ENHANCED BAYESIAN ESTIMATION AND PREDICTION FOR BIVARIATE LIFETIME DATA USING FGM COPULA-BASED MARSHALL-OLKIN WEIBULL-RAYLEIGH MODEL

This paper introduces the Bayesian approach designed for analysis of the bivariate Marshall-Olkin Weibull-Rayleigh model, significantly enhanced by the incorporation of Farlie-Gumbel-Morgenstern copula. The core objective is to first precisely estimate the model's unknown parameters and then conduct a two-sample Bayesian prediction for future observations. A key contribution lies in the derivation of Bayes estimators and predictors, considering risk in detail and utilizing two distinct loss functions: the squared error loss function, which represents a symmetric approach to estimation error, and the linear exponential loss function, which accounts for asymmetric costs associated with overestimation or underestimation. To rigorously validate our theoretical findings, a simulation study is conducted. This involves extensive data generation and analysis via the Markov chain Monte Carlo method, implemented efficiently using the R programming language. Beyond theoretical validation, the practical utility and adaptability of the proposed bivariate Marshall-Olkin Weibull-Rayleigh model based on Farlie-Gumbel-Morgenstern copula are demonstrated through its application to two diverse real-life datasets, presenting its potential for analysis in various applied domains.