mev: Modelling Extreme values

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 (via fit.rho)

• 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) comparison of piecewise generalized Pareto versus generalized Pareto models
• thselect.egp: Comparison of extended generalized Pareto versus 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
• rmnorm: 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 $\varphi$, with common functionalities, returning data frames with coefficient estimates and confidence intervals

• xdep.eta: coefficient of extremal dependence $\eta$ (including routine for the estimator of Kruspskii and Joe in kjtail)
• xdep.chi: tail correlation $\chi$.
• xdep.chibar: coefficient $\overline{\chi}$
• xdep.xindex: extremal index estimators based on interexceedance time and gap of exceedances
• xdep.asym: estimators of the extremal asymmetry coefficient $\varphi$.

Older functions that return similar summaries

• adf: bivariate angular dependence function of Wadsworth and Tawn (2013)
• extcoef: estimators of the extremal coefficient
• taildep: estimators of coefficients of tail dependence $\eta$ and tail correlation $\chi$
• angextrapo: bivariate tail dependence $\eta$ across rays
• extremo: pairwise extremogram as a function of distance for spatial data

Datasets

Various datasets

• 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, dgeoaniso: 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