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Some new results on multivariate dispersive ordering of generalized order statistics

By Hongmei Xie and Taizhong Hu

Abstract

AbstractLet {X1,n∗,X2,n∗,…,Xn,n∗} 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 (X0,n∗,X1,n∗,…,Xn−1,n∗)≤disp(X1,n+1∗,X2,n+1∗,…,Xn,n+1∗)≤disp(X1,n∗,X2,n∗,…,Xn,n∗), where X0,n∗≡0, and ≤disp is the Shaked–Shanthikumar multivariate dispersive order. Since the order ≤disp 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 ≤disp. This is answered affirmatively in this paper. Some comparison results for generalized order statistics from two samples are presented. Potential applications are also mentioned

Publisher: Elsevier Inc.
Year: 2010
DOI identifier: 10.1016/j.jmva.2009.08.007
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