Bayesian Analysis of Heterogeneous Doubly Censored Lifetime Data using the 3-Component Mixture of Rayleigh Distributions: A Monte Carlo Simulation Study

Abstract

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