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

Abstract

In this study, we introduce a novel generator known as the Generalized Odd Gompertz distribution, which includes an extra shape parameter. We examine various mathematical properties of this new generator and explicitly derive its characteristics such as moments, moment-generating function, survival function, hazard function, entropies, quantile function, and the distribution of order statistics. Within this family of distributions, we focus on one member, the Generalized Odd Gompertz-Exponential distribution, defining and analyzing its properties. To assess the flexibility and performance of the model's parameters, we employ Monte Carlo simulations. We further evaluate the versatility of the Generalized Odd Gompertz- Exponential distribution by applying it to real-world datasets and comparing its performance with other existing models. Additionally, we explore the estimation of model parameters using the maximum likelihood method, demonstrating the potential applicability of this distribution family to real-life data analysis.