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ORDERING CONVOLUTIONS OF HETEROGENEOUS EXPONENTIAL AND GEOMETRIC DISTRIBUTIONS REVISITED

Published online by Cambridge University Press:  23 April 2010

Tiantian Mao ,
Taizhong Hu  and
Peng Zhao
Tiantian Mao
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of ChinaE-mail: mttiy@mail.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 ChinaE-mail: mttiy@mail.ustc.edu.cn; thu@ustc.edu.cn
Peng Zhao
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China, E-mail: zhaop07@gmail.com
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Abstract

Let Sn(a1, …, an) be the sum of n independent exponential random variables with respective hazard rates a1, …, an or the sum of n independent geometric random variables with respective parameters a1, …, an. In this article, we investigate sufficient conditions on parameter vectors (a1, …, an) and under which Sn(a1, …, an) and are ordered in terms of the increasing convex and the reversed hazard rate orders for both exponential and geometric random variables and in terms of the mean residual life order for geometric variables. For the bivariate case, all of these sufficient conditions are also necessary. These characterizations are used to compare fail-safe systems with heterogeneous exponential components in the sense of the increasing convex and the reversed hazard rate orders. The main results complement several known ones in the literature.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 3 , July 2010 , pp. 329 - 348
Copyright
Copyright © Cambridge University Press 2010

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