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A flexible parametric survival model which allows a bathtub-shaped hazard rate function

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A new parametric (three-parameter) survival distribution, the lognormal–power function distribution, with flexible behaviour is introduced. Its hazard rate function can be either unimodal, monotonically decreasing or can exhibit a bathtub shape. Special cases include the lognormal distribution and the power function distribution, with finite support. Regions of parameter space where the various forms of the hazard-rate function prevail are established analytically. The distribution lends itself readily to accelerated life regression modelling. Applications to five data sets taken from the literature are given. Also it is shown how the distribution can behave like a Weibull distribution (with negative aging) for certain parameter values.
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Keywords: AL regression; bathtub hazard; lognormal–power function distribution; parametric hazard rate function; survival analysis

Document Type: Research Article

Affiliations: Department of Mathematics and Statistics,University of Victoria, PO Box 3060VictoriaBC, CanadaV8W 3R4

Publication date: August 1, 2011

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