Journal of Data Science 397-418 , DOI: 10.6339/JDS.201804_16(2).0009 Transmuted Weibull Power Function Distribution: its Properties and Applications Muhammad Ahsan ul Haq* 1 , M. Elgarhy 2 , Sharqa Hashmi 3 , Gamze Ozel 4 and Qurat ul Ain 5 1 Quality Enhancement Cell (QEC), National College of Arts, Lahore-Pakistan. 2 Vice Presidency for Graduate Studies and Scientific Research, University of Jeddah, Jeddah, KSA. 3 Lahore College for Women University, Lahore, Pakistan. 4 Department of Statistics, Hacettepe University, Turkey. 5 Department of Mathematics and Statistics, University of Lahore, Lahore. Abstract: In this paper, we introduce a new four-parameter distribution called the transmuted Weibull power function (TWPF) distribution which extends the transmuted family proposed by Shaw and Buckley [1]. The hazard rate function of the TWPF distribution can be constant, increasing, decreasing, unimodal, upside down bathtub shaped or bathtub shape. Some mathematical properties are derived including quantile functions, expansion of density function, moments, moment generating function, residual life function, reversed residual life function, mean deviation, inequality measures. The estimation of the model parameters is carried out using the maximum likelihood method. The importance and flexibility of the proposed model are proved empirically using real data sets. Key words: Weibull distribution, transmuted family, maximum likelihood, moments, order statistics, entropy. 1. Introduction There are hundreds of continuous distributions in the statistical literature. These distributions have several applications in many applied fields such as reliability, life testing, biomedical sciences, economics, finance, environmental and engineering, among others. However, these applications have proven that the real data following the well-known models are more often the exception rather than the reality. In order to increase the flexibility of the well-known distributions, many authors have proposed different transformations of these models and used these extended forms in several areas. The power function (PF) distribution is a flexible model which can be obtained from the Pareto distribution by using a simple transformation Y = X −1 . The probability density function (pdf) and the cumulative distribution function (cdf) of the PF distribution are, respectively, given by