EM algorithm for estimating the Burr XII parameters with multiple censored data

The two-parameter Burr XII distribution has been widely used in various practical applications such as business, chemical engineering, quality control, medical research and reliability engineering. In this paper, we present maximum likelihood estimation (MLE) via the expectation-maximization (EM) algorithm to estimate the Burr XII parameters with multiple censored data. We also provide a method that can be used to construct the confidence intervals of the parameters, a method that computes the asymptotic variance and the covariance of the MLE from the complete and missing information matrices. A simulation study is conducted to compare the performance of the MLE via the EM algorithm and the Netwon-Raphson (NR) algorithm. The simulation results show that the EM algorithm outperforms the NR algorithm in most cases in terms of bias and errors in the root mean square. A numerical example is also used to demonstrate the performance of the proposed method.