An R package for the analysis of univariate, multivariate and functional extreme values. The package includes routine functions for univariate analyses multiple threshold selection diagnostics, optimization, bias-correction and tangent exponential model approximations, non-parametric spectral measure estimation using empirical likelihood methods, etc. Multivariate functionalities revolve around simulation algorithms for multivariate models, empirical likelihood, empirical dependence measures. Likelihood functions for elliptical processes and user-provided methodologies.

To install from Github, use

remotes::install_github("lbelzile/mev")

after installing remotes.

Functionalities

The functionalities of the development version of the package (GIthub) are sorted below by topic.

Univariate

The package focuses on likelihood based inference for parametric models.

Log likelihood, score and information matrices for the following univariate models:

gpd: generalized Pareto distribution (alternative parametrizations gpde, gpdN, gpdr)
gev: generalized extreme value distribution (alternative parametrizations gevN, gevr)
pp: inhomogeneous Poisson process for extremes
rlarg: asymptotic r-largest order statistics

Fitting procedures and higher order asymptotic inference for univariate extremes

fit.* for maximum likelihood estimation
*.bcor for bias correction via score vectors or by subtraction
*.pll: profile likelihood for objects
*.tem for tangent exponential model approximation to profile likelihood

Two additional models and utilities for penultimate approximations

egp: extended generalized Pareto models of Papastathopoulos and Tawn (2013), and Gamet and Jonathan (2022)
extgp: extended generalized Pareto models of Naveau et al. (2017)
smith.penult: Smith (1987) penultimate approximations to parametric models

Nonparametric estimators of shape and second order regular variation

The routine fit.shape, or alternatively one of subroutines for real or positive (*) shape parameters.

shape.hill*: Hill’s estimator
shape.osz: Pickands extreme U-statistic of Oorschot, Segers and Zhou
shape.moment: moment estimator of Dekkers and de Haan.
shape.pickands: Pickands estimator (poor performance)
shape.vries*: de Vries estimator of de Haan and Peng.
shape.genjack*: generalized jacknnife shape estimator of Gomes et al.
shape.rbm*: Wager’s random block maxima estimator
shape.genquant*: generalized quantile
shape.trimhill*: trimmed Hill estimator
shape.lthill*: left-truncated Hill estimator

Note that both of the trimmed and truncated Hill estimators are not vectorized.

Second-order regular variation estimators

rho.dk: estimator of Drees and Kaufmann (1998)
rho.gbw: estimator of Goegebeur, Beirland and de Wet (2008)
rho.fagh: estimator of Fraga Alves, Gomes and de Haan (2003)
rho.ghp: estimator of Gomes, de Haan and Peng (2002)

Threshold selection diagnostics

Functions for automatic selection of threshold with the peaks over threshold method

thselect.wseq: Wadsworth (2016) sequential analysis threshold diagnostics
thselect.vmetric: metric-based threshold selection of Varty et al. (2025+)
thselect.ncpgp: Northrop and Coleman (2014) piecewise generalized Pareto
thselect.cv: del Castillo and Padilla (2016) coefficient of variation method
thselect.sdinfo: Suveges and Davison (2010) information matrix test
thselect.mrl: Langousis et al. (2016) automatization of mean residual life diagnostics
thselect.pickands: Pickands (1985) goodness-of-fit threshold selection diagnostic
thselect.alrs: automatic L-moments ratio selection method of Silva Lomba and Fraga Alves (2020)
thselect.ksmd: Mahalanobis distance-based selection method based on L-moments of Kiran and Srivinas (2021)

