Rate of Occurrence Estimation in Geometric Processes with Maxwell Distribution: A Comparative Study between Artificial Intelligence and Classical Methods

The Geometric Process is a powerful alternative to the Non-Homogeneous Poisson Process for modeling event occurrences across various domains, including engineering, finance, and epidemiology. This study focuses on enhancing parameter estimation for the GP when the time distribution of the first event follows a Maxwell distribution. To achieve this, we applied and compared three estimation techniques: parametric Maximum Likelihood Estimation, nonparametric Modified Moments, and the Firefly Optimization Algorithm. Simulated data from a gas power plant in Mosul was used to assess the performance of these methods. Results demonstrated that all three methods yielded accurate estimates, with FFA outperforming the others in terms of Mean Squared Error. Additionally, the Kolmogorov-Smirnov test validated the data's adherence to the Maxwell distribution, confirming the model's suitability. This study highlights the GP's applicability in real-world scenarios, particularly in reliability engineering and event modeling. However, reliance on simulated data limits the findings, as it may not fully reflect real operational complexities. Future work should extend these methods to diverse datasets and explore different distributional assumptions. The practical implications are significant, as precise parameter estimation can enhance decision-making in engineering processes and resource management. On a broader level, the findings may influence risk assessment approaches and improve operational efficiency in critical infrastructure systems, contributing to societal gains in service reliability and delivery