Exponentiated additive Weibull distribution

Additive Weibull distribution combining two Weibull distributions was proposed by Xie and Lai [1]. In this paper, we propose a generalization of this distribution which is called exponentiated additive Weibull distribution. It includes a set of exponentiated distributions such as modified generalized linear failure rate, exponentiated Weibull and exponentiated exponential distributions in addition to some widely well known distributions such as additive Weibull, modified Weibull distributions, among others. It represents a flexible model for reliability analysis such as reliability engineering, firmware reliability, decision-making reliability, and cost analysis. Some statistical properties of the new distribution are presented. The estimation of five parameters by maximum likelihood is studied and the observed information matrix is computed. Finally, three real data sets are used to compare the proposed distribution to five of its sub-models. The results showed that the new distribution provides a better fit than its sub-models.