New multivariate Gini’s indices
定义了新的多元基尼指数来测量多维数据的离散程度，并给出了二元情况下的依赖-离散指数性质、协方差表示和条件分布解释，还讨论了半相干系统的效率基尼指数及经验版本。
The Gini’s mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini’s index, denotes two times the area between the egalitarian line and the Lorenz curve. Both are dispersion indices because they quantify how far a random variable and its independent copy are. Aiming to measure dispersion in the multivariate case, we define and study new Gini’s indices. For the bivariate case we provide several results and we point out that they are “dependence-dispersion” indices. Covariance representations are exhibited, with an interpretation also in terms of conditional distributions. Further results, bounds and illustrative examples are discussed too. Multivariate extensions are defined, aiming to apply both indices in more general settings. Then, we define efficiency Gini’s indices for any semi-coherent system and we discuss about their interpretation. Empirical versions are considered as well in order to apply multivariate Gini’s indices to data.