The exact region determined by Blomqvist’s beta, Spearman’s footrule and Gini’s gamma

Kokol-Bukovšek, Damjana (author), Mojškerc, Blaž (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, Spearman’s footrule and Gini’s gamma. In other words, given the values of Blomqvist’s beta and Spearman’s footrule, we determine the degree of freedom a copula has at taking the value of Gini’s gamma. We explicitly determine the 3-dimensional region representing the relation. We also provide copulas where bounds of the region are attained.

• Language: English
• Keywords: copula, dependence concepts, supremum and infimum of a set of copulas, measures of concordance, quasi-copula, local bounds, concordance measure, gini’s gamma, Blomqvist’s beta, spearman’s footrule
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: EF - School of Economics and Business
• Publication status: Published
• Publication version: Version of Record
• Publication date: 24.06.2025
• Year: 2026
• Number of pages: 13 str.
• Numbering: Vol. 473, article no. ǂ116861
• PID: 20.500.12556/RUL-177622
• UDC: 519.2
• ISSN on article: 0377-0427
• DOI: 10.1016/j.cam.2025.116861
• COBISS.SI-ID: 240610307
• Publication date in RUL: 30.12.2025

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-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.

Secondary language

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

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika