aspg-21-3555-1791472219 20261008151019 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 4 Afrah Al Bossly Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia Adnan Amin School of Economics, Beijing technology and business university, Beijing, China In this work, we present and analyze new probability distribution by generalizing the classical Maxwell–Boltzmann model to neutrosophic structure. The generalized structure, known as the neutrosophic Maxwell (NMX) model that is designed to analyze data with imprecise or vague information. Closed-form expressions for cumulative distribution functions, probability density functions, survival functions, hazard functions, and moments, moment generating functions, mode, skewness, and kurtosis are derived as part of its detailed mathematical and statistical characteristics. The parameter estimation of the suggested model is carried out employing the maximum likelihood estimation (MLE) technique, and the statistical properties of the estimators are discussed in uncertain environments. The inverse cumulative distribution method is established to generate random samples from the proposed model and to evaluate the efficiency of the MLE method. Eventually, a real-world healthcare data set is used to show the efficacy of the proposed model. This research provides new knowledge in the field of neutrosophic statistics, laying a foundation for further exploration in this area 2025 444 452 3555 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250438 https://www.americaspg.com/journal/21/article/3555 https://www.americaspg.com/storage/11740351171.pdf