The Lamé class of Lorenz curves

ABSTRACT

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 obtained 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 configurations are proposed. Empirical applications with real data are given. Finally, some relationships with other curves are included.

KEYWORDS:

• Donaldson–Weymark–Kakwani
• Gini
• Limited information
• Lorenz curves
• Pietra and Wolfson indices.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62H05

Acknowledgments

We are grateful for the constructive suggestions provided by the reviewers, which improved the paper.

Funding

The authors thank Ministerio de Economía y Competitividad, project ECO2010-15455, for partial support. The second author thanks Ministerio de Educación (FPU AP-2010-4907) for partial support.