Basic Theory of Multivariate Maxima

Michael Falk (), Rolf-Dieter Reiss () and Jürg Hüsler ()
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Michael Falk: University of Würzburg, Institute of Applied Mathematics and Statistics
Rolf-Dieter Reiss: University of Siegen, Department of Mathematics
Jürg Hüsler: University of Berne, Department of Mathematical Statistics and Actuarial Science

Chapter Chapter 4 in Laws of Small Numbers: Extremes and Rare Events, 2004, pp 107-130 from Springer

Abstract: Abstract In this chapter, we study the limiting distributions of componentwise denned maxima of iid d-variate random vectors. Such distributions are again max-stable as in the univariate case. Some technical results and first examples of max-stable dfs are collected in Section 4.1. In the Sections 4.2 to 4.4, we describe different representations of max-stable dfs such as the de Haan-Resnick and the Pickands representations and show their relationships to each other. Of special interest for the subsequent Chapters 5 and 6 will be the concepts of a Pickands representation and a Pickands dependence function which will be introduced in Section 4.3.

Keywords: Poisson Process; Univariate Case; Borel Subset; Dependence Function; Generalize Pareto Distribution (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-0348-7791-6_4

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