The Marshall-Olkin additive Weibull distribution with variable shapes for the hazard rate

Year 2018, Volume: 47 Issue: 2, 365 - 381, 01.04.2018

Ahmed Z. Afify Gauss M. Cordeiro Haitham M. Yousof Abdus Saboor Edwin M.m. Ortega

Abstract

We introduce and study the Marshall-Olkin additive Weibull distribution in order to allow a wide variation in the shape of the hazard rate, including increasing, decreasing, bathtub and unimodal shapes. The new distribution generalizes at least eleven lifetime models existing in the literature. Various of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, moments of the residual and reversed residual life functions and order statistics are derived. The parameters of the new distribution are estimated by the maximum likelihood method. We illustrate empirically the superiority of the new model over other distributions by means of a real life data set.

Keywords

Additive Weibull, Goodness of fit, Lifetime data, Maximum likelihood, Moment, Order statistic, Residual life function

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