Abstract

A five-parameter model, called the Burr XII negative binomial  distribution, is defined and studied. The new model contains as special cases some important lifetime distributions discussed in the literature, such as the  log-logistic, Weibull, Pareto type II and  Burr XII distributions, among several others. We derive the ordinary and incomplete moments, generating and quantile functions, mean deviations,  reliability and two types of entropy. The order statistics and their moments are investigated. The method of maximum likelihood is proposed for estimating the model parameters. We obtain the observed information matrix. An application to  real data  demonstrates that the new distribution can provide a better fit than other classical lifetime models.

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