Bayesian analysis of heterogeneous doubly censored lifetime data using the 3-component mixture of Rayleigh distributions: A Monte Carlo simulation study

This study considers Bayesian estimation of parameters of a heterogeneous 3- Component Mixture of Rayleigh Distributions (3-CMRD) generating a mixture of data. Being the most popular and reasonable sampling scheme in reliability and survival analyses, the doubly censored sampling scheme is considered in this research. The Bayes estimators and their posterior risks were derived under various situations. In addition, hyperparameters were elicited, and algebraic expressions for posterior predictive distribution and Bayesian predictive intervals were derived. Assuming the informative and the non-informative priors, a comprehensive Monte Carlo simulation was conducted to examine the performance of the Bayes estimators under symmetric and asymmetric loss functions. Finally, to highlight its practical importance, the proposed 3-component mixture model was applied to doubly censored lifetime data from a real-life situation. It was observed that in the analysis of doubly censored data in Bayesian framework, the SRIGP paired with SELF (DLF) was a suitable choice for estimating mixing proportion (component) parameters.