Read the full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=49744 DOI: 10.4236/ojs.2014.48053 Author(s) Al Omari Mohammed Ahmed Affiliation(s) Department of Mathematics, Faculty of Arts and Science in Qilwah, Al Baha University, Baha, KSA. ABSTRACT This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically thus Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters. eww140919gjr KEYWORDS Weibull Distribution, Bayesian Method, Interval Censored, Metropolis-Hastings Algorithm, Lindley’s Approximation