Classical inequality curves and inequality measures are defined for distributions with finite mean value. Moreover, their empirical counterparts are not resistant to outliers. For these reasons, quantile versions of known inequality curves such as the Lorenz, Bonferroni, Zenga and $D$ curves, and quantile versions of inequality measures such as the Gini, Bonferroni, Zenga and $D$ indices have been proposed in the literature. We propose various nonparametric estimators of quantile versions of inequality curves and inequality measures, prove their consistency, and compare their accuracy in a~simulation study. We also give examples of the use of quantile versions of inequality measures in real data analysis.

翻译：经典的不平等曲线和不平等指标是为有限均值分布定义的。然而，它们的经验对应量对异常值不敏感。为此，文献中提出了已知不平等曲线（如洛伦兹曲线、邦费罗尼曲线、曾加曲线和$D$曲线）的分位数版本，以及不平等指标（如基尼系数、邦费罗尼指数、曾加指数和$D$指数）的分位数版本。我们提出了不平等曲线和不平等指标分位数版本的各种非参数估计量，证明了它们的一致性，并通过模拟研究比较了它们的精度。我们还给出了在真实数据分析中使用不平等指标分位数版本的实例。