Some general results on usual stochastic ordering of the extreme order statistics from dependent random variables under Archimedean copula dependence

Abstract

In this paper, we provide some general results for the usual stochastic ordering of the extreme order statistics arising from two sets of random variables with different marginal distributions and different underlying Archimedean copulas structure. Application to some general models as marginal distributions which are including the well-known semiparametric family of distributions in statistics, is discussed.