Hindawi Publishing Corporation Journal of Probability and Statistics Volume 2011, Article ID 904705, 18 pages doi:10.1155/2011/904705 Research Article The Beta-Half-Cauchy Distribution Gauss M. Cordeiro 1 and Artur J. Lemonte 2 1 Departamento de Estat´ ıstica, Universidade Federal de Pernambuco, 50749-540 Recife, PE, Brazil 2 Departamento de Estat´ ıstica, Universidade de S˜ ao Paulo, 05311-970 S˜ ao Paulo, SP, Brazil Correspondence should be addressed to Artur J. Lemonte, arturlemonte@gmail.com Received 28 May 2011; Accepted 13 September 2011 Academic Editor: Jos´ e Mar´ ıa Sarabia Copyright q 2011 G. M. Cordeiro and A. J. Lemonte. 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. On the basis of the half-Cauchy distribution, we propose the called beta-half-Cauchy distribution for modeling lifetime data. Various explicit expressions for its moments, generating and quantile functions, mean deviations, and density function of the order statistics and their moments are provided. The parameters of the new model are estimated by maximum likelihood, and the observed information matrix is derived. An application to lifetime real data shows that it can yield a better fit than three- and two-parameter Birnbaum-Saunders, gamma, and Weibull models. 1. Introduction The statistics literature is filled with hundreds of continuous univariate distributions see, e.g., 1, 2. Numerous classical distributions have been extensively used over the past decad- es for modeling data in several areas such as engineering, actuarial, environmental and medi- cal sciences, biological studies, demography, economics, finance, and insurance. However, in many applied areas like lifetime analysis, finance, and insurance, there is a clear need for ex- tended forms of these distributions, that is, new distributions which are more flexible to model real data in these areas, since the data can present a high degree of skewness and kur- tosis. So, we can give additional control over both skewness and kurtosis by adding new para- meters, and hence, the extended distributions become more flexible to model real data. Recent developments focus on new techniques for building meaningful distributions, including the generator approach pioneered by Eugene et al. 3. In particular, these authors introduced the beta normal BN distribution, denoted by BNμ, σ, a, b, where μ ∈ R,σ> 0 and a and b are positive shape parameters. These parameters control skewness through the relative tail weights. The BN distribution is symmetric if a  b, and it has negative skewness when a<b and positive skewness when a>b. For a  b> 1, it has positive excess kurtosis, and for