Journal of Computational and Applied Mathematics ( IF 2.037 ) Pub Date : 2021-01-13 , DOI: 10.1016/j.cam.2021.113385
Damjana Kokol Bukovšek; Tomaž Košir; Blaž Mojškerc; Matjaž Omladič

Copulas are becoming an essential tool in analyzing data thus encouraging interest in related questions. In the early stage of exploratory data analysis, say, it is helpful to know local copula bounds with a fixed value of a given measure of association. These bounds have been computed for Spearman’s rho, Kendall’s tau, and Blomqvist’s beta. The importance of another two measures of association, Spearman’s footrule and Gini’s gamma, has been reconfirmed recently. It is the main purpose of this paper to fill in the gap and present the mentioned local bounds for these two measures as well. It turns out that this is a quite non-trivial endeavor as the bounds are quasi-copulas that are not copulas for certain values of the two measures. We also give relations between these two measures of association and Blomqvist’s beta.

Spearman的法则和Gini的gamma：双变量copula的局部界限以及关于Blomqvist beta的确切区域

Copulas正在成为分析数据的重要工具，从而引起人们对相关问题的兴趣。例如，在探索性数据分析的早期阶段，了解具有特定关联度的固定值的局部copula边界会很有帮助。这些界限是针对Spearman的rho，Kendall的tau和Blomqvist的beta计算的。斯皮尔曼的尺规和吉尼的伽玛系数是另外两项关联度量的重要性，这一点最近已经得到确认。本文的主要目的是填补这两个方面的空白，并提出上述两种措施的局限性。事实证明，这是一项相当不平凡的努力，因为对于这两个量度的某些值，边界是拟对数而不是对数。我们还给出了这两种关联度量与Blomqvist beta之间的关系。

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