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2015 Log-location-scale-log-concave distributions for survival and reliability analysis
M. C. Jones, Angela Noufaily
Electron. J. Statist. 9(2): 2732-2750 (2015). DOI: 10.1214/15-EJS1089


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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M. C. Jones. Angela Noufaily. "Log-location-scale-log-concave distributions for survival and reliability analysis." Electron. J. Statist. 9 (2) 2732 - 2750, 2015.


Received: 1 January 2015; Published: 2015
First available in Project Euclid: 18 December 2015

zbMATH: 1329.62409
MathSciNet: MR3435809
Digital Object Identifier: 10.1214/15-EJS1089

Primary: 62N99
Secondary: 60E05 , 62N05

Keywords: Bathtub , exponentiated Weibull , generalised $F$ , generalised gamma , hazard shape , log-concave , log-convex , mean residual life

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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