A New Poisson Mixture Distribution: Characterization and Biomedical Application

Abstract

This study presents a novel Poisson mixture distribution, combining elements of the Poisson and Suja distributions. The structural properties of this distribution are derived, including the formulation of the r-th central moments. Additionally, formulas for the coefficient of variation, skewness, and kurtosis are provided, with their behaviors illustrated through graphical representations. Key statistical properties, such as the hazard rate function and generating functions, are also discussed. Methods for parameter estimation, including maximum likelihood estimation and the method of moments, are explored. A simulation study has been conducted to assess the model. In many practical scenarios, real-world datasets do not fit well with conventional distributions. In this case, a dataset of newborn babies' weights from a hospital in Kerala over a specific period is analyzed, focusing on the number of newborns with critically low birth weight (Extremely Low Birth Weight, or ELBW). This data is fitted using the Poisson-Suja distribution. The goodness of fit of the proposed distribution is demonstrated using the count dataset, showing it outperforms the Poisson, Poisson Lindley (PL), and Poisson Akash (PA) distributions.