In this paper some identities and inequalities which involve the joint distribution of order statistics in a set of dependent and nonidentically distributed random variables are derived. These identities and inequalities provide a unified way to handle the joint distribution of order statistics...

In a wide subclass of dual generalized order statistics (dgos) (which contains the most important models of descendingly ordered random variables), when the parameters [gamma]1,...,[gamma]n are assumed to be pairwise different, we study the weak convergence of the lower extremes, under general...

In this paper we study the weak convergence of the generally normalized extremes (extremes under nonlinear monotone normalization) of random number of independent (nonidentically distributed) random variables. When the random sample size is assumed to converge in probability and the...

The main purpose of this paper is to correct the statement of Theorem 3.1 of Werner Hürlimann [2004. Statist. Probab. Lett. 66, 355-362]. This theorem yields a non-parametric criterion of asymptotically independence between order statistics. A very short proof of the corrected statement is...