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

R remotes::install_github("lbelzile/mev")

after installing remotes.

Functionalities

The functionalities of the package 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 penultimate models and utilities for approximations

• egp: extended generalized Pareto models of Papastathopoulos and Tawn (2013)
• extgp: extended generalized Pareto models of Naveau et al. for rainfall
• smith.penult: Smith (1987) penultimate approximations to parametric models

Threshold selection

Multiple functions can be used for threshold selection for the peaks over threshold method

• automrl: automatic threshold selection for mean residual life plots
• cvselect: threshold selection via coefficient of variation
• tstab.egp: threshold stability plots for egp models
• infomat.test: information matrix test for time series
• NC.diag: Northrop and Coleman (2014) score tests
• tstab.gp: threshold stability plot for generalized Pareto distribution
• vmetric.diag: metric-based threshold selection of Varty et al.
• W.diag: Wadsworth (2016) sequential analysis threshold diagnostics

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

• maxstabtest: test of max-stability
• 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
• geomagnetic: magnitude of geomagnetic storms
• maiquetia: Maiquetia daily rainfall series
• nidd: river Nidd daily flow
• 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: conver 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