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Jones, M. C.; Noufaily, Angela

Log-location-scale-log-concave distributions for survival and reliability analysis. (English) Zbl 1329.62409

Electron. J. Stat. 9, No. 2, 2732-2750 (2015).
Summary: We consider a novel sub-class of log-location-scale models for survival and reliability data formed by restricting the density of the underlying location-scale distribution to be log-concave. These models display a number of attractive properties. We particularly explore the shapes of the hazard functions of these, LLSLC, models. A relatively elegant, if partial, theory of hazard shape arises under a further minor constraint on the hazard function of the underlying log-concave distribution. Perhaps the most useful LLSLC models are contained in a class of three-parameter distributions which allow constant, increasing, decreasing, bathtub and upside-down bathtub shapes for their hazard functions.

Cited in 3 Documents

MSC:

62N99 Survival analysis and censored data
60E05 Probability distributions: general theory
62N05 Reliability and life testing

Keywords:

bathtub; exponentiated Weibull; generalised \(F\); generalised gamma; hazard shape; log-concave; log-convex; mean residual life
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\textit{M. C. Jones} and \textit{A. Noufaily}, Electron. J. Stat. 9, No. 2, 2732--2750 (2015; Zbl 1329.62409)
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