On the odd Weibull distribution

Based on the idea of evaluating the distribution of the ‘odds of death’ of a lifetime variable, the odd Weibull distribution proposed by Cooray has recently been shown to be useful for testing the goodness of fit of the Weibull and inverse Weibull distributions. The model is also very versatile in modelling lifetime data in that its failure rate function can be increasing, decreasing, constant, bathtub shaped, and unimodal. In this paper, a detailed parametric characterization of the statistical properties of this distribution is carried out. The shapes of the Weibull probability plot with different model parameters are presented and the graphic parameter estimation steps are iterated. Burn-in and useful period-related issues of the bathtub-shaped failure rate curve are discussed. An application example is shown to illustrate the parameter estimation procedure and the superior fit of the model for some real data to the two-parameter Weibull distribution and some other three-parameter Weibull-related distributions. © 2008, Institution of Mechanical Engineers. All rights reserved.