Modified proportional hazard rates and proportional reversed hazard rates models via Marshall-Olkin distribution and some stochastic comparisons. (English) Zbl 1387.60033
Summary: Adding parameters to a known distribution is a useful way of constructing flexible families of distributions. A. W. Marshall and I. Olkin [Biometrika 84, No. 3, 641–652 (1997; Zbl 0888.62012)] introduced a general method of adding a shape parameter to a family of distributions. In this paper, based on the Marshall-Olkin extension of a specified distribution, we introduce two new models, referred to as modified proportional hazard rates (MPHR) and modified proportional reversed hazard rates (MPRHR) models, which include as special cases the well-known proportional hazard rates and proportional reversed hazard rates models, respectively. Next, when two sets of random variables follow either the MPHR or the MPRHR model, we establish some stochastic comparisons between the corresponding order statistics based on majorization theory. The results established here extend some well-known results in the literature.
MSC:
| 60E15 | Inequalities; stochastic orderings |
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
Keywords:
modified proportional hazard rates model; modified proportional reversed hazard rates model; proportional hazard rates model; proportional reversed hazard rates model; weak majorization order; \(P\)-larger order; order statistics; usual stochastic order; Marshall-Olkin distributionCitations:
Zbl 0888.62012References:
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