Modeling biological count data with the Poisson-Mgamma distribution: Applications to radiation and yeast cell analysis

• Introduces the Poisson-Mgamma (PMga) distribution, a new one-parameter discrete model formed by compounding the Poisson and Mgamma distributions. • Derives key theoretical properties, showing that higher parameter values reduce the mean, variance, and interquartile range while increasing skewness. • Demonstrates efficient and accurate parameter estimation via maximum likelihood, supported by Monte Carlo simulation results. • Validates the model’s applicability and superior fit through analysis of dicentric chromosome counts and yeast cell count datasets. • Applicable to modeling bioengineering systems, including reliability analysis and radiation risk assessment. This study introduces a novel one-parameter discrete probability distribution, the Poisson-Mgamma (PMga), constructed by compounding the classical Poisson distribution with the Mgamma distribution. The model combines enhanced flexibility for analyzing count data with the mathematical tractability of the Poisson framework. Theoretical analysis shows that as the model parameter increases, the mean, variance, and interquartile range decrease, while skewness increases. With closed-form moments and adaptable tail behavior, the PMga distribution serves as a simple yet powerful tool for modeling dispersion in count data. Parameter estimation is performed using the maximum likelihood estimation, with Monte Carlo simulation results indicating that MLE consistently yields greater accuracy and efficiency. The practical applicability of the PMga model is demonstrated through its analysis of two biologically significant datasets: dicentric chromosome counts in human peripheral blood following exposure to 1.600 Gy of 1480 MeV oxygen ion radiation, and yeast cell counts obtained via hemocytometer measurements. Comparative goodness-of-fit assessments indicate that the PMga distribution provides improved performance relative to several existing models, highlighting its potential as a versatile tool for modeling biological count data.