The Kumaraswamy exponential-Weibull distribution: theory and applications

Signicant progress has been made towards the generalization of some wellknown lifetime models, which have been successfully applied to problems 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-known special 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 new distribution lies in its ability to model monotone and non-monotone failure 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, quantile and generating functions, mean deviations and Shannon entropy. The method of maximum likelihood and a Bayesian procedure are used for estimating the model parameters. By means of a real lifetime data set, we prove that the new distribution provides a better t than the Kumaraswamy Weibull, Marshall-Olkin exponential-Weibull, extended Weibull, exponential-Weibull and Weibull models. The application in- dicates that the proposed model can give better ts than other well- known lifetime distributions.