aspg-34-4482-1791482494 20261008180134 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2026 6 1 Khalifa AlShaqsi Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, Oman In practice, we encounter many systems that cannot be studied directly, either due to high costs or because some of these systems are not directly detectable. Therefore, we resort to simulation, which involves applying the study to systems similar to real-world systems and then projecting the results if they are suitable for the real system. The simulation process requires a thorough understanding of probability distributions and the methods used to transform random numbers following a regular distribution on [0,1] into random variables that follow it. This allows us to maximize the benefits of the simulation process and obtain more accurate results for all emerging conditions. The generalized gamma distribution is a family of three parameters characterized by high flexibility. It includes several important distributions as special cases, including the gamma, Weibull, exponential, and Rayleigh distributions, making it exceptionally valuable in engineering and reliability analysis. In previous research, we presented a neutrosophic view of the process of generating random numbers and some techniques used to generate random variables. In this research, we present a neutrosophic study for generating neutrosophic random variables following the generalized gamma distribution, a distribution widely used in engineering applications. The neutrosophic approach takes into account the uncertainty and indeterminacy of the parameters, resulting in random intervals for the variables rather than specific values, and thus provides more accurate simulation results that adapt to all the conditions that the system in operation may encounter. 2026 23 28 4482 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.060104 https://www.americaspg.com/journal/34/article/4482 https://www.americaspg.com/storage/articles/manuscripts/01KZWGKDGE4NMQR5DT5XHNC3M8.pdf