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 2023-03-30. 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 maintainers gratefully acknowledge E. Gilleland, M. Ribatet and A. Stephenson for their review for extreme value analysis packages (2013) 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 Distributions task view 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.

package function models[^1] covariates sampling[^2] prior choice generic functions
extRemes fevd 1–4,* all RWMH custom plot, summary
MCMC4Extremes ggev,gpdp 1–2,* no RWMH fixed plot, summary
revdbayes rpost 1–4 no RU custom plot, summary
texmex evm 1–2,* all IMH gaussian plot, 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)

Summary of GEV density functions and GEV fitting functions

package density function location scale shape fit function argdata outputS4 outputS3 outputS3par
climextRemes NA location scale shape fit_gev y NA mle NA
evd dgev loc scale shape fgev x NA estimate NA
evir dgev mu sigma xi gev data NA par.ests NA
extraDistr dgev mu sigma xi NA NA NA NA NA
extRemes devd loc scale shape fevd x NA results par
fExtremes dgev mu beta xi gevFit x fit par.ests NA
ismev NA NA NA NA xdat NA mle NA
lmomco pdfgev xi alpha kappa NA NA NA NA NA
QRM dGEV mu sigma xi fit.GEV maxima NA par.ests NA
revdbayes dgev loc scale shape NA NA NA NA NA
SpatialExtremes dgev loc scale shape NA NA NA NA NA
texmex dgev mu sigma xi evm y NA coefficients NA
TLMoments dgev loc scale shape NA NA NA NA NA

Summary of GPD density functions and GPD fitting functions

package density function location scale shape fit function argdata argthres outputS4 outputS3 outputS3par
ercv NA NA NA NA fitpot data threshold NA coeff NA
eva dgpd loc scale shape gpdFit data threshold NA par.ests NA
evd dgpd loc scale shape fpot x threshold NA estimate NA
evir dgpd mu beta xi gpd data threshold NA par.ests NA
extraDistr dgpd mu sigma xi NA NA NA NA NA NA
extRemes devd loc scale shape fevd x threshold NA results par
fExtremes dgpd mu beta xi gpdFit x u fit fit par
ismev NA NA NA NA xdat threshold NA mle NA
lmomco pdfgpa xi alpha kappa NA NA NA NA NA NA
mev NA NA scale shape fit.gpd xdat threshold NA estimate NA
POT dgpd loc scale shape fitgpd data threshold NA fitted.values NA
QRM dGPD NA beta xi fit.GPD data threshold NA par.ests NA
ReIns dgpd mu sigma gamma GPDfit data NA NA NA NA
Renext dGPD loc scale shape fGPD x NA NA estimate NA
revdbayes dgp loc scale shape NA NA NA NA NA NA
SpatialExtremes dgpd loc scale shape gpdmle x threshold NA NA NA
tea dgpd loc scale shape gpdFit data threshold NA par.ests NA
texmex dgpd u sigma xi evm y th NA coefficients NA
TLMoments dgpd loc scale shape NA NA NA NA NA NA

Bivariate Extreme Value Theory:

Multivariate Extreme Value Theory:

Classical graphics:

Graphics for univariate extreme value analysis

Graphic name Packages Function names
Dispersion index plot POT diplot
Distribution fitting plot extremeStat distLplot
Hill plot evir hill
Hill plot evmix hillplot
Hill plot extremefit hill
Hill plot QRM hillPlot
Hill plot ReIns Hill
Hill plot ExtremeRisks HTailIndex
L-moment plot POT lmomplot
Mean residual life plot POT mrlplot
Mean residual life plot evd mrlplot
Mean residual life plot evir meplot
Mean residual life plot evmix mrlplot
Mean residual life plot ismev mrl.plot
Mean residual life plot QRM MEplot
Mean residual life plot ReIns MeanExcess
Pickand’s plot evmix pickandsplot
QQ Pareto plot POT qplot
QQ Pareto plot RTDE qqparetoplot
QQ Pareto plot QRM plotFittedGPDvsEmpiricalExcesses
QQ Pareto plot ReIns ParetoQQ
QQ Exponential plot QRM QQplot
QQ Exponential plot ReIns ExpQQ
QQ Exponential plot Renext expplot
QQ Lognormal plot ReIns LognormalQQ
QQ Weibull plot ReIns WeibullQQ
QQ Weibull plot Renext weibplot
Risk measure plot QRM RMplot
Threshold choice plot evd tcplot
Threshold choice plot evmix tcplot
Threshold choice plot POT tcplot
Threshold choice plot QRM xiplot
Return level plot POT retlev
Return level plot POT Return
Return level plot Renext plot,lines

Graphics for multivariate extreme value analysis

Graphic Package Function
Angular densities plot ExtremalDep AngDensPlot
Bivariate threshold choice plot evd bvtcplot
Dependence measure (chi) plot POT chimeas
Dependence measure (chi) plot evd chiplot
Dependence diagnostic plot within time series POT tsdep.plot
Extremal index plot POT exiplot
Extremal index plot evd exiplot
(2D)map for a max-stable process SpatialExtremes map
madogram for a max-stable process SpatialExtremes madogram
madogram for a max-stable process ExtremalDep madogram
F-madogram for a max-stable process SpatialExtremes fmadogram
lambda-madogram for a max-stable process SpatialExtremes lmadogram
Multidimensional Hill plot ExtremeRisks MultiHTailIndex
Pickands’ dependence function plot POT pickdep
Pickands’ dependence function plot ExtremalDep bbeed
QQ-plot for the extremal coefficient SpatialExtremes qqextcoeff
Spectral density plot POT specdens

Classical books and review papers:

CRAN packages

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

Related links

Other resources