The Kumaraswamy Birnbaum-Saunders Distribution

Motivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy Birnbaum-Saunders (Kw-ℬS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mathcal B}{\mathcal S}$ \end{document}) distribution. This distribution provides an enormous flexibility in modeling heavy-tailed and skewed data. We derive some mathematical properties of the Kw-ℬS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mathcal B}{\mathcal S}$ \end{document} including moments, quantile function, average lifetime function, mean residual lifetime function, and order statistics. In addition, we discuss maximum likelihood estimation of the model parameters.