A New Class of Exponentiated Exponential Distributions: Bimodality, Regression, and Application

Developing families of distributions that can be flexible in modeling different shapes of data remains a strong emphasis in research. Many families of distributions appeared in the literature in search of more flexibility in fitting different data shapes, especially when modeling unimodal patterns; however, in real-life scenarios, it is possible to encounter data that exhibit a bimodal pattern. Henceforth, the focus of this article is on developing a family of distributions that can be used to fit different shapes of data, including unimodal and bimodal patterns. In this article, a new family of generalized exponentiated exponential distributions is defined using the T-R{Y} framework method, and four examples are studied in detail. Some of the structural properties of the generalized family are discussed. The method of maximum likelihood is proposed to estimate the parameters, and a simulation study is conducted to assess its performance. Six data sets are utilized to illustrate the usefulness of using members of the proposed family in application, and the fits are compared to other existing distributions. A regression model is proposed, and right-censored lifetime data are used in application of the proposed regression model. When compared to other regression models in the literature, the proposed regression model provides an adequate flexibility, which implies that it is suitable and can be used in explaining and describing lifetime data.