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Hazard rate ordering of the largest order statistics from geometric random variables

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  26 July 2018

Bara Kim  and
Jeongsim Kim
Bara Kim*
Affiliation:
Korea University
Jeongsim Kim*
Affiliation:
Chungbuk National University
*
* Postal address: Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Korea.
** Postal address: Department of Mathematics Education, Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju, Chungbuk, 28644, Korea. Email address: [email protected]
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Abstract

Mao and Hu (2010) left an open problem about the hazard rate order between the largest order statistics from two samples of n geometric random variables. Du et al. (2012) solved this open problem when n = 2, and Wang (2015) solved for 2 ≤ n ≤ 9. In this paper we completely solve this problem for any value of n.

Keywords

Hazard rate orderorder statisticsparallel system

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62N05: Reliability and life testing
Type
Short Communications
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 652 - 658
Copyright
Copyright © Applied Probability Trust 2018 

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References

[1]Du, B., Zhao, P. and Balakrishnan, N. (2012). Likelihood ratio and hazard rate orderings of the maxima in two multiple-outlier geometric samples. Prob. Eng. Inf. Sci. 26, 375–391, 613. Google Scholar
[2]Dykstra, R., Kochar, S. and Rojo, J. (1997). Stochastic comparisons of parallel systems of heterogeneous exponential components. J. Statist. Planning Infer. 65, 203–211. Google Scholar
[3]Khaledi, B.-E. and Kochar, S. (2000). Some new results on stochastic comparisons of parallel systems. J. Appl. Prob. 37, 1123–1128. Google Scholar
[4]Kochar, S. and Xu, M. (2007). Stochastic comparisons of parallel systems when components have proportional hazard rates. Prob. Eng. Inf. Sci. 21, 597–609. Google Scholar
[5]Kochar, S. and Xu, M. (2009). Comparisons of parallel systems according to the convex transform order. J. Appl. Prob. 46, 342–352. Google Scholar
[6]Mao, T. and Hu, T. (2010). Equivalent characterizations on orderings of order statistics and sample ranges. Prob. Eng. Inf. Sci. 24, 245–262. Google Scholar
[7]Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York. Google Scholar
[8]Wang, J. (2015). A stochastic comparison result about hazard rate ordering of two parallel systems comprising of geometric components. Statist. Prob. Lett. 106, 86–90. Google Scholar