Electronic Journal of Statistics

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

M. C. Jones and Angela Noufaily

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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.

Article information

Electron. J. Statist., Volume 9, Number 2 (2015), 2732-2750.

Received: January 2015
First available in Project Euclid: 18 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62N99: None of the above, but in this section
Secondary: 60E05: Distributions: general theory 62N05: Reliability and life testing [See also 90B25]

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


Jones, M. C.; Noufaily, Angela. Log-location-scale-log-concave distributions for survival and reliability analysis. Electron. J. Statist. 9 (2015), no. 2, 2732--2750. doi:10.1214/15-EJS1089. https://projecteuclid.org/euclid.ejs/1450456320

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