The Kumaraswamy exponential-Weibull distribution: theory and applications

Abstract

Signicant progress has been made towards the generalization of somewellknown lifetime models, which have been successfully applied toproblems arising in several areas of research. In this paper, some prop-erties of the new Kumaraswamy exponential-Weibull (KwEW) distribu-tion are provided. This distribution generalizes a number of well-knownspecial lifetime models such as the Weibull, exponential, Rayleigh, mod-ied Rayleigh, modied exponential and exponentiated Weibull dis-tributions, among others. The beauty and importance of the newdistribution lies in its ability to model monotone and non-monotonefailure rate functions, which are quite common in environmental stud-ies. We derive some basic properties of the KwEW distribution in-cluding ordinary and incomplete moments, skewness, kurtosis, quantileand generating functions, mean deviations and Shannon entropy. Themethod of maximum likelihood and a Bayesian procedure are used forestimating the model parameters. By means of a real lifetime dataset, we prove that the new distribution provides a better t than theKumaraswamy Weibull, Marshall-Olkin exponential-Weibull, extendedWeibull, exponential-Weibull and Weibull models. The application in-dicates that the proposed model can give better ts than other well-known lifetime distributions.