The exact region determined by Spearman’s footrule, Gini’s gamma and Kendall’s tau

Kokol-Bukovšek, Damjana (author), Lazić, Petra (author), Mojškerc, Blaž (author), Stopar, Nik (author)

To quantify the degree of association between random variables, concordance measures are employed. To express such a degree, a single measure might give too much space, so several are used for comparison. In this paper we study the ternary relation between three well-known (weak) concordance measures, namely Blomqvist’s beta, Concordance measures are used to express the degree of association between random variables. Practitioners may use several distinct concordance measures to narrow down the space of possible dependence structures. Consequently, the relations between different (weak) concordance measures have been extensively studied in recent years. The goal of this paper is to study the relation between Kendall’s tau, Gini’s gamma and Spearman’s footrule. In particular, we describe the exact region determined by these three measures, using shuffles of M and ordinal sums of copulas. We also provide the formulas for five main (weak) concordance measures and Chatterjee’s xi of ordinal sums of copulas.

• Language: English
• Keywords: copula, dependence concepts, supremum and infimum of a set of copulas, measures of concordance, quasi-copula, local bounds
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: EF - School of Economics and Business; FMF - Faculty of Mathematics and Physics; FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.11.2026
• Year: 2026
• Number of pages: 19 str.
• Numbering: Vol. 486, article no. 117639
• PID: 20.500.12556/RUL-181441
• UDC: 519.2
• ISSN on article: 0377-0427
• DOI: 10.1016/j.cam.2026.117639
• COBISS.SI-ID: 273645315
• Publication date in RUL: 08.04.2026

Record is a part of a journal

• Title: Journal of computational and applied mathematics
• Shortened title: J. comput. appl. math.
• Publisher: Elsevier
• ISSN: 0377-0427
• COBISS.SI-ID: 27496960

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: kopula, koncepti odvisnosti, supremum in infimum množice kopul, mere skladnosti, kvazikopula, lokalne meje