Limit theorems for bivariate extremes of non-identically distributed random variables
Volume 29 / 2002
Applicationes Mathematicae 29 (2002), 371-386
MSC: Primary 60F05; Secondary 62E15, 62E20, 62G30.
DOI: 10.4064/am29-4-1
Abstract
The limit behaviour of the extreme order statistics arising from $n$ two-dimensional independent and non-identically distributed random vectors is investigated. Necessary and sufficient conditions for the weak convergence of the distribution function (d.f.) of the vector of extremes, as well as the form of the limit d.f.'s, are obtained. Moreover, conditions for the components of the vector of extremes to be asymptotically independent are studied.
