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Journal of Probability and Statistics
Volume 2014 (2014), Article ID 864396, 21 pages
http://dx.doi.org/10.1155/2014/864396
Research Article

The Exponentiated Half-Logistic Family of Distributions: Properties and Applications

1Departamento de Estatística, Universidade Federal de Pernambuco, 50740-540 Recife, PE, Brazil
2Department of Statistics, Ferdowsi University, Mashhad 9177948974, Iran
3Departamento de Ciências Exatas, Universidade de São Paulo, 13418-900 Piracicaba, SP, Brazil

Received 3 September 2013; Accepted 5 December 2013; Published 13 March 2014

Academic Editor: Ricardas Zitikis

Copyright © 2014 Gauss M. Cordeiro 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.

Abstract

We study some mathematical properties of a new generator of continuous distributions with two extra parameters called the exponentiated half-logistic family. We present some special models. We investigate the shapes of the density and hazard rate function. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, and order statistics, which hold for any baseline model. We introduce two bivariate extensions of this family. We discuss the estimation of the model parameters by maximum likelihood and demonstrate the potentiality of the new family by means of two real data sets.