Generalized transmuted family of distributions: properties and applications

Authors : Morad ALİZADEH, Faton MEROVCİ, G.g. HAMEDANİ

Pages : 645-667

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Publication Date : 2017-08-01

Article Type : Research Paper

Abstract :We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Rényi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new family. We discuss the different methods of estimation of the model parameters and illustrate the potential application of the model via real data. A brief simulation for evaluating Maximum likelihood estimator is done. Finally certain characterziations of our model are presented.
Keywords : Transmuted distribution, Generated family, Maximum likelihood, Moment, Order statistic, Quantile function, Rényi entropy, Characterizations