International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3964 2020 2020 Department of Mathematics, University of Kerbala, Iraq Hazim Hazim Directorate of Education Babylon, Babylon, Iraq Majida T. Abdul Sada The probability distribution holds considerable importance within the realm of probability theory, a concept that permeates nearly all scientific disciplines. Nevertheless, the principal aim of the present research endeavor is to introduce a novel distribution referred to as the neutrosophic Alpha logarithm Exponential, abbreviated as NALE. Various mathematical attributes that elucidate life survival and associated characteristics such as hazard rates, moment’s functions, moment-generating functions, and additional metrics including mean and variance are also examined. Two methods were used to estimate the parameters; the Monte Carlo simulation has been employed to evaluate the efficacy of the NALE distribution estimation and to compare the two estimation methods. Therefore, the outcomes from the simulation executed in this research imply that a satisfactory level of precision in estimation is feasible only when the sample size is notably large. The real data has been utilized to demonstrate the specific manner in which the proposed NALE distribution has been recommended for application. Based on the analyses presented in the preceding sections, it can be inferred that the NALE distribution possesses a broad applicability since it is capable of accommodating of neutrosophic data; it does not differentiate between certainty, probabilities of uncertainty, ambiguities, or imprecisions. 2026 2026 100 110 10.54216/IJNS.270110 https://www.americaspg.com/articleinfo/21/show/3964