The Modified Burr XII distribution is a generalization of the Burr XII distribution by adding a new parameter. Adding one or more parameters to a distribution function makes it richer and more flexible to analyzing data, hence it is better than the Burr XII and has been applied to a wide range of situations including applications in medicine, reliability, and ecology.
In this paper, the parameters of the modified Burr XII distribution are estimated under a progressive Type-II censoring scheme. The model parameters are estimated using the maximum likelihood and the Bayes estimation methods. We also use the observed Fisher information matrix to calculate the approximate confidence intervals. We apply the MCMC method to get the processes for Bayesian estimation under different loss functions. After that, the pertinent credible intervals are computed in turn. At last, the real data set is analyzed to investigate the models, and meaningful results are acquired for illustrative purposes.