Generalized transmuted family of distributions: properties and applications

Year 2017, Volume: 46 Issue: 4, 645 - 667, 01.08.2017

Morad Alizadeh , Faton Merovci , G.g. Hamedani

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

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