An Extended Burr-XII Distribution with Application to Lifetime Data

Abstract In this article, a new distribution named the extended Burr-XII distribution is developed. This new distribution combines the Burr-XII and Weibull distributions by using the method of T-X family. Probability density, hazard rate, residual and reversed residual lifetime functions, and the s th raw moment of the distribution are studied. We obtain the stress-strength reliability. The extended Burr-XII is able to model distributions with monotonically decreasing and upside down bathtub hazard rates. The maximum likelihood, ordinary least squares, weighted least squares, maximum product of spacings, Cramér-von Mises, Anderson-Darling, Kolmogorov-Smirnov, and Bayes methods are adopted for estimating the parameters of the model. The asymptotic confidence intervals of the parameters are obtained according to the observed Fisher’s information matrix. Also, the posterior density credible intervals of the parameters are obtained under gamma prior using Gibbs sampling technique. The new distribution and other distributions are fitted to two real data sets, and the results indicate that the new distribution is quite a reasonable model for the given data sets. Lastly, the performance of the proposed estimation methods is compared by a Monte Carlo simulation.