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Journal of Probability and Statistics
Volume 2016, Article ID 7208425, 12 pages
Research Article

General Results for the Transmuted Family of Distributions and New Models

1Departamento de Estatística, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, RN, Brazil
2Department of Mathematics and Statistics, University of North Carolina Wilmington, Wilmington, NC, USA
3Departamento de Estatística, Universidade Federal de Pernambuco, 50740-540 Recife, PE, Brazil

Received 4 October 2015; Accepted 29 December 2015

Academic Editor: Zacharias Psaradakis

Copyright © 2016 Marcelo Bourguignon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The transmuted family of distributions has been receiving increased attention over the last few years. For a baseline G distribution, we derive a simple representation for the transmuted-G family density function as a linear mixture of the G and exponentiated-G densities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Rényi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.