The Generalized Gompertz-G Family of Distributions: Statistical Properties and Applications

This research aimed at presenting a new statistical model called the Generalized Gompertz-G family of distribution via the method of Alzaatreh, which introduces additional shape parameters for any baseline distribution. We investigate various mathematical aspects of this model, explicitly deriving properties such as moments, moment-generating function, survival function, hazard function, entropies, quantile function, and order statistics distribution. We explore a particular member of this family of distributions, the Generalized Gompertz-Exponential Distribution (GGED), by defining its properties and doing a detailed analysis. A Monte Carlo simulation was utilized to evaluate the model's flexibility and performance, and the distribution family's potential utility in real-world data analysis was further highlighted by investigating the model's parameter estimation using the method of maximum likelihood. We also assess the adaptability of the Generalized Gompertz-Exponential distribution using a real-life dataset and relating its performance with other established models through information criterion. The results show that the Generalized Gompertz-Exponential distribution (GGED) outperformed the compared distributions, emphasizing its potential applicability in diverse practical scenarios for data modeling.