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Some properties of the proportional odds model. (English) Zbl 1194.60021

Summary: A. W. Marshall and I. Olkin [Biometrika 84, No. 3, 641–652 (1997; Zbl 0888.62012)] introduced a new family of distributions by adding a tilt parameter. The same family was obtained by J. Kirmani and P. Gupta [Ann. Inst. Stat. Math. 53, No.2, 217-243 (2001; Zbl 1027.62012)] as the proportional odds model, which had been proposed by D. G. Clayton [Biometrika 61, 525–531 (1974; Zbl 0295.62016)]. In this paper, stochastic ordering of distributions from this class and preservation of classes of life distributions by adding a parameter are obtained. The proportional odds family is also considered as a family of weighted distributions.

MSC:

60E15 Inequalities; stochastic orderings
60E05 Probability distributions: general theory
62N05 Reliability and life testing
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