The Pickands Approach in the Bivariate Case

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.