Bayesian Estimator for Weibull Distribution with Censored Data using Extension of Jeffrey Prior Information

Abstract

The Weibull distribution provides a statistical model which has a wide variety of applications in many areas, including life testing and reliability theory. The main advantageous of this distribution is its ability to provide reasonably accurate failure analysis and failure forecasts with extremely small samples. Bayesian approach has received much attention and in contention with other estimation methods. In this study we explore and compare the performance of the Bayesian using Jeffrey prior and the extension of Jeffrey prior information with maximum likelihood method for estimating the parameters of Weibull distribution with censored data. Through the simulation study comparisons are made on the performance of these estimators with respect to the Mean Square Error (MSE) and Mean Percentage Error (MPE). For all the varying sample size, several specific values of the scale parameter of the Weibull distribution and for the values specify for the extension of Jeffrey prior, the estimators of Jeffrey prior result in smaller MSE and MPE compared to Bayesian estimator using extension of Jeffrey prior in majority of the cases. Nevertheless in all cases for both methods the MSE and MPE decrease as sample size increases.