Bayesian and Non-Bayesian Approaches for Estimating the Extended Exponential Distribution: Applications to COVID-19 and Carbon Fibers

Abstract

This study focuses on estimating the parameters of the Odd Burr XII–Exponential (OBXII‑E) distribution using both Bayesian and classical approaches. For the non‑Bayesian framework, seven estimation methods were considered: Maximum Likelihood, Least Squares, Weighted Least Squares, Maximum Product Space, Anderson–Darling, right‑Tailed Anderson–Darling, and Kolmogorov estimators. In the Bayesian context, parameter estimation was carried out using the Markov Chain Monte Carlo (MCMC) technique under different loss functions, including Squared Error, General Entropy, and Linear‑Exponential. Through extensive simulation experiments, the accuracy and consistency of each estimator were evaluated, revealing that all methods converge toward the true parameter values as sample size increases. The OBXII‑E distribution was further applied to two real datasets, where it consistently outperformed competing models based on multiple goodness‑of‑fit criteria. Overall, the results confirm the robustness and flexibility of the OBXII‑E distribution in modeling daily COVID-19 and carbon fibers data.