Basic Theory of Multivariate Maxima

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

Chapter Chapter 4 in Laws of Small Numbers: Extremes and Rare Events, 2011, pp 135-169 from Springer

Abstract: Abstract In this chapter, we study the limiting distributions of componentwise defined maxima of iid d-variate rv. Such distributions are again max-stable as in the univariate case. Some technical results and first examples of max-stable df are collected in Section 4.1. In Section 4.2 and 4.3, we describe representations of max-stable df such as the de Haan-Resnick and the Pickands representation. Of special interest for the subsequent chapters will be the Pickands dependence function in Section 4.3 and the D-norm, which will be introduced in Section 4.4.

Keywords: Basic Theory; Borel Subset; Dependence Function; Bivariate Case; Total Dependence (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0009-9_4

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DOI: 10.1007/978-3-0348-0009-9_4

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