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STOCHASTIC ORDERING OF A CLASS OF SYMMETRIC DISTRIBUTIONS

Published online by Cambridge University Press:  14 July 2009

Weiwei Zhuang  and
Taizhong Hu
Weiwei Zhuang
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: weizh@ustc.edu.cn; thu@ustc.edu.cn
Taizhong Hu
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: weizh@ustc.edu.cn; thu@ustc.edu.cn
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Abstract

In this article, we investigate the sufficient and/or necessary conditions in order to stochastically compare the order statistics and their spacing vectors of two random vectors X and Y with special symmetric distributions. The conditions are imposed on the sample ranges Xn:n–X1:n and Yn:n–Y1:n or on (X1:n, Xn:n–X1:n) and (Y1:n, Yn:n–Y1:n). In particular, we consider the multivariate usual stochastic order, the convex order, the increasing convex order, and the directionally convex order. Several examples are also given to illustrate the power of the main results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 4 , October 2009 , pp. 583 - 595
Copyright
Copyright © Cambridge University Press 2009

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