Modeling radiation and electronic devices data with Poisson-Darna distribution

Count data modeling is essential in many scientific fields when the data observations are discrete and non-negative. In this paper, we use a mixed Poisson technique to propose a novel two-parameter distribution known as the Poisson-Darna distribution. We investigated several mathematical features, including moments, dispersion index, and associated measures. The parameters of the new count distribution were estimated using the maximum likelihood estimation approach. Through a comprehensive Monte Carlo simulation study, we assess the performance of the estimators under various sample sizes. It demonstrates that the estimators are consistent and efficient with bias, mean relative and mean squared error decreasing as the sample size increases. We also test the model adequacy of our proposed distribution on two datasets associated with radiation and electronic device fields, comparing its performance to current distributions. Bayesian approaches were also used for data analysis. In comparison to competing distributions, the Poisson-Darna distribution examined both datasets more effectively. The findings contribute to the ongoing development of statistical methodology for count data modeling.