Log-location-scale-log-concave distributions for survival and reliability analysis

Jones, M. C. and Noufaily, Angela (2015). Log-location-scale-log-concave distributions for survival and reliability analysis. Electronic Journal of Statistics, 9(2) pp. 2732–2750.

DOI: https://doi.org/10.1214/15-EJS1089

URL: http://projecte


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.

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