On a property of the inequality curve $\lambda(p)$

TL;DR

This paper investigates the unique property of the Zenga inequality curve being constant for Pareto distributions, providing insights into tail analysis and estimation for heavy-tailed distributions.

Contribution

It establishes that the constancy of the Zenga curve is exclusive to Pareto distributions and asymptotically valid for power tail distributions with index greater than 1.

Findings

The Zenga curve is exactly constant only for Pareto distributions.

Asymptotically, the property holds for distributions with power tail index > 1.

These properties enable new tools for tail analysis and estimation.

Abstract

The Zenga (1984) inequality curve is constant in p for Type I Pareto distributions. We show that this property holds exactly only for the Pareto distribution and, asymptotically, for distributions with power tail with index -a, with a greater than 1. Exploiting these properties one can develop powerful tools to analyze and estimate the tail of a distribution.