Markov Chain Monte Carlo and Lindley’s Approximation for Estimation Weibull Distribution Based on Right Censored Data

This paper contains the Bayesian Estimator using Markov Chain Monte Carlo and Lindley’s approximationestimation of the Weibull distribution based on Type I censored data. The Maximum likelihood estimation is used, where the shape parameter estimation is not available in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions cannot be solved analytically. Hence Markov Chain Monte Carlo and Lindley’s approximationmethod are used, where the full conditional distribution for the parameters of Weibull distribution are obtained via Gibbs sampling and Metropolis-Hastings algorithm followed by the survival and hazard functions estimates. The methods are compared to Maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in parameters, the survival and hazard functions.