Abstract
We have considered the posterior estimation of two-component mixture of Weibull distribution under type-I right censoring. As the resultant Bayes estimators and posterior risks are not in close form, we have proposed Lindley's approximation and importance sampling for the approximate solutions. The performance of the approximation methods and estimators under study has been compared using simulated and real-life datasets. The results indicated that importance sampling has some edge over Lindley's approximation in terms of performance and computational easiness.