The Poisson-Garima Distribution: Additional Key Features and Its Significance on Statistical Process Control in Agriculture

Abstract

This study primarily advances the theoretical development of the Poisson-Garima (PSNG) distribution by establishing several novel properties not previously addressed in existing literature. These theoretical enrichments enhance the model’s statistical foundation and extend its applicability to overdispersed count data commonly observed in fields such as agriculture, biology, and medicine. As a secondary contribution, the improved PSNG model is applied to statistical process control through the development of PSNG-based control charts for monitoring count data. The proposed charts are evaluated via simulation studies and validated with an empirical agricultural dataset, where their performance is benchmarked against eight competing models. Additionally, comparisons between PSNG- and Poisson-based control charts demonstrate the superiority of the proposed approach in detecting process shifts under overdispersion. This integrated approach reinforces the PSNG distribution’s theoretical depth while demonstrating its practical relevance in quality monitoring contexts.