Gompertz-Weibull {Gompertz} Type I: A Four-Parameter Generalization of the Weibull Family

In this paper, we provide a construction method that provides greater flexibility in modeling real-world phenomenon by generalizing univariate probability distributions. The Gompertz distribution is used to provide new classes of models through T-X{Y} construction, in a manner we will define as a “proper” generalization, illustrated by application to the popular Weibull family. We provide moments and other properties of the model, including the necessary equations for maximum likelihood estimation, and we fit a set of real data to the model. A framework for classifying generalizations that includes many previously discovered methods and considerations for the research infrastructure are proposed in our methods and discussion.