A novel discrete statistical model with applications on medical and health real data

This study introduces and examines a novel two-parameter count probability distribution. The new distribution is developed by combining Poisson and two-parameter Chris-Jerry distributions and is named as “Poisson two-parameter Chris-Jerry” distribution. Key mathematical characteristics of this model are analyzed, including moments, moment-generating functions, variance, dispersion index, skewness, and kurtosis. Additionally, reliability features such as the hazard rate, and Shannon entropy are explored. The parameter estimation is performed using a renowned maximum likelihood estimation approach. A comprehensive simulation study is utilized to evaluate the performance of derived estimators. The model's flexibility is tested on four datasets from different domains, revealing that it offers greater flexibility compared to existing distributions.