Abstract
ABSTRACTIn 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.
Highlights
The Lorenz curve (LC) is an important and convenient statistical instrument used in the analysis of economical data
The family of Lame Lorenz curves is defined by two simple functional forms, which depend on one single parameter
In relation to the probability density function (PDF )f (x) associated with a Lorenz curve L(p) we have the following (Arnold, 1987), Theorem 2.2 If the second derivative L (p) exists and is positive everywhere in an interval (x1, x2), the corresponding cumulative distribution function F has a finite positive probability density function in the interval (μL (x+1 ), μL (x−2 )), which is given by f (x) =
Summary
Arnold (1986), Pakes (1986), Arnold et al (1987), Villasenor and Arnold (1989), Basmann et al (1990), Ortega et al (1991), Chotikapanich (1993), Holm (1993), Ryu and Slottje (1996), Sarabia (1997), Sarabia, Castillo and Slottje (1999, 2001), Ogwang and Rao (1996, 2000), Sarabia and Pascual (2002), Sarabia et al (2005, 2010), Rhode (2009) and Helene (2010). In a recent paper, Henle et al (2008) introduces a family of Lorenz curves, the so called Lame family, which is characterized by a single inequality parameter. This family presents several practical and theoretical advantages. The family of Lame Lorenz curves is defined by two simple functional forms, which depend on one single parameter. The class of Lame Lorenz curves is studied This family has the advantage of modeling inequality with a single parameter, and many of the most important statistical and economic measures for studying the inequality can be obtained in a closed form.
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