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Dynamic proportional hazard rate and reversed hazard rate models. (English) Zbl 1209.62244

Summary: D. R. Cox’s [J. R. Stat. Soc., Ser. B 34, 187–220 (1972; Zbl 0243.62041)] proportional hazard (PH) model has been used to model failure time data in reliability and survival analysis. A recently proportional reversed hazard model [R. C. Gupta and R. D. Gupta, J. Stat. Plann. Inference 137, No. 11, 3525–3536 (2007; Zbl 1119.62098)] has been analyzed in the literature. Sometimes, the hazard rate (or the reversed hazard rate) may not be proportional over the whole time interval, but may be proportional differently in different intervals. In order to take care of this kind of problems, we introduce the dynamic proportional hazard rate model, and the dynamic proportional reversed hazard rate model, and study their properties for different aging classes. The closure of the models under different stochastic orders has also been studied. Examples are presented to illustrate different properties of the models.

MSC:

62N99 Survival analysis and censored data
60E15 Inequalities; stochastic orderings
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