The Beta Exponentiated Pareto Distribution with Application to Bladder Cancer Susceptibility

Abstract

A general class of univariate distributions generated by beta random variables, proposed by Eugene et al. (2002) and Jones (2009), has been discussed for many authors. In this paper, the beta exponentiated Pareto distribution is introduced and studied. Its density and failure rate functions can have different shapes. It contains as special models several important distributions discussed in the literature, such as the beta-Pareto and exponentiated Pareto distributions. We provide a comprehensive mathematical treatment of the distribution and derive expressions for the moments, generating and quantile functions and incomplete and L-moments. An explicit expression for R\'enyi entropy is obtained. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. The flexibility of the new model is illustrated with an application to a real data set.