Bayesian Inference of the Parameters from the Beta Log-logistic Model based on Progressive Type-II Censoring

Based on progressive type-II censored samples, the MLEs (maximum likelihood estimators) and Bayes estimators for the four parameters, 𝛼, 𝛽, 𝛼 and 𝑏 of BLLog (beta log-logistic) distribution are derived. The MLEs are found by Newton-Raphson method and bootstrap method. Then we show the conditions of existence of MLEs of the four parameters. Also, we used MCMC methods for obtaining their Bayes estimates. In simulation study, as expected, the RMSEs of all estimators decrease as a sample size increases. For the fixed sample size, the mean squared error typically increases as the number of censored data increases. Also, Bayesian estimators are better than MLE and bootstrap estimators in terms of the values of their corresponding RMSEs, SE (standard error)s and lengths of confidence intervals.