POT-pkg: Overview of the 'POT' package

In POT: Generalized Pareto Distribution and Peaks Over Threshold

Overview of the POT package

Description

The POT package aims to provide operational tools to analyze peak over threshold. This package relies on the extreme value theory (EVT) to model the tail of any continuous distribution. Tail modelling, in particular POT modelling, is of great importance for many financial and environmental applications.

The POT package was first committed to the CRAN in April 2005 and is still in development. The package is hosted in R-forge. Since November 2016, the package has a new maintainer.

The main motivation was to provide practical tools for probabilistic modelling of high flood flows. However, the strength of the EVT is that results do not depend on the process to be modelled. Thus, one can use the POT package to analyze precipitations, floods, financial times series, earthquakes and so on...

The POT package can perform univariate and bivariate extreme value analysis; first order Markov chains can also be considered. For instance, the (univariate) GPD is currently fitted using 18 estimators. These estimators rely on three different techniques:

• Likelihood maximization: MLE, LME, MPLE

• Moment Approaches: MOM, PWM, MED

• Distance Minimization: MDPD and MGF estimators.

Contrary to the univariate case, there is no finite parametrisation to model bivariate exceedances over thresholds. The POT packages allows 6 parametrisation for the bivariate GPD: the logistic, negative logistic and mixed models - with their respective asymmetric counterparts.

Lastly, first order Markov chains can be fitted using the bivariate GPD for the joint distribution of two consecutive observations.

The POT package proposes several S3 classes to handle fits. The overal class is "pot" which provides usual generic functions coef.pot, logLik.pot, summary.pot.

• Inheriting from "pot" class, the class "uvpot" provides univariate POT objects (see fitgpd and fitpp) with the usual generic functions

  • anova.uvpot for analysis of deviance,

  • confint.uvpot for confidence interval,

  • plot.uvpot for plots,

  • print.uvpot for print,

  as well as new generic functions

  • convassess.uvpot for convergence assessment,

  • dens.uvpot for density plot,

  • pp.uvpot for probability plot,

  • qq.uvpot for quantile plot,

  • retlev.uvpot for return level plot.

• Inheriting from "pot" class, the class "bvpot" provides bivariate POT objects (see fitbvgpd) with the usual generic functions

  • anova.bvpot for analysis of deviance,

  • plot.bvpot for plots,

  • print.bvpot for print,

  as well as new generic functions

  • convassess.bvpot for convergence assessment,

  • retlev.bvpot for return level plot.

• Inheriting from "uvpot" class, the class "mcpot" provides Markov Chain POT objects (see fitmcgpd) with the usual generic functions

  • plot.mcpot for plots,

  • print.mcpot for print,

  as well as new generic functions

  • convassess.mcpot for convergence assessment,

  • retlev.mcpot for return level plot.

We have written a package vignette to help new users. This users guide is a part of the package - just run vignette("POT") once the package is loaded.

Author(s)

Mathieu Ribatet and Christophe Dutang.

POT documentation built on May 6, 2025, 3:01 a.m.