eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2021-12-20 9 3 52 64 10.12691/tjant-9-3-4 TJANT2021934 article Anyiam Kizito Ebere kizito.anyiam@futo.edu.ng 1 Onyeagu Sydney Iheanyi 2 Njoku Modestus Onyekachi 2 Department of Statistics, School of Physical Sciences, Federal University of Technology, Owerri, Imo State, Nigeria Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria 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. http://pubs.sciepub.com/tjant/9/3/4/tjant-9-3-4.pdf T-R{Y} family quantile function moments Shannon entropy