Modeling failure time data by Lehman alternatives. (English) Zbl 0900.62534

Gupta, Ramesh C.; Gupta, Rameshwar D.; Gupta, Pushpa L.

Commun. Stat., Theory Methods 27, No. 4, 887-904 (1998).

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

Keywords:

monotonic and non-monotonic failure rates; exponentiated Weibull; exponentiated Pareto; exponentiated gamma; order relations

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