A note on the covergence of bivariate extreme order statistics

Abstract

In this note an interesting fact is proved that, for any vector of bivariate extreme order statistics there exists (at least) a sequence of vectors of real numbers for which the distrihution function (d.f.) of this vector converges to a nondegenerate limit if and only if its marginals converge to nondegenerate limits. Moreover, the limit splits into the product of the limit: marginals if the bivariate d.f., from which the order statistics are drawn, is of negative quadrant dependent random variables (r.v., s).