Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/1654 2022 2022 Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria Mohamed Bisher Zeina Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria Mohamad Taher Anan Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria Yousef Marjamak This paper presents an algorithm for generating random numbers that follow literal neutrosophic distributions using algebraic isomorphisms. The algorithm was applied to three distributions: literal neutrosophic uniform distribution, literal neutrosophic exponential distribution, and literal neutrosophic normal distribution. We also proposed a development of the Kolmogorov-Smirnov test to analyze goodness-of-fit for literal neutrosophic data. To evaluate the effectiveness of the proposed method, a simulation study was conducted, and the power results showed that increasing the sample size improved the test power. Our research contributes to the development of statistical methods for analyzing literal neutrosophic data, which has applications in a wide range of fields. 2023 2023 08 23 10.54216/GJMSA.040201 https://www.americaspg.com/articleinfo/33/show/1654