Neutrosophic Poisson moment exponential distribution: Properties and applications

We propose the neutrosophic Poisson moment exponential distribution (NPMExD) as an extension of the Poisson moment exponential distribution (PMExD) originally developed by Ahsan-ul Haq. We detail the application of neutrosophic logic to the PMExD framework, enhancing its capability to handle uncertainty and indeterminacy. The study explores various statistical and mathematical properties of the NPMExD, including the survival function, moment generating function, hazard rate function, order statistics distribution, cumulative hazard function, index of dispersion, and related measures. Parameter estimation is performed using the maximum likelihood estimation method, followed by a comprehensive simulation study to assess the estimator performance. Finally, the practical efficacy of the proposed distribution is demonstrated through the analysis of two real-world data sets: remission times (in weeks) for 20 leukemia patients and 59 months of actual tax revenue (monthly) data from Egypt. The results indicate that the NPMExD provides a superior fit compared to the neutrosophic discrete Ramos?Louzada distribution for these data sets.