CRAN Task View: Extreme Value Analysis

Maintainer:Christophe Dutang
Contact:dutangc at
Contributions:Suggestions and improvements for this task view are very welcome and can be made through issues or pull requests on GitHub or via e-mail to the maintainer address. For further details see the Contributing guide.
Citation:Christophe Dutang (2023). CRAN Task View: Extreme Value Analysis. Version 2023-11-04. URL
Installation:The packages from this task view can be installed automatically using the ctv package. For example, ctv::install.views("ExtremeValue", coreOnly = TRUE) installs all the core packages or ctv::update.views("ExtremeValue") installs all packages that are not yet installed and up-to-date. See the CRAN Task View Initiative for more details.

Extreme values modelling and estimation are an important challenge in various domains of application, such as environment, hydrology, finance, actuarial science, just to name a few. The restriction to the analysis of extreme values may be justified since the extreme part of a sample can be of a great importance. That is, it may exhibit a larger risk potential such as high concentration of air pollutants, flood, extreme claim sizes, price shocks in the four previous topics respectively. The statistical analysis of extreme may be spread out in many packages depending on the topic of application. In this task view, we present the packages from a methodological side.

Applications of extreme value theory can be found in other task views: for financial and actuarial analysis in the Finance task view, for environmental analysis in the Environmetrics task view. General implementation of probability distributions is studied in the Distributions task view.

The maintainer gratefully acknowledges L. Belzile, E. Gilleland, P. Northrop, T. Opitz, M. Ribatet and A. Stephenson for their review papers, Kevin Jaunatre for his helpful advice and Achim Zeileis for his useful comments. If you think information is not accurate or if we have omitted a package or important information that should be mentioned here, please send an e-mail or submit an issue or pull request in the GitHub repository linked above.

Table of contents

Univariate Extreme Value Theory

Several packages export the probability functions (quantile, density, distribution and random generation) for the Generalized Pareto and the Generalized Extreme Value distributions, often sticking to the classical prefixing rule (with prefixes "q", "d", "p", "r") and allowing the use of the formals such as log and lower tail, see the view Distributions for details. Several strategies can be used for the numeric evaluation of these functions in the small shape (near exponential) case. Also, some implementations allow the use of parameters in vectorized form and some can provide the derivatives w.r.t. the parameters. Nevertheless, the nieve package provides symbolic differentiation for two EVT probability distribution (GPD and GEV) in order to compute the log-likelihood.

Bayesian approach

packagefunctionmodels[^1]covariatessampling[^2]prior choicegeneric functions
extRemesfevd1–4,*allRWMHcustomplot, summary
MCMC4Extremesggev,gpdp1–2,*noRWMHfixedplot, summary
revdbayesrpost1–4noRUcustomplot, summary
texmexevm1–2,*allIMHgaussianplot, summary, density,correlogram

[^1] model family: generalized extreme value distribution (1), generalized Pareto distribution (2), inhomogeneous Poisson process (3), order statistics/r-largest (4) or custom/other (*).

[^2] sampling: random walk Metropolis–Hastings (RWMH), exact sampling ratio-of-uniform (RU), independent Metropolis–Hastings (IMH)

Block Maxima approach

Summary of GEV density functions and GEV fitting functions

packagedensity functionlocationscaleshapefit functionargdataoutputS4outputS3outputS3par

Extremal index estimation approach

Mixture distribution or composite distribution approach

Peak-Over-Threshold by GPD approach

Summary of GPD density functions and GPD fitting functions

packagedensity functionlocationscaleshapefit functionargdataargthresoutputS4outputS3outputS3par

Record models:

Regression models:

Threshold selection

Bivariate Extreme Value Theory

Copula approach

Maxima approach

Peak-Over-Threshold by GPD approach

Tail dependence coefficient approach

Multivariate Extreme Value Theory

Bayesian approach

Copula approach

Multivariate Maxima

Peak-Over-Threshold by GPD approach

Tail dependence coefficient approach

Statistical tests

Classical graphics

Graphics for univariate extreme value analysis

Graphic namePackagesFunction names
Dispersion index plotPOTdiplot
Distribution fitting plotextremeStatdistLplot
Hill plotevirhill
Hill plotevmixhillplot
Hill plotextremefithill
Hill plotQRMhillPlot
Hill plotReInsHill
Hill plotExtremeRisksHTailIndex
L-moment plotPOTlmomplot
Mean residual life plotPOTmrlplot
Mean residual life plotevdmrlplot
Mean residual life plotevirmeplot
Mean residual life plotevmixmrlplot
Mean residual life plotismevmrl.plot
Mean residual life plotQRMMEplot
Mean residual life plotReInsMeanExcess
Pickand’s plotevmixpickandsplot
QQ Pareto plotPOTqplot
QQ Pareto plotRTDEqqparetoplot
QQ Pareto plotQRMplotFittedGPDvsEmpiricalExcesses
QQ Pareto plotReInsParetoQQ
QQ Exponential plotQRMQQplot
QQ Exponential plotReInsExpQQ
QQ Exponential plotRenextexpplot
QQ Lognormal plotReInsLognormalQQ
QQ Weibull plotReInsWeibullQQ
QQ Weibull plotRenextweibplot
Risk measure plotQRMRMplot
Threshold choice plotevdtcplot
Threshold choice plotevmixtcplot
Threshold choice plotPOTtcplot
Threshold choice plotQRMxiplot
Return level plotPOTretlev
Return level plotPOTReturn
Return level plotRenextplot,lines

Graphics for multivariate extreme value analysis

Angular densities plotExtremalDepAngDensPlot
Bivariate threshold choice plotevdbvtcplot
Dependence measure (chi) plotPOTchimeas
Dependence measure (chi) plotevdchiplot
Dependence diagnostic plot within time seriesPOTtsdep.plot
Extremal index plotPOTexiplot
Extremal index plotevdexiplot
(2D)map for a max-stable processSpatialExtremesmap
madogram for a max-stable processSpatialExtremesmadogram
madogram for a max-stable processExtremalDepmadogram
F-madogram for a max-stable processSpatialExtremesfmadogram
lambda-madogram for a max-stable processSpatialExtremeslmadogram
Multidimensional Hill plotExtremeRisksMultiHTailIndex
Pickands’ dependence function plotPOTpickdep
Pickands’ dependence function plotExtremalDepbbeed
QQ-plot for the extremal coefficientSpatialExtremesqqextcoeff
Spectral density plotPOTspecdens


Review papers

Classical books

Scientific papers

CRAN packages

Core:evd, evir, extRemes, SpatialExtremes.
Regular:BMAmevt, climextRemes, copula, ercv, eva, evgam, evmix, ExtremalDep, extremefit, ExtremeRisks, extremeStat, extremis, fCopulae, fExtremes, GJRM, graphicalExtremes, in2extRemes, ismev, lmom, lmomco, lmomRFA, MCMC4Extremes, mev, NHPoisson, nieve, POT, QRM, RecordTest, ReIns, Renext, revdbayes, RTDE, SimCop, tailDepFun, texmex, threshr, VGAM.

Other resources