"The rich are getting richer" implies that the population income distributions are getting more right skewed and heavily tailed. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are all mean-based. In view of this, Professor Gastwirth sounded an alarm back in 2014 by suggesting to incorporate the median into the definition of the Gini index, although noted a few shortcomings of his proposed index. In the present paper we make a further step in the modification of classical indices and, to acknowledge the possibility of differing viewpoints, arrive at three median-based indices of inequality. They avoid the shortcomings of the previous indices and can be used even when populations are ultra heavily tailed, that is, when their first moments are infinite. The new indices are illustrated both analytically and numerically using parametric families of income distributions, and further illustrated using capital incomes coming from 2001 and 2018 surveys of fifteen European countries. We also discuss the performance of the indices from the perspective of income transfers.

翻译："富人越来越富"意味着人口收入分布越来越右偏且尾部厚重。对于此类分布，均值并非最佳的集中趋势度量指标，而经典的不平等指数（包括著名的基尼指数）均基于均值。有鉴于此，Gastwirth教授早在2014年就提出警示，建议将中位数纳入基尼指数的定义中，尽管其提出的指数存在若干缺陷。本文在修正经典指数方面迈出新的一步，考虑到不同视角的可能性，提出了三种基于中位数的不平等指数。这些指数避免了先前指数的缺陷，即使在人群收入分布呈现超厚尾特征（即一阶矩无穷大）时仍可适用。我们通过收入分布的参数族从解析和数值角度对新指数进行了阐释，并利用十五个欧洲国家2001年和2018年的资本收入调查数据进一步验证。此外，我们还从收入转移视角讨论了这些指数的性能。