aspg-21-2292-1791472099 20261008150819 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 1 Hanaa Saad M. Shebib Department of Economics, Faculty of Administration and Economics, University of Al-Kufa, Iraq Rawaa S. AL-Saffar Department of Statistics, Faculty of Administration and Economics, Mustanisiryah University, Iraq In this article, we used approximate methods to obtain Bayes method estimations for the shape and scale parameters of the generalized exponential distribution, as three approximation methods were employed: Lindley approximation and neutrosophic Lindley approximation, Gibbs sampling and neutrosophic Gibbs sampling, the most important samples based on the gamma informative prior under the squared error loss function. Through different simulation experiments a comparison was made between those estimators of these three approximate methods, from the simulation results we found a relative preference for the important sampling method over the other two methods. The results of simulation experiments were also confirmed by applying these approximate methods to real data representing the operating times of one of the machines of the publishing, printing, and translation house in Baghdad. On the other hand, we apply the same method to the neutrosophic exponential distribution, and the results will be compared to the classical case. 2024 273 286 2292 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230124 https://www.americaspg.com/journal/21/article/2292 https://www.americaspg.com/storage/71702124303.pdf