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Basic Theory of Multivariate Maxima

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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.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    Michael Falk

  2. Department of Mathematical Statistics and Actuarial Science, University of Berne, Sidlerstrasse 5, 3012, Bern, Switzerland

    Jürg Hüsler

  3. Department of Mathematics, University of Siegen, Walter Flex Str. 3, 57068, Siegen, Germany

    Rolf-Dieter Reiss

Authors
  1. Michael Falk
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  2. Jürg Hüsler
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  3. Rolf-Dieter Reiss
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Correspondence to Michael Falk .

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Falk, M., Hüsler, J., Reiss, RD. (2011). Basic Theory of Multivariate Maxima. In: Laws of Small Numbers: Extremes and Rare Events. Springer, Basel. https://doi.org/10.1007/978-3-0348-0009-9_4

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