We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward transfers of probability mass along the rearranged profile of the predictive distribution. For finite outcome spaces, this yields a normalized sharpness measure with transparent mass--length representation and equivalent formulations as a Gini-type coefficient on the probability vector and a scaled 1-Wasserstein distance from the uniform distribution in rearranged space. We extend the functional to bounded continuous and multidimensional domains for predictive distributions with finite first moment, and establish normalization, symmetry, continuity, and monotonicity properties. The diagnostic application of the measure is illustrated with real and simulated data, and a relationship to the multivariate energy score is discussed.

翻译：我们提出一种用于概率模型的锐度泛函，该泛函将锐度量化为概率分布的内在属性。该度量基于秩相关的浓度原理导出，通过追踪预测分布重排剖面上概率质量的上行转移。对于有限结果空间，该原理可导出具有明确质量-长度表征的归一化锐度度量，其等价形式包括概率向量上的基尼型系数，以及重排空间中与均匀分布的缩放1-瓦瑟斯坦距离。我们将该泛函扩展至具有有限一阶矩的预测分布的有界连续域与多维域，并建立了归一化、对称性、连续性与单调性等性质。通过真实数据与模拟数据展示了该度量的诊断应用，并讨论了其与多元能量评分的关系。