Abstract
This paper aims to suggest the various options for the Bayesian estimation of the parameters from the Weibull distribution under left censored samples. Five approximation methods, namely Quadrature method, Gibbs sampler, importance sampling, Lindley's approximation and Tierney and Kadane's approximation, have been used for this purpose. A couple of priors and loss functions have been assumed for the posterior estimation. As the analytical comparison among the different estimators is not possible, we have used the simulated and real life datasets for the numerical comparison among the proposed estimators. Based on these comparisons, it has been assessed that the performance of the importance sampling and Tierney and Kadane's approximation is better as compared to their counterparts with certain constraints on the parameters.