# A multivariate extension of the Lorenz curve based on copulas and a related multivariate Gini coefficient

arXiv: https://arxiv.org/abs/2101.04748 · HTML: https://mlsanity.com/paper/2101.04748/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2021.

## Built on by (most cited first, 2 of 2)

- [From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties](https://mlsanity.com/paper/2507.11387/) (2025)
- [Measuring AI harms with multidimensional Lorenz Zonoids](https://mlsanity.com/paper/2609.16004/) (2026)

## Abstract (arXiv)

We propose an extension of the univariate Lorenz curve and of the Gini coefficient to the multivariate case, i.e., to simultaneously measure inequality in more than one variable. Our extensions are based on copulas and measure inequality stemming from inequality in every single variable as well as inequality stemming from the dependence structure of the variables. We derive simple nonparametric estimators for both instruments and apply them exemplary to data of individual income and wealth for various countries.