aspg-34-2576-1791482608 20261008180328 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2023 3 1 Maissam Jdid Faculty of Science, Damascus University, Damascus, Syria Florentin Smarandache University of New Mexico، Mathematics, Physics and Natural Sciences Division 705 Gurley Ave., Gallup, NM 87301, USA The main interest in statistical analysis is to generate a series of random variables that follow the probability distribution in which the system under study operates. In almost all simulation tests, we need to generate random variables that follow a distribution, a distribution that adequately describes and represents the physical process involved in the experiment at That point. During the experiment, it may be necessary to simulate a real and perform the process of generating a random variable from a distribution many times depending on the complexity of the model to be simulated in order to obtain more accurate simulation results. In previous research, we presented a neutrosophical study of the process of generating random numbers and some techniques that can be used to convert these random numbers into variables. Randomness follows the probability distributions according to which the system to be simulated operates. These techniques were specific to probability distributions defined by a probability density function that is easy to deal with in terms of finding the cumulative distribution function and the inverse function of the cumulative distribution function or by calculating the values of this function at a certain value, and in reality, we encounter Many systems operate according to these distributions, which requires techniques other than the techniques presented. Therefore, in this research we will present a neutrosophical study of the approximation technique for generating random variables that follow probability distributions known as a complex probability density function. We will apply this study to find random variables that follow the distribution. Standard natural 2023 09 14 2576 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.030102 https://www.americaspg.com/journal/34/article/2576 https://www.americaspg.com/storage/articles/manuscripts/01M1SZ54BEZGBRGCXG5DYJ8HPD.pdf