Research Article The Exponentiated Half-Logistic Family of Distributions: Properties and Applications Gauss M. Cordeiro, 1 Morad Alizadeh, 2 and Edwin M. M. Ortega 3 1 Departamento de Estat´ ıstica, Universidade Federal de Pernambuco, 50740-540 Recife, PE, Brazil 2 Department of Statistics, Ferdowsi University, Mashhad 9177948974, Iran 3 Departamento de Ciˆ encias Exatas, Universidade de S˜ ao Paulo, 13418-900 Piracicaba, SP, Brazil Correspondence should be addressed to Gauss M. Cordeiro; gausscordeiro@uol.com.br Received 3 September 2013; Accepted 5 December 2013; Published 13 March 2014 Academic Editor: Ricardas Zitikis Copyright © 2014 Gauss M. Cordeiro et al. his 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. 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 R´ enyi 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. 1. Introduction he use of new generators of continuous distributions from classic distributions has become very common in recent years. One example is the beta-generated family of distri- butions proposed by Eugene et al. [4]. Another example is the gamma-generated family of distributions deined by Zografos and Balakrishnan [5]. Based on a baseline continu- ous distribution () with survival function () and density (), their families are deined by the cumulative distribution function (cdf) and probability density function (pdf) (for ∈ R): ()= 1 Γ() ∫ − log[ (;)] 0  −1  − , ()= 1 Γ() {− log [ (;)]} −1 (;), (1) respectively, where Γ() = ∫ ∞ 0  −1  −  is the gamma function. Based on Zografos and Balakrishnan’s [5] paper, we replace the gamma distribution by the exponentiated half- logistic (“EHL” for short) distribution to deine a new family of continuous distributions by the cdf: ()=∫ − log[1−(;)] 0 2 − [1− − ] −1 [1+ − ] +1  ={ 1−[1−(;)]  1+[1−(;)]  }  , (2) where (;) is the baseline cdf depending on a parameter vector  and >0 and >0 are two additional shape parameters. For any continuous  distribution, the EHL- distribution is deined by the cdf (2). Equation (2) is a wider family of continuous distributions and includes some special models as those listed in Table 1. Hindawi Publishing Corporation Journal of Probability and Statistics Volume 2014, Article ID 864396, 21 pages http://dx.doi.org/10.1155/2014/864396