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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: jeongsimkim@chungbuk.ac.kr
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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

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