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McDonald Power Function Distribution with Theory and Applications

Muhammad Ahsan ul Haq, Rana Muhammad Usman, Nurbanu Bursa, Gamze Öze


This study presents a new distribution named as McDonald power function (McPF) distribution which extends power function distribution to increase the flexibility of model. The proposed distribution is a generalized form of numerous distributions such as power function, exponentiated power function, Kumaraswamy power function and beta power function distribution discussed in the literature. We derive some fundamental properties including ordinary moments, moment generating function, mode, entropy and order statistics. Reliability analysis is also performed and explains different behavior of the model. Parameters are obtained via maximum likelihood estimation method to fit new model and show its potentiality with three applications to real data sets.


McDonald power function, Maximum likelihood estimation, Moment generating function, Entropy, Order statistics.

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