International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3475 2020 2020 Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia Afrah Afrah School of Economics, Beijing technology and business university, Beijing, China Adnan Amin Real data modelling of extreme events, such as rainfall, temperature, financial costs is very important in neutrosophic statistical methods. The Cauchy distribution is one of statistical models used for modelling such extreme events in natural processes. In cases of imprecise data which most often involve vague, incomplete and ambiguous information, standard statistical methods cannot fully describe the spectrum of uncertainty. In this study, we have considered a new Cauchy distribution under neutrosophic context to deal with uncertain data. The proposed neutrosophic Cauchy distribution (NCD) may analysis extreme events data involving incomplete observations. We provide basic mathematical characteristics and important statistical functions of the Cauchy model under neutrosophic framework. A complete procedure of random numbers generation using neutrosophic quantile function is discussed. The unknown parameters of the proposed are estimated using the maximum likelihood approach. Numerical results show that the proposed model adequately fits the data involving extreme and imprecise values. The performance and flexibility of the model are also supported by an application to a real data set. 2025 2025 262 271 10.54216/IJNS.250422 https://www.americaspg.com/articleinfo/21/show/3475