FUZZY DATA-DRIVEN ESTIMATION FOR DUAL WEIBULL POPULATIONS: EM AND BAYESIAN METHODS WITH GIBBS SAMPLING

In statistical analysis, accurately estimating parameters in the presence of uncertain and imprecise data is critical, particularly when dealing with complex, dual population models. Fuzzy data, which effectively represents real-world ambiguity, provides a framework for handling such uncertainties. While parameter estimation for single-population models with fuzzy data has been explored extensively, extending these methods to dual populations remains challenging. This study addresses this gap by developing estimation techniques for two Weibull populations that share a common shape parameter but differ in scale parameters, under fuzzy data conditions. We employ the Expectation-Maximization (EM) algorithm for Maximum Likelihood estimation and a Bayesian framework with TK approximation for parameter estimation. To refine our Bayesian estimates, we use Gibbs sampling to compute posterior densities. Through Monte Carlo simulations, for generated data as well as for a real dataset, we evaluate the accuracy and robustness of the proposed estimators, demonstrating their practical utility in applications where data imprecision is a significant factor. This research highlights the importance of robust methodologies for dual-population Weibull models, contributing to enhanced reliability in statistical analysis across diverse fields.