New Practical Bayes Estimators for the 2-Parameter Weibull Distribution

New Bayes estimators for the 2-parameter Weibull model are proposed when both parameters are unknown. In many life testing situations there is prior information which can be reasonably quantified in terms of: 1) range of the shape parameter, and 2) anticipated value of a quantile (reliable life) of the sampling distribution. This paper directly incorporates such information into the estimation process, using a new (not completely specified) prior distribution. Since analytic tractability is not possible, the estimates are obtained with easy numerical integration. A Monte Carlo simulation (carried out each time on 1000 samples and also using very poor priors) has shown that these estimators are quite s-unbiased and s-efficient for a large range of parameter values of poor priors.