On the dependence function of Sibuya in multivariate extreme value theory

Abstract

The set of the functions H, which are limiting distributions of linearly normalized maxima of n independent and identically distributed random vectors, is treated. It is shown that there is a connection between Pickands' representation for H and the one given by D. G. Kendall for the p-function of Kingman. This is realized through the dependence function of Sibuya.independent and identically distributed random vectors multivariate extreme value distributions dependence function p-function of Kingman Pickands' representation Kendall's representation concave functions