In this contribution, we derive explicit bounds on the Kolmogorov distance for multivariate max-stable distributions with Fr\'echet margins. We formulate those bounds in terms of (i) Wasserstein distances between de Haan representers, (ii) total variation distances between spectral/angular measures - removing the dimension factor from earlier results in the canonical sphere case - and (iii) discrepancies of the Psi-functions in the inf-argmax decomposition. Extensions to different margins and Archimax/clustered Archimax copulas are further discussed. Examples include logistic, comonotonic, independent and Brown-Resnick models.

翻译：本文针对具有弗雷歇边缘的多元极大稳定分布，推导了其柯尔莫哥洛夫距离的显式界。我们将这些界表述为以下三种形式：(i) 德哈恩表示元之间的瓦瑟斯坦距离，(ii) 谱测度/角测度之间的全变差距离——在典型球面情形下消除了先前结果中的维度因子，以及(iii) 下确界-最大值分解中Psi函数的差异。本文进一步讨论了不同边缘分布及阿基米德-极大/聚类阿基米德-极大连接函数的扩展情形。示例涵盖逻辑模型、共单调模型、独立模型及布朗-雷斯尼克模型。