A Poisson distribution Model Based on Uncertainty

As an extension of the classical Poisson model, this paper presents the Neutrosophic Poisson Distribution (NPD), which incorporates an indeterminacy parameter to manage uncertainty in practical situations. We obtain analytically the basic characteristics of the NPD, such as reliability measures, skewness, kurtosis, variance, mean, and moments about the origin. Important generating functions like the characteristic function and moment generating function (MGF) are also developed. The effect of uncertainty is demonstrated by numerical analyses of mean, variance, and higher-order moments for various parameter values and degrees of indeterminacy. Simulation findings show that the NPD is more flexible and efficient than traditional models, as evidenced by bias, mean squared error (MSE), mean relative error (MRE), and entropy metrics. The usefulness of the NPD in quantifying uncertainty and making decisions is validated by real-world applications, such as simulating customer arrivals and equipment breakdowns.