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Correlation of powers of Hüsler–Reiss vectors and Brown–Resnick fields, and application to insured wind losses
Hüsler–Reiss vectors and Brown–Resnick fields are popular models in multivariate and spatial extreme-value theory, respectively, and are widely used...
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Extremes of Markov random fields on block graphs: Max-stable limits and structured Hüsler–Reiss distributions
We study the joint occurrence of large values of a Markov random field or undirected graphical model associated to a block graph. On such graphs,...
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Inference on extremal dependence in the domain of attraction of a structured Hüsler–Reiss distribution motivated by a Markov tree with latent variables
A Markov tree is a probabilistic graphical model for a random vector indexed by the nodes of an undirected tree encoding conditional independence...
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Spatial Wildfire Risk Modeling Using a Tree-Based Multivariate Generalized Pareto Mixture Model
Wildfires pose a severe threat to the ecosystem and economy, and risk assessment is typically based on fire danger indices such as the McArthur...
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Stochastic ordering in multivariate extremes
The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple...
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A modeler’s guide to extreme value software
This review paper surveys recent development in software implementations for extreme value analyses since the publication of Stephenson and Gilleland...
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Regression-type analysis for multivariate extreme values
This paper devises a regression-type model for the situation where both the response and covariates are extreme. The proposed approach is designed...
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Conditional normal extreme-value copulas
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are...
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Remembering Ross Leadbetter: some personal recollections
Ross Leadbetter had had a broad and deep influence on the development of probabilistic and statistical theory of extreme values and on the...
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Regional pooling in extreme event attribution studies: an approach based on multiple statistical testing
Statistical methods are proposed to select homogeneous regions when analyzing spatial block maxima data, such as in extreme event attribution...
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New characterizations of multivariate Max-domain of attraction and D-Norms
In this paper we derive new results on multivariate extremes and D -norms. In particular we establish new characterizations of the multivariate...
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Multivariate extreme value copulas with factor and tree dependence structures
Parsimonious extreme value copula models with O ( d ) parameters for d observed variables of extrema are presented. These models utilize the dependence...
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Extremes of stationary random fields on a lattice
Extremal behavior of stationary Gaussian sequences/random fields is widely investigated since it models common cluster phenomena and brings a bridge...
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Bivariate Copula Classes, Their Visualization, and Estimation
There are three major construction approaches of copulas. One arising from applying the probability integral transform (see Definition...
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Trend detection for heteroscedastic extremes
There are some suggestions that extreme weather events are becoming more frequent due to global warming. From a statistical point of view, this...
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Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach
In this study, a new nonparametric approach using Bernstein copula approximation is proposed to estimate Pickands dependence function. New data...
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Classes and Families
This chapter introduces the main copula classes and the corresponding sampling procedures, along with some copula transformations that are important...
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Estimating the Extremal Coefficient: A Simulation Comparison of Methods
Tail dependence is an important issue to evaluate risk. The multivariate extreme values theory is the most suitable to deal with the extremal...
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Multivariate Order Statistics: the Intermediate Case
Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random...
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Generalised least squares estimation of regularly varying space-time processes based on flexible observation schemes
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such stationary...