The Lamé Class of Lorenz Curves.
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© Taylor & Francis. "This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Statistics. Theory and Methods on 14 Jan 2014, available online: http://wwww.tandfonline.com/10.1080/03610926.2013.775306."
Communications in Statistics. Theory and Methods, Received 08 Oct 2012, Accepted 06 Feb 2013, Accepted author version posted online: 14 Jan 2014
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Pietra and Wolfson indices
In this paper, the class of Lamé Lorenz curves is studied. This family has the advantage of modeling inequality with a single parameter. The family has a double motivation: it can be obtain from an economic model and from simple transformations of classical Lorenz curves. The underlying cumulative distribution functions have a simple closed form, and correspond to the Singh-Maddala and Dagum distributions, which are well known in the economic literature. The Lorenz order is studied and several inequality and polarization measures are obtained, including Gini, Donaldson-Weymark-Kakwani, Pietra and Wolfson indices. Some extensions of the Lamé family are obtained. Fitting and estimation methods under two different data configuration are proposed. Empirical applications with real data are given. Finally, some relationships with other curves are included.