The Pickands Approach in the Bivariate Case

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 6 in Laws of Small Numbers: Extremes and Rare Events, 2004, pp 161-202 from Springer

Abstract: Abstract The restriction to bivariate random vectors enables the study of their distributions in much greater detail. For example, we introduce a certain measure generating function M, see Section 6.1, and prove that the pertaining Pickands dependence function D is absolutely continuous, see Lemma 6.2.1 and the subsequent discussion, a property which is unknown in higher dimensions. Also, we introduce an expansion of order 2 of the spectral df in the bivariate case, see Section 6.1, which turns out to be useful in a testing problem.

Keywords: Random Vector; Dependence Function; Tail Dependence; Independent Copy; Bivariate Case (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-0348-7791-6_6

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