The new extended exponential gamma (NEEG) distribution: properties and applications to infectious disease modelling

This study introduces the New Extended Exponential-Gamma (NEEG) distribution, a flexible lifetime model developed to address the limitations of classical and generalized distributions in capturing real-world data complexity. The statistical properties of the proposed distribution are thoroughly explored, including its probability density function, cumulative distribution function, and parameter estimation via the maximum likelihood method. The practical effectiveness of the NEEG model is demonstrated using two real-life COVID-19 datasets from Italy and Nigeria, where it is benchmarked against several existing models such as the Gamma, Exponential, UYEG, and two variants of the Generalized Lindley distribution. Model comparison was conducted using a combination of information criteria (AIC, AICc, BIC, HQIC) and graphical tools such as density plots overlaid on empirical histograms. The results consistently show that the NEEG distribution provides the best fit across both datasets, outperforming all competing models in terms of flexibility, goodness-of-fit, and alignment with the empirical data. The model’s adaptability to skewed and peaked data structures is particularly evident in pandemic-related scenarios, where traditional models often fail. These findings position the NEEG distribution as a powerful and versatile tool for statistical modelling in public health, reliability analysis, and other domains requiring robust handling of non-normal, skewed, or heavy-tailed data. Future research may extend the model into regression frameworks or multivariate contexts to enhance its applicability further.