In this paper we derive inferential results for a new index of inequality, specifically defined for capturing significant changes observed both in the left and in the right tail of the income distributions. The latter shifts are an apparent fact for many countries like US, Germany, UK, and France in the last decades, and are a concern for many policy makers. We propose two empirical estimators for the index, and show that they are asymptotically equivalent. Afterwards, we adopt one estimator and prove its consistency and asymptotic normality. Finally we introduce an empirical estimator for its variance and provide conditions to show its convergence to the finite theoretical value. An analysis of real data on net income from the Bank of Italy Survey of Income and Wealth is also presented, on the base of the obtained inferential results.

中文翻译：

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一种新的不平等程度的推论结果

在本文中，我们得出了一个新的不平等指数的推论结果，该指数专门用于捕获在收入分配的左尾和右尾观察到的重大变化。在过去的几十年中，后一种转变对于美国，德国，英国和法国等许多国家来说是显而易见的事实，也是许多决策者关注的问题。我们为该指数提出了两个经验估计量，并证明它们在渐近上是等价的。然后，我们采用一个估计量，证明其一致性和渐近正态性。最后，我们为它的方差引入了一个经验估计量，并提供了条件来证明其收敛于有限理论值。在得出的推论结果的基础上，还对意大利银行的收入和财富调查中的净收入的真实数据进行了分析。