Multivariate generalized Pareto distributions: Parametrizations, representations, and properties

Rootzen, Holger and Segers, Johan and Wadsworth, Jennifer Lynne (2018) Multivariate generalized Pareto distributions: Parametrizations, representations, and properties. Journal of Multivariate Analysis, 165. pp. 117-131. ISSN 0047-259X

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Abstract

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.