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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
##### Keywords:
hazard rate order; order statistics; parallel system
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##### References:
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