Multivariate generalized Pareto distributions: parametrizations, representations, and properties

2017/05/22 by Holger Rootzén, Johan Segers, Rootzén, Holger +3 · 5 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #math.ST #msc:62G32 #stat.TH

paper · pdf · doi:10.48550/arxiv.1705.07987

20 pages

arxiv created 2017/05/22 · arxiv updated 2017/05/24

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 are 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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