On the finite mixture of exponential, Rayleigh and Burr Type-XII Distributions: Estimation of Parameters in Bayesian framework

In recent years, the finite mixtures of distributions have been proved to be of considerable attention in terms of their practical applications. This paper aims about studying the problem of estimating the parameters of a 3-component mixture of Exponential, Rayleigh and Burr Type-XII distributions using type-I right censoring scheme in Bayesian framework. The elegant closed form expressions for the Bayes estimators and their variances using the non-informative and the informative priors are derived for censored sample as well as for complete sample. The hyperparameters are elicited using prior predictive distribution when no or little prior information is available. The posterior predictive distribution with different priors is derived and the equations necessary to find the lower and upper limits of the Bayesian predictive intervals are constructed. A detailed simulation study is carried out to investigate the performance (in terms of variances) of the Bayes estimators. Finally, the model is illustrated using the real life data. Bayes estimators using the informative prior have been observed performing superior.