Some new results on multivariate dispersive ordering of generalized order statistics

Let be generalized order statistics based on a continuous distribution function F with parameters k and (m1,...,mn-1). Chen and Hu (2007) [8] investigated the sufficient conditions on F and on the parameters k and mi's such that , where , and is the Shaked-Shanthikumar multivariate dispersive order. Since the order does not possess the closure property under marginalization, one may naturally wonder whether the corresponding multivariate margins of the above random vectors are also ordered in the order . This is answered affirmatively in this paper. Some comparison results for generalized order statistics from two samples are presented. Potential applications are also mentioned.