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Modeling failure time data by Lehman alternatives. (English) Zbl 0900.62534
Summary: The proportional hazards model has been extensively used in the literature to model failure time data. In this paper we propose to model failure time data by $$F^*(t) = [F(t)]^{\theta}$$ where $$F(t)$$ is the baseline distribution function and $$\theta$$ is a positive real number. This model gives rise to monotonic as well as nonmonotonic failure rates even though the baseline failure rate is monotonic. The monotonicity of the failure rates are studied, in general, and some order relations are examined. Some examples including exponentiated Weibull, exponential, gamma and Pareto distributions are investigated in detail.

MSC:
 62N05 Reliability and life testing
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References:
 [1] DOI: 10.1007/BF01897826 · Zbl 0584.62030 [2] Cox D.R., Journal of the Royal Statistical Society, series B 34 pp 187– (1972) [3] DOI: 10.1080/01621459.1952.10501160 [4] DOI: 10.1080/01621459.1988.10478612 [5] DOI: 10.1080/01621459.1980.10477530 [6] DOI: 10.1080/03610929008830371 · Zbl 0734.62093 [7] DOI: 10.1080/15326348708807050 · Zbl 0617.60084 [8] Lehman , E.L. 1953. The power of rank tests. Annals of Mathematical Statistics 28–43. · Zbl 0050.14702 [9] DOI: 10.1109/24.229504 · Zbl 0800.62609 [10] DOI: 10.1080/00401706.1995.10484376 [11] DOI: 10.1080/03610929608831886 · Zbl 0887.62019
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