STATISTICAL MODELING OF EXTREME VALUES: THE GOMPERTZ INVERSE PARETO DISTRIBUTION METHOD

Abstract

In real-life scenarios, classical probability distributions often fail to adequately capture the characteristics of empirical data. To address this limitation, researchers have introduced various distribution generators, each characterized by one or more parameters, offering enhanced flexibility in modeling data. Some notable generators include the MarshalOlkin family (MO-G), the Beta-G, the Kumaraswamy-G (KwG), the McDonald-G (Mc-G), various types of gamma-G distributions, the log gamma-G, the Exponentiated generalized-G, Transformed-Transformer (T-X), Exponentiated (T-X), Weibull-G, and the Exponentiated half logistic generated family. Additionally, Ghosh et al. (2016) introduced the Gompertz-G generator, which extends continuous distributions with two extra parameters, further enriching the spectrum of available distribution generators. This paper explores the Gompertz-G generator and its general mathematical properties, contributing to the growing toolbox of distribution generators that offer more versatile modeling options for diverse data sets.