On Fourier-based inequality indices

TL;DR

This paper introduces a novel inequality index based on Fourier transforms, revealing new properties and expressing existing measures like Gini and Pietra indices in a unified framework, enhancing understanding of wealth heterogeneity.

Contribution

The paper proposes a new Fourier-based inequality index and demonstrates how existing measures can be expressed through Fourier transforms, offering new insights.

Findings

Fourier-based inequality index has promising properties.

Existing indices like Gini can be expressed via Fourier transforms.

The approach simplifies understanding of inequality measures.

Abstract

Originally developed for measuring the heterogeneity of wealth measures, inequality indices are quantitative scores that take values in the unit interval, with the zero score characterizing perfect equality. In this paper, we draw attention to a new inequality index, based on the Fourier transform, which exhibits a number of interesting properties that make it very promising in applications. As a by-product, it is shown that other inequality measures, including Gini and Pietra indices can be fruitfully expressed in terms of the Fourier transform, which allows to enlighten properties in a new and simple way.