Improving parameters estimation of a truncated Poisson regression model based on meta-heuristic optimization algorithms

The paper discusses computational and numerical challenges that are associated with the truncation of the information and which change the usual Poisson likelihood by the introduction of black kite optimization algorithm. Real data is used to demonstrate a significant improvement in healthcare and medical research. Truncated Poisson regression models (TPRM) are essential for analyzing count data where zero counts are unobserved, a common scenario in many real-world applications, such as healthcare and medical research. However, parameter estimation in such models often suffers from bias and inefficiency due to the complexity induced by truncation. This study proposes an improved parameter estimation approach for TPRM by leveraging meta-heuristic optimization algorithms. Specifically, we integrate state-of-the-art meta-heuristics, black kite optimization algorithm (BKA), to optimize the likelihood function and overcome the limitations of traditional iterative methods such as Newton-Raphson and quasi-Newton algorithms. Using extensive Monte Carlo simulations and real data application, we evaluate the performance of the proposed method under varying sample sizes and covariate structures. The results demonstrate that our meta-heuristic-based estimator significantly reduces mean squared error compared to conventional estimators, enhancing model reliability and predictive accuracy. The proposed approach offers a robust and efficient alternative for parameter estimation in truncated Poisson regression, with potential applications in epidemiology, ecology, and other fields dealing with truncated count data.