Some semiparametric methods

thselect.bab: Bladt, Albrecher and Beirlant (2020) minimization of AMSE for Hill estimator via lower truncated Hill
thselect.expgqt Exponential generalized quantile threshold selection of Beirlant, Vynckier and Teugels (1996)
thselect.gbw: Kernel-based threshold selection of Goegebeur, Beirlant and de Wet (2008)
thselect.rbm: Random block maximum estimator of Wager (2014), with empirical Bayes risk minimization
thselect.pec: prediction error C-criterion with non-robust estimator of Dupuis and Victoria-Feser (2003)
thselect.mdps: minimum distance threshold selection procedure of Clauset, Shalizi and Newman (2009)
thselect.samsee: smooth asymptotic mean squared error estimator of Schneider, Krajina, and Krivobokova (2021)

Threshold stability plots

tstab.gpd: threshold stability plots for generalized Pareto
tstab.egp: threshold stability plots for extended generalized Pareto
tstab.cv: coefficient of variation stability plot
tstab.mrl: mean residual life plot
tstab.hill: Hill plot

Multivariate

Some functionalities (incomplete) for multivariate models. There is currently no function to optimize multivariate threshold models, but likelihoods are provided for logistic, Brown–Resnick, Huesler–Reiss and extremal Student models

ibvpot: interpretation of bivariate models (extension of evir for all bivariate models from evd)
likmgp, clikmgp: (censored) likelihood for multivariate generalized Pareto
expme: exponent measure of parametric extreme value models

Two tests, one for max-stability and the other for asymptotic independence

test.maxstab: graphical test of max-stability (P-P plot)
test.scoreindep: score test of asymptotic independence for bivariate logistic model

Nonparametric

Estimation of the angular distribution using empirical estimation or empirical likelihood, with or without smoothing

angmeas: rank-based estimation of the angular measure
angmeasdir: Dirichlet mixture smoothing of angular measure

Simulation

Sampling algorithms for parametric models, multivariate and spatial extreme values, angular distribution and (generalized) risk-Pareto processes using accept-reject or composition sampling (approximate).

rrlarg: simulation of $r$ -largest observations from point process of extremes
rdir: simulation of Dirichlet vectors
mvrnorm: simulation of multivariate normal vectors
rmev: exact simulation of multivariate extreme value distributions
rmevspec: random samples from angular distributions of multivariate extreme value models.
rparp: simulation from R-Pareto processes
rparpcs: simulation from Pareto processes (max) using composition sampling
rparpcshr: simulation of generalized Huesler-Reiss Pareto vectors via composition sampling
rgparp: simulation from generalized R-Pareto processes

Extremal dependence measures

Measures of tail dependence $\theta$ , $\eta$ , $\chi$ and $\varphi$ .

taildep: estimators of coefficients of tail dependence $\eta$ and tail correlation $\chi$
extcoef: estimators of the extremal coefficient
xasym: estimators of the extremal asymmetry coefficient
angextrapo: bivariate tail dependence $\eta$ across rays
lambdadep: bivariate function of Wadsworth and Tawn (2013)
ext.index: extremal index estimators based on interexceedance time and gap of exceedances
extremo: pairwise extremogram as a function of distance for spatial data

Datasets

Various datasets collected here and there, (exclusively?) for univariate peaks over threshold analysis

abisko: Abisko rainfall
eskrain: Eskdalemuir observatory daily rainfall
frwind: time series of wind speeds
geomagnetic: magnitude of geomagnetic storms
leedspollution: multivariate air pollutant from Leeds
maiquetia: Maiquetia daily rainfall series
nidd: river Nidd daily flow
nutrients: interview component from NHANES on nutrients
pandemics: estimated records on number of death from pandemics
venice: Venice sea level data
w1500m: women 1500m track records

Spatial

Some functionalities for fitting spatial data

distg: matrix of pairwise distance with geometric anisotropy
Variogram models (unexported functions powerexp.cor, power.vario, schlather.vario)
Lambda2cov: convert variogram to covariance of conditional random field

Miscellaneous

Functions used internally that could be of more general use.

emplik: empirical likelihood for vector mean
wecdf: weighted empirical distribution function
spline.corr and tem.corr: corrections for Fraser–Reid objects to remove singularities nead the mode

mev: Modelling Extreme values