Al Omari Mohammed Ahmed
Al Baha University
Saudi Arabia
Title: Markov Chain Monte Carlo estimation for Bayesian approach based on type-I censored data
Biography
Biography: Al Omari Mohammed Ahmed
Abstract
This study consider the estimation of Maximum Likelihood Estimator and the Bayesian Estimator using Jeffrey’s prior and Extension of Jeffrey’s prior information of the Weibull distribution with type-I censored data. The shape parameter estimation by maximum likelihood method has been seen that are not available in closed forms, although they can be solved them by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and the hazard functions we can’t solve it analytical for that Markov Chain Mote Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Gibbs sampling and Metropolis-Hastings algorithm following by estimated the survival and hazard functions. The methods are compared to Bayesian using Lindley’s approximation and maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the best estimating of the parameters, the survival and the hazard functions.