A novel two-parameter discrete probability model: regression framework and healthcare applications

Abstract This study introduces a new statistical model, called the Poisson EGamma model (P-EG), for analyzing count response data. The model integrates the advantages of the Poisson distribution and the Two-Parameter EGamma distribution, providing a versatile approach to count data analysis. Extensive research has been conducted on the structural properties of this newly proposed discrete model, including its probability mass function, moments, probability and moment generating functions, reliability and hazard rate function, order statistics, dispersion index, and zero-inflation characteristics. Parameter estimation is performed using the method of moments and the method of maximum likelihood. The simulation study is conducted to evaluate the efficiency of estimation methods. Furthermore, count regression model based on the Poisson EGamma distribution is introduced with its residual analysis. The applicability of the P-EG regression model is illustrated using real-world healthcare data involving infected blood cell counts and doctor visits. Results show that the Poisson EGamma model effectively captures the complexities of cells and Doctor visits data, outperforming traditional count regression models in terms of both goodness of fit and predictive accuracy. The proposed model presents a promising tool for researchers and practitioners in healthcare data analysis, particularly in cases of over-dispersion with excess zeros in count data. ARTICLE HIGHLIGHTS Development of new two-parameter discrete distribution and extended its regression model construction. Addressing the application of maximum likelihood estimation to estimate the unknown parameters. Applying the proposed regression model for analyzing two healthcare real datasets.