The beta Burr XII distribution with application to lifetime data

For the first time, a five-parameter distribution, the so-called beta Burr XII distribution, is defined and investigated. The new distribution contains as special sub-models some well-known distributions discussed in the literature, such as the logistic, Weibull and Burr XII distributions, among several others. We derive its moment generating function. We obtain, as a special case, the moment generating function of the Burr XII distribution, which seems to be a new result. Moments, mean deviations, Bonferroni and Lorenz curves and reliability are provided. We derive two representations for the moments of the order statistics. The method of maximum likelihood and a Bayesian analysis are proposed for estimating the model parameters. The observed information matrix is obtained. For different parameter settings and sample sizes, various simulation studies are performed and compared in order to study the performance of the new distribution. An application to real data demonstrates that the new distribution can provide a better fit than other classical models. We hope that this generalization may attract wider applications in reliability, biology and lifetime data analysis.