Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical justification is given, followed by experiments illustrating that they are reasonable measures of these distributional characteristics and computing confidence regions with the desired coverage.

翻译：本文定义了几种新的基于几何分位数的多元离散度、偏度、峰度及球面对称性度量方法。这些度量与现有基于体积的度量方法不同，且易于计算。我们提供了相应的理论依据，并通过实验证明这些度量能够合理表征相应分布特征，且能计算出具有预期覆盖度的置信区域。