Two-Parameter Marshall Olkin Extended Exponentiated Gamma Distribution: Different Methods of Estimation

Abstract

In this paper, we investigate ten different methods for estimating the unknown parameters of the Marshall–Olkin Extended Exponentiated Gamma (MOEEG) distribution. We first present several frequentist approaches, including maximum likelihood, ordinary least squares, weighted least squares, Cramér–von Mises, Kolmogorov, and five variants of the Anderson–Darling statistic (standard, right-tail, left-tail, second-order left-tail). We also develop a Bayesian estimator assuming independent Gamma priors for the parameters. The performance of all estimators is evaluated through extensive Monte Carlo simulations based on bias, root mean square error, and goodness-of-fit metrics. Finally, an application to a real dataset is provided to illustrate the practical relevance of the proposed methods.