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Multivariate generalized Pareto distributions: Parametrizations, representations, and properties

Journal article
Authors Holger Rootzén
Johan Segers
Jennifer L. Wadsworth
Published in Journal of Multivariate Analysis
Volume 165
Pages 117-131
ISSN 0047-259X
Publication year 2018
Published at Department of Mathematical Sciences
Pages 117-131
Language en
Keywords Exceedances, Linear combination, Maxima, Stable tail dependence function, Tail copula
Subject categories Computer Systems, Probability Theory and Statistics, Other Computer and Information Science


© 2017 Elsevier Inc. Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized and represented in a number of different ways. Moreover, generalized Pareto distributions enjoy a number of interesting stability properties. An overview of the main features of such distributions is given, expressed compactly in several parametrizations, giving the potential user of these distributions a convenient catalogue of ways to handle and work with generalized Pareto distributions.

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