Generalized Pareto copulas: A key to multivariate extremes

JOURNAL OF MULTIVARIATE ANALYSIS

卷:174

Article

Falk, Michael¹  Padoan, Simone A.²  Wisheckel, Florian¹ 

[1] Univ Wurzburg, Inst Math, Wurzburg, Germany

[2] Bocconi Univ Milan, Dept Decis Sci, Milan, Italy

关键词: Confidence interval;    Copula;    D-norm;    Domain of attraction;    Exceedance probability;    Exceedance stability;    Generalized Pareto copula;    Multivariate generalized Pareto distribution;    Multivariate max-stable distribution;   

DOI  :  10.1016/j.jmva.2019.104538

来源: Elsevier

【 摘 要 】

This paper reviews generalized Pareto copulas (GPC), which are a key to multivariate extreme value theory. Any generalized Pareto copula can be represented in an easy analytical way using a particular type of norm on R-d, called D-norm. The characteristic property of a generalized Pareto copula is its exceedance stability. They might help to end the following debate: What is a multivariate generalized Pareto distribution? We present an easy way to simulate data from an arbitrary generalized Pareto copula and, thus, form an arbitrary generalized Pareto distribution. As an application we derive nonparametric estimates of the probability that a random vector, which follows a generalized Pareto copula, exceeds a high threshold, together with confidence intervals. A case study on joint exceedance probabilities for air pollutants completes the paper. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free