Inference In The Log-Logistic Distribution Based On An Adaptive Progressive Type-Ii Censoring Scheme

Abstract

The primary aim of this study is to explore the maximum likelihood estimation (MLE) and the Bayesian approach to estimate the parameters of log-logistic model and calculate the approximate confidence interval for the parameters and the survival function in both methods based on an adaptive progressive type-II censoring scheme. The parameters of the probability distribution are estimated via the Newton-Raphson Method and the Bayes estimators, based on squared error loss function (SELF). The approximate confidence interval for the reliability function has been calculated using the delta method; the approximate credible intervals for the unknown parameters and the survival function using the Bayesian approach have been constructed using Markov Chain Monte Carlo (MCMC) method. Moreover, a Monte Carlo study has performed to examine the proposed methods under different situations, based on mean squared error, bias, coverage probability, and expected length estimated criteria. Application to real life data is included, in order to view how the proposed methods, work in practice. It is observed that the Bayesian approach is better than MLE for estimating the log-logistic model parameters.