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STOCHASTIC COMPARISONS OF LARGEST ORDER STATISTICS FROM MULTIPLE-OUTLIER EXPONENTIAL MODELS

Published online by Cambridge University Press:  27 April 2012

Peng Zhao  and
N. Balakrishnan
Peng Zhao
Affiliation:
School of Mathematical Sciences, Jiangsu Normal University, Xuzhou 221116, China E-mail: [email protected]
N. Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada E-mail: [email protected]
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Abstract

In this paper, we carry out stochastic comparisons of largest order statistics from multiple-outlier exponential models according to the likelihood ratio order (reversed hazard rate order) and the hazard rate order (usual stochastic order). It is proved, among others, that the weak majorization order between the two hazard rate vectors is equivalent to the likelihood ratio order (reversed hazard rate order) between largest order statistics, and that the p-larger order between the two hazard rate vectors is equivalent to the hazard rate order (usual stochastic order) between largest order statistics. We also extend these results to the proportional hazard rate models. The results established here strengthen and generalize some of the results known in the literature.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 2 , April 2012 , pp. 159 - 182
Copyright
Copyright © Cambridge University Press 2012

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