Hostname: page-component-84b7d79bbc-4hvwz Total loading time: 0 Render date: 2024-07-25T19:52:58.790Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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