aspg-24-4172-1791482269 20261008175749 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2025 10 1 Alhasan Kawther Department of Mathematics, College of Education for Pure Science, University of Babylon, Iraq Abad Al-Kadim Kareema Department of Mathematics, College of Education for Pure Science, University of Babylon, Iraq In this paper, we are concerned with truncated distributions that have multiple truncations, due to being very useful in representing natural phenomena that cannot be studied at all intervals of their growth or development, for example, phenomena that are related to Agriculture, airplanes, health, and the environment. left truncation is utilized in this study. The statistical characteristics, such as the rth moments, moment generating function, order statistics, reliability function, hazard rate function, and reversed Hazard function, have been introduced. triple left truncated exponential distribution has been applied. Employed the maximum likelihood method to estimate. Also, the performance of triple left truncated exponential distribution was tested by calculating some statistical criteria and testing the goodness of fit for distribution, with comparisons between the distributions and testing them on real data for patients infected with covid-19. 2025 52 59 4172 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.100105 https://www.americaspg.com/journal/24/article/4172 https://www.americaspg.com/storage/41762111623.pdf