Neutrosophic Maxwell–Boltzmann Distribution: Properties and Application to Healthcare Data

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.