Parametric Lorenz curves based on the beta system of distributions

Abstract

Some families of Lorenz curves only approximate specific segments of the income distribution. This potential limitation motivates the consideration of more flexible models, which depart from a convenient form of the Lorenz curve. We begin with a Lorenz curve from which we generate a more flexible family of Lorenz curves through two new parameters. We explore the main properties of this family, including the Lorenz ordering, inequality measures, and Leimkhuler curves. An empirical application with US data suggests that the proposed models fit income data accurately.

Keywords:

• Income
• Gini index
• Leimkuhler curve
• order statistics
• parametric Lorenz curve

JEL Classification:

• C80
• D30

Mathematics Subject Classification (2020):

• 62P20
• C80
• D30

Acknowledgements

The authors thank the Editor and two anonymous referees for their constructive comments and suggestions, which significantly improved the paper.

Notes

1 For a detailed reading about the LC concept, we refer the reader to Chotikapanich (2008).

2 See Sarabia et al. (2005) for details about these basic LCs.

3 for a review of different generalisations of the Beta distribution see Gupta and Nadarajah (2004) and Nadarajah (2005).

4 Computed according to Brown’s formula see Brown (1994) given by $G=|1-{\sum }_{k=0}^{n-1}(p_{k+1}-p_k)(q_{k+1}+q_k)|.$

Additional information

Funding

EGD was partially funded by grant ECO2017-85577-P (Ministerio de Economía, Industria y Competitividad. Agencia Estatal de Investigación). JMS was partially funded by grant PID2019-105986GB-C22 (Ministerio de Ciencia e Innovación).