Bayesian using Markov Chain Monte Carlo Estimation Based on Type I Censored Data

This paper describe the Bayesian Estimator using non informative prior and the Maximum Likelihood Estimation of the Weibull distribution with Type I censored data. The maximum likelihood method can’t estimate the shape parameter in closed forms, although it can be solved by Newton Raphson methods. Moreover, the Bayesian estimates of the parameters, the survival function and hazard rate cannot be solved analytically. Hence Markov Chain Monte Carlo method is 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 function and hazard rate estimates. The methods are compared to MLE counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in scale and shape parameters, the survival function and the hazard rate.