On the 3-Component Mixture of Exponential, Rayleigh and Burr Type-XII Distributions: A Simulation Study in Bayesian Framework

Abstract

This study aims at modeling a heterogeneous population assuming the 3-component mixture of Exponential, Rayleigh and Burr Type-XII distributions using type-I right censored data in Bayesian perspective. The censored sampling situation is considered due to its popularity in reliability theory and survival analysis. The elegant closed form expressions for the Bayes estimators and posterior risks using the non-informative (uniform and Jeffreys’) priors under squared error loss function are derived for censored data as well as for complete sample. In case when no or little prior information is available, elicitation of hyperparameters is given. Some mathematical expressions for different functions of survival time are also derived. To examine, numerically, the performance of the Bayes estimators, we have simulated their statistical properties under different scenarios.