Estimation of the Burr XII-exponential Distribution Parameters

The Burr XII distribution is one of the most important distributions in Survival analysis. In this article, we introduce the new wider Burr XII-G family of distributions. A special model in the new family called Burr XII-exponential distribution that has constant, decreasing and unimodal hazard rate functions is investigated. We discuss the estimation of this distribution parameters by maximum likelihood, three modifications of maximum likelihood and Bayes methods. In Bayes method, we use the uniform, triangular and Burr XII-uniform priors for posterior analysis and obtain Bayes estimations under two different loss functions. We obtain two approximations of the Bayes estimations, the first one is by importance sampling and the second is based on Lindley's approximation. Monte Carlo simulated data are used to evaluate these methods. Finally, we fit this distribution to a set of real data set by estimation procedures.