A SIMULATION STUDY OF THE BAYES ESTIMATOR FOR PARAMETERS IN WEIBULL DISTRIBUTION

Abstract

The Weibull distribution is one of the most popular distributionsin analyzing the lifetime data. In this study, we consider the Bayes estimatorsof the scale and shape parameters of Weibull distribution under the assumptions of Gamma priors and squared error loss function. While computing theBayes estimates for a Weibull distribution, the continuous conjugate joint priordistribution of the shape and scale parameters does not exist and the closedform expressions of the Bayes estimators cannot be obtained.In this study Örst we will consider the Bayesian inference of the scale parameter under the assumption that the shape parameter is known. We willassume that the scale parameter has a Gamma prior. Under these assumptionsBayes estimate can be obtained in explicit form. When both the parametersare unknown, the Bayes estimates cannot be obtained in closed form. In thiscase, we will assume that the scale parameter has the Gamma prior, and theshape parameter also has the Gamma prior and they are independently distributed. We will use the Lindley approximation to obtain the approximateBayes estimators.Under these assumptions, we will compute approximate Bayes estimatorsand compare with the maximum likelihood estimators by Monte Carlo simulations.