On the Families of Generalized Exponentiated Weibull Distributions: Properties and Applications

Abstract

Some new families of exponentiated Weibull (EW) distribution named T-Exponentiated Weibull{Y} using the T-R{Y} context are presented in this article. The quantile functions of five notable distributions, namely, Logistic, Log-Logistic, Rayleigh, Exponential and Lomax were used to develop five sub-families T-EW{Logistic}, T-EW{Log-Logistic}, T-EW{Rayleigh}, T-EW{Exponential} and T-EW{Lomax} and some general properties such as the quantile functions, Moments, mean deviations from the mean and median, Shannon entropies are obtained. The shapes of the exponentiated Weibull family densities shows can be unimodal, bimodal, monotonically decreasing, skewed to the left, skewed to the right and almost symmetric curves while the hazard function can be bathtub shaped, up-side down bathtub shaped, and increasing-deceasing-increasing. To demonstrate the flexibility and usefulness of the model, three real-life datasets analyzed and the results compared with some competing models.