Parameter Estimation for a Log-Linear Nonhomogeneous Poisson Process Via Classical and Intelligent Approaches: A Case Study of Erbil International Airport

The Nonhomogeneous Poisson Process (NHPP), characterized by rate functions that vary over time, is generally used to model the occurrence of events over time. A key challenge lies in accurately estimating the intensity function that derive the process. This paper focuses on estimating the parameters of a log-linear intensity function using the traditional Maximum Likelihood Estimation (MLE), Method of Moments (MoM) and two intelligent optimization techniques - Particle Swarm Optimization (PSO) and Firefly Algorithm (FFA). The objective is to evaluate and compare these estimation methods to identify the most effective approach, followed by the application of a NHPP to model the number of passenger arrivals at Erbil International Airport (EIA) - an important factor for improving airport facility planning. The analysis utilizes passenger arrival data recorded at Erbil International Airport (EIA) in Kurdistan Region (KR) of Iraq from January 1, 2021, to September 30, 2024. The passenger arrival rate is initially analyzed through a homogeneity test, and then the Cross-Validation technique is applied to evaluate the model's predictive performance. Additionally, two simulation techniques are employed to assess the performance of the estimation methods by calculating the Root Mean Square Error (RMSE). The findings reveal that the PSO technique outperforms MLE, MoM and FFA, providing more accurate parameter estimates and faster convergence for the log-linear model.