On five-parameter Burr XII distribution: Properties and applications

Abstract

A new five-parameter distribution is defined and studied. The new model is referred to as the Kumaraswamy exponentiated Burr XII distribution. The new distribution includes eleven special models, namely, the Kumaraswamy exponentiated log-logistic, Kumaraswamy exponentiated Lomax, Kumaraswamy Burr XII and Kumaraswamy log-logistic distributions among others. Various structural properties of this model including moments, moment generating function, incomplete moments, order statistics and Rényi entropy are derived. The maximum likelihood method is used for estimating the model parameters. We illustrate the improved performance of the proposed distribution over other distributions available in the literature when modelling two real data sets. Keywords: Burr XII distribution, Kumaraswamy-G family, Maximum likelihood estimation, Order statistics