Neutrosophic moment exponential distribution: properties and modeling of child mortality rate data

This research extends traditional statistical distribution theory, which often neglects issues such as ambiguity, imprecision, or indeterminacy. The primary aim is to develop the neutrosophic moment exponential distribution as a refined version of the moment exponential distribution, specifically to tackle situations involving uncertainty. The study derives the proposed model's quantile function, Mills ratio, and elasticity, as well as its mean, variance, $r^{\text{th}}$ moment, index of dispersion, and moment-generating function. It also establishes expressions for the survival function, hazard rate function, cumulative hazard function, and mean residual life function, which are visually explored through graphs. Furthermore, the research calculates information measures including extropy, weighted extropy, cumulative residual extropy, Shannon entropy, and Rényi entropy. The parameters of the proposed model are determined using maximum likelihood estimation, followed by a simulation study and an illustration of the distribution of the order statistics. Finally, the practical superiority of the proposed distribution over several existing models in the literature is demonstrated using a child mortality rate dataset.