Parametric estimation of quantile versions of Zenga and D inequality curves: methodology and application to Weibull distribution

TL;DR

This paper introduces parametric estimators for quantile-based inequality curves like Zenga and D, proves their statistical properties, and applies them to Weibull distribution data.

Contribution

It proposes a minimum distance estimator for quantile inequality curves and demonstrates its theoretical properties and practical application to Weibull-distributed data.

Findings

The MD estimator is consistent and asymptotically normal.

The methods effectively estimate inequality measures in Weibull models.

Application to precipitation data illustrates practical utility.

Abstract

Inequality (concentration) curves such as Lorenz, Bonferroni, Zenga curves, as well as a new inequality curve -- the $D$ curve, are broadly used to analyse inequalities in wealth and income distribution in certain populations. Quantile versions of these inequality curves are more robust to outliers. We discuss several parametric estimators of quantile versions of the Zenga and $D$ curves. A minimum distance (MD) estimator is proposed for these two curves and the indices related to them. The consistency and asymptotic normality of the MD estimator is proved. The MD estimator can also be used to estimate the inequality measures corresponding to the quantile versions of the inequality curves. The estimation methods considered are illustrated in the case of the Weibull model, which is often applied to the precipitation data or times to the occurrence of a certain event.