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Hazard rate ordering of the largest order statistics from geometric random variables. (English) Zbl 1401.60025
Summary: In [Probab. Eng. Inf. Sci. 24, No. 2, 245–262 (2010; Zbl 1193.60025)], T. Mao and T. Hu left an open problem about the hazard rate order between the largest order statistics from two samples of \(n\) geometric random variables. In [ibid. 26, No. 3, 375–391 (2012; Zbl 1271.60031)], B. Du et al. solved this open problem when \(n = 2\), and J. Wang solved for \(2 \leq n\leq 9\) [Stat. Probab. Lett. 106, 86–90 (2015; Zbl 1397.60058)]. In this paper, we completely solve this problem for any value of \(n\).
MSC:
60E15 Inequalities; stochastic orderings
62N05 Reliability and life testing
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