# Extremal points of Lorenz curves and applications to inequality analysis

*Amparo Ba\'illo*,
*Javier C\'arcamo* and
*Carlos Mora-Corral*

Papers from arXiv.org

**Abstract:**
We find the set of extremal points of Lorenz curves with fixed Gini index and compute the maximal $L^1$-distance between Lorenz curves with given values of their Gini coefficients. As an application we introduce a bidimensional index that simultaneously measures relative inequality and dissimilarity between two populations. This proposal employs the Gini indices of the variables and an $L^1$-distance between their Lorenz curves. The index takes values in a right-angled triangle, two of whose sides characterize perfect relative inequality-expressed by the Lorenz ordering between the underlying distributions. Further, the hypotenuse represents maximal distance between the two distributions. As a consequence, we construct a chart to, graphically, either see the evolution of (relative) inequality and distance between two income distributions over time or to compare the distribution of income of a specific population between a fixed time point and a range of years. We prove the mathematical results behind the above claims and provide a full description of the asymptotic properties of the plug-in estimator of this index. Finally, we apply the proposed bidimensional index to several real EU-SILC income datasets to illustrate its performance in practice.

**Date:** 2021-03

**New Economics Papers:** this item is included in nep-ecm

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

http://arxiv.org/pdf/2103.03286 Latest version (application/pdf)

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:arx:papers:2103.03286

Access Statistics for this paper

More papers in Papers from arXiv.org

Bibliographic data for series maintained by arXiv administrators ().