Bayesian Estimation and MCMC-Based Analysis of the Inverse Exponentiated Exponential Poisson Distribution

Abstract

This study takes a Bayesian approach to estimating and analyzing the parameters of the Inverse Exponentiated Exponential Poisson distribution (IEEP), using Markov Chain Monte Carlo (MCMC) sampling. To make sure the MCMC chains are mixing well, we used convergence diagnostics like the Gelman-Rubin diagnostic and trace plots. These checks confirm that our posterior estimates for both the rate and shape parameters are reliable and well-behaved, showing clear unimodal distributions and credible intervals that give us a probabilistic range of the estimates. We also performed residual analysis along with normality tests like Shapiro-Wilk and Anderson-Darling, which showed the residuals follow a normal distribution. So our model’s assumptions hold up. Besides, posterior predictive checks and various models fit techniques demonstrated that the Bayesian model captures the underlying data distribution effectively. Overall, these results emphasize the robustness of Bayesian inference when modeling the IEEP distribution, supporting its usefulness and validity for both statistical analysis and realworld data applications.