Bayesian analysis of left-censored data using Weibull mixture model

Though there have been many contributions dealing with classical and Bayesian analysis of mixture data under right-censored samples, the Bayesian analysis of left-censored heterogeneous data is lacking in the literature. This paper attempts to bridge up the said gap in the literature by proposing Bayesian methods for estimation of left-censored heterogeneous data. The paper also explored two-component Weibull mixture distribution (2CMWD) as a suitable model for modeling left-censored mixture data. As the explicit derivations for the estimators of the parameters are not possible, MCMC methods and Lindley’s approximation (LA) have been considered for approximate estimation of the model parameters. The sensitivity of the proposed Bayes estimates with respect to change in sample size, mixing parameter, censoring rates, loss function, prior, true parametric value and approximate methods has been discussed. The reliability characteristics for the left-censored 2CMWD have been studied in detail. The proposed estimators performed efficiently to estimate the parameters and reliability characteristics from the left-censored 2CMWD. The proposed estimators were insensitive with respect to change in censoring rates, true parametric values, prior parameters and mixing weights. Three different real datasets have been used to discuss the applicability of the proposed estimators in different real-life studies.