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LIKELIHOOD RATIO AND HAZARD RATE ORDERINGS OF THE MAXIMA IN TWO MULTIPLE-OUTLIER GEOMETRIC SAMPLES

Published online by Cambridge University Press:  08 June 2012

Baojun Du ,
Peng Zhao  and
N. Balakrishnan
Baojun Du
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Peng Zhao
Affiliation:
School of Mathematical Sciences, Jiangsu Normal University, Xuzhou 221116, China
N. Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, CanadaL8S 4K1 E-mail: [email protected]
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Abstract

In this paper, we study some stochastic comparisons of the maxima in two multiple-outlier geometric samples based on the likelihood ratio order, hazard rate order, and usual stochastic order. We establish a sufficient condition on parameter vectors for the likelihood ratio ordering to hold. For the special case when n = 2, it is proved that the p-larger order between the two parameter vectors is equivalent to the hazard rate order as well as usual stochastic order between the two maxima. Some numerical examples are presented for illustrating the established results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 3 , July 2012 , pp. 375 - 391
Copyright
Copyright © Cambridge University Press 2012

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