Inference for the log-logistic distribution based on an adaptive progressive type-II censoring scheme

The primary aim of this study is to explore and investigate the maximum likelihood (ML) estimation and the Bayesian approach to estimating the parameters of log-logistic distribution and to calculate the approximate intervals for the parameters and the survival function based on adaptive progressive type-II censored data. The ML estimators of the parameters of the probability distribution were obtained via the Newton-Raphson Method. The approximate confidence intervals for the reliability function were calculated using the delta method. The Bayes estimators based on squared error loss function (SELF) and the approximate credible intervals for the unknown parameters and the survival function using the Bayesian approach were constructed using the Markov Chain Monte Carlo (MCMC) method. A Monte Carlo study was performed to examine the proposed methods under different situations, based on mean-squared error, bias, coverage probability, and expected length-estimated criteria. The Bayesian approach appears to be better than the likelihood for estimating the log-logistic model parameters. An application to real data was included.