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Basic Theory of Multivariate Maxima

In: Laws of Small Numbers: Extremes and Rare Events

Author

Listed:
  • 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)

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.

Suggested Citation

  • Michael Falk & Rolf-Dieter Reiss & Jürg Hüsler, 2004. "Basic Theory of Multivariate Maxima," Springer Books, in: Laws of Small Numbers: Extremes and Rare Events, edition 0, chapter 0, pages 107-130, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7791-6_4
    DOI: 10.1007/978-3-0348-7791-6_4
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