Poisson Distribution and Its Applications

Poisson distribution, a foundational discrete probability distribution, describes the probability of observingkindependent events within a fixed temporal or spatial interval under conditions of constant mean occurrence rate (). Therefore, it can be used to address a variety of real-world challenges across diverse domains, particularly in the application of low-probability phenomena. This paper investigates the application of the Poisson distribution through rigorous theoretical analysis and case studies specifically spanning on two fields, which arehealthcare resource allocation andcommunication network optimization. Although the Poisson distribution has inherent limitations in some phenomena, our study reveals that as long as the model is optimized based on statistical principles and specific domain contexts, this framework can effectively provide valuable and actionable insights to inform data-driven decision-making across diverse domains ranging from healthcare resource allocation to telecommunications network optimization in complex systems.