Bayesian analysis of doubly censored lifetime data using two- component mixture of Weibull distribution

In recent years analysis of the mixture models under Bayesian framework has received considerable attention. However, the Bayesian estimation of the mixture models under doubly censored samples has not yet been reported. This paper proposes a Bayesian estimation procedure for analyzing lifetime data under doubly censored sampling when the failure times belong to a two-component mixture of the Weibull model. An extended version of the likelihood function for doubly censored samples for the analysis of a mixture of lifetime models has been introduced. The posterior estimation has been considered under the assumption of gamma prior using a couple of loss functions. The performance of the different estimators has been investigated and compared through the analysis of simulated data. A real-life example has been included to demonstrate the practical applicability of the results. The results indicated the preference of the estimates under squared logarithmic loss function (SLLF) for the estimation of the mixture model. The proposed method can be extended for more than two component mixtures.