Analysis of Marshall–Olkin extended Gumbel type-II distribution under progressive type-II censoring with applications

In this study, we explore the practical applications of maximum likelihood and Bayesian estimation methods in the context of progressive type-II censoring, focusing specifically on the Marshall–Olkin extended Gumbel type-II distribution. We begin by computing maximum likelihood estimates for the distribution’s parameters and constructing asymptotic confidence intervals. Additionally, we employ the Markov chain Monte Carlo method to establish credible intervals for Bayes estimates, considering both squared error and linear exponential loss functions. To showcase the effectiveness of our approach, we analyze two real datasets and conduct a simulation study to evaluate the performance of our proposed estimators across varying sample sizes. Our findings reveal that the Bayes estimators for the parameters outperform the maximum likelihood estimators.