An alternative functional form for estimating the Lorenz curve

Abstract

We We propose a simple single parameter functional form for the Lorenz curve. The underlying probability density function and cumulative density functions for the Lorenz curve are derived and are shown to have some useful properties. The proposed functional form is fitted to existing data sets and is shown to provide a better fit than existing single parameter Lorenz curves for the given data.

Distorted Lorenz curves: models and comparisons

“…Different parametric models for the Lorenz curve have been proposed by Kakwani and Podder (1976), Rasche et al (1980), Aggarwal (1984), Aggarwal and Singh (1984), Gupta (1984), Arnold (1986), Pakes (1986), Arnold et al (1987), Villaseñor and Arnold (1989), Basmann et al (1990), Ortega et al (1991), Chotikapanich (1993), Holm (1993), Ryu and Slottje (1996), Sarabia (1997), Sarabia et al (1999), Sarabia et al (2001), Ogwang and Rao (1996), Ogwang and Rao (2000), Sarabia and Pascual (2002), Sarabia et al (2010a,b), Rohde (2009), Helene (2010, Wang et al (2009Wang et al ( , 2011, and recently, Sarabia et al (2013). As we show in this section, a number of these models have been obtained by distorting a baseline Lorenz curve L .…”

“…With a different parametrization, this family was considered by Aggarwal (1984), Aggarwal and Singh (1984), Rohde (2009) and Sarabia et al (2010a). Using (10) we obtain the class…”

A piecewise method for estimating the Lorenz curve

“…Many models are available in the literature (eg. Ryn and Slottje, 1996;Sarabia et al, 1999Sarabia et al, , 2001Rohde, 2009). A drawback of these models is that they do not simultaneously provide a good fit for both the Lorenz curve values and frequencies (Wang et al, 2011).…”

Income Inequality Measures

“…Therefore, they can easily be analyzed. Rohde [22] and Fellman [2] [13] paid these models special attention and examined them in more detail. However, they are so simple that it is impossible to distinguish be- Figure 6, we present the Pareto distribution as a function of the parameter α .…”