Tehran University of Medical Sciences Journal of Biostatistics and Epidemiology 2383-4196 9 4 2023 12 15 484 499 Ibrahim Sule Ahmadu Bello University, Zaria Kolawole Ismail 1Department of Mathematics and Statistics, School of Applied Sciences, Kaduna Polytechnic, Kaduna, Nigeria Olalekan Bello Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria 2024 01 17 2024 04 28 Many experts in the field of distribution theory have focused on extending probability distributions utilizing extended families of continuous distributions to improve the modeling adaptability of the conventional probability distributions. This study introduced a brand-new, five-parameter generalized exponentiated exponential distribution, which is a continuous probability distribution. With the aid of the quantile function, moments, moment generating function, survival function, hazard function, mean, and median, among other mathematical and statistical aspects, the new distribution's shape was deduced and researched. It was also possible to derive the probability density function for the minimum and maximum order statistics for this distribution. The method of maximum likelihood estimate was used to produce a conventional estimation of the unknown parameters. A simulation study was carried out to assess the efficiency and consistency of the estimation method used. To evaluate the fit and adaptability of the new model, it was applied to four real-world datasets in the field of medicine. The analysis's findings demonstrated that the new model performs better than its counterparts and offers a better fit than the Topp-Leone exponentiated exponential (TLEtEx), Topp-Leone Kumaraswamy exponential (TLKEx), exponentiated exponential (EtEx), and exponential (Ex) distributions. https://jbe.tums.ac.ir/index.php/jbe/article/view/1372