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ORDER STATISTICS FROM HETEROGENOUS NEGATIVE BINOMIAL RANDOM VARIABLES

Published online by Cambridge University Press:  21 July 2011

Maochao Xu  and
Taizhong Hu
Maochao Xu
Affiliation:
Department of Mathematics, Illinois State University, Normal, IL E-mail: mxu2@ilstu.edu
Taizhong Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: thu@ustc.edu.cn
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Abstract

In this article, we study the order statistics from heterogenous negative binomial random variables. Sufficient conditions are provided for comparing the extreme order statistics according to the usual stochastic order. For the special case of geometric distribution, a sufficient condition is established for comparing order statistics in the sense of multivariate stochastic order. Applications in the Poisson–Gamma shock model and redundant systems have been described as well.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 4 , October 2011 , pp. 435 - 448
Copyright
Copyright © Cambridge University Press 2011

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