Abstract
As of the past century, the analysis and the graphical representation of inequality play a very important role in economics. In the literature, several curves have been proposed and developed to simplify the description of inequality. The aim of this paper is a review and a comparison of the most known inequality curves, evaluating the features of each, with a particular focus on interpretation.
Highlights
Inequality is an important characteristic of non-negative distributions
In the remainder of this paper, given a distribution function F, F −1 will denote the inverse function of F or, if needed, the generalized inverse function of F. It is well recognized in the literature that the inequality does not change in case of scale-transformations, the inequality curves must be non dependent on the scale parameters of the distribution
The Lorenz curve introduced in the widely known paper by Lorenz (1905) is the most famous inequality curve used in the literature
Summary
The I(p) curve (Zenga 2007) is the most recent related to the other two curves, it can assume different shapes which allow to distinguish different situations in terms of inequality. One of the first proposals is the δ(p) of Gini which has the important feature of being uniform for the Pareto distribution, but it does not lie in the unitary square Another which can be mentioned is the Z(p) curve, proposed by Zenga (1984). An important application of the inequality curves is that they can be used to define some orderings Such orderings allow the comparison of distributions in terms of inequality.
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