The Marshall-Olkin alpha power family of distributions with applications

In this paper, we introduce the Marshall-Olkin alpha power family of distributions to extend the alpha power transform class defined by Mandavi and Kundu (2017) and several other distributions. The new family is analytically tractable and it can be used quite effectively for real data analysis. Some of its structural properties are established. Members of the new family can have symmetrical, right-skewed and reversed-J shaped densities, and increasing, decreasing, upside-down bathtub and reversed-J shaped hazard rates. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of three real data sets and the data sets show the new family of distributions is more appropriate as compared to the Marshall-Olkin generalized Lindley, Marshall-Olkin generalized exponential, Marshall-Olkin logistic exponential, Marshall-Olkin exponential, exponentiated exponential, transmuted generalized exponential, alpha power exponential and exponential distributions. (C) 2018 Elsevier B.V. All rights reserved.