Gamma exponentiated generalized family of distributions with properties and applications

This manuscript introduces the Gamma Exponentiated Generalized-G (GEG-G) family of distributions, developed by integrating the gamma distribution with the exponentiated generalized (EG) family. The resulting class offers enhanced flexibility and can accommodate a broad spectrum of distributional behaviors. Several special cases within the GEG-G family are presented to illustrate its versatility. Parameter estimation is carried out using maximum likelihood point estimation techniques, and the accuracy and efficiency of these estimators are evaluated through a comprehensive Monte Carlo simulation study. To demonstrate practical applicability, a specific member of the GEG-G family is applied to real-world lifetime count datasets.