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In this paper, we introduce a univariate four-parameter distribution. Several known distributions like exponentiated Weibull or extended generalized exponential distribution can be obtained as special case of this distribution. The new distribution is quite flexible and can be used quite effectively in analysing survival or reliability data. It can have a decreasing, increasing, decreasing-increasing-decreasing (DID), upside-down bathtub (unimodal) and bathtub-shaped failure rate function depending on its parameters. We provide a comprehensive account of the mathematical properties of the new distribution. In particular, we derive expressions for the moments, mean deviations, Rényi and Shannon entropy. We discuss maximum likelihood estimation of the unknown parameters of the new model for censored and complete sample using the profile and modified likelihood functions. One empirical application of the new model to real data are presented for illustrative purposes., Statistica, Vol 78, No 4 (2018)