distribution Fitter | Fit probability distributions to data |
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.