Estimation and prediction for a unified hybrid-censored Burr Type XII distribution

The unified hybrid censoring is a mixture of generalized Type I and Type II hybrid censoring schemes. This paper presents the statistical inference and prediction of the Burr Type XII distribution for unified hybrid-censored data. The maximum likelihood estimators for estimating the unknown parameters are developed using the expectation-maximization algorithm. The Bayesian estimates of the unknown parameters under the assumption of independent gamma priors are obtained using two approximations, namely Lindley's approximation and the Markov Chain Monte Carlo (MCMC) technique. Also, MCMC samples are used to construct the highest posterior density credible intervals as well. Simulation experiments are performed to compare the different proposed methods. The prediction of the future observations based on a unified hybrid-censored sample is also provided. A real dataset representing the droplet splashing reported in 90 degrees spray angle is used to illustrate the derived results. Furthermore, a useful interval say tracking interval is introduced for comparing the distance of the two rival models from the true model.