Extreme mass distributions for quasi-copulas

Omladič, Matjaž (author), Vuk, Martin (author), Zalar, Aljaž (author)

The recent survey [3] nicknamed “Hitchhiker’s Guide” has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. In our previous work we addressed the question of extreme values of the mass distribution associated with a mutidimensional quasi–copulas. Using linear programming approach we were able to settle [3, Open Problem 5] up to $d = 17$ and disprove a recent conjecture from [14] on solution to that problem. In this note we use an analytical approach to provide a complete answer to the original question.

• Language: English
• Keywords: mass distribution, d-quasi-copula, volume, Lipschitz condition, bounds
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics; FRI - Faculty of Computer and Information Science
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.03.2026
• Year: 2026
• Number of pages: 22 str.
• Numbering: Vol. 527, art. no. 109698
• PID: 20.500.12556/RUL-176448
• UDC: 519.2
• ISSN on article: 0165-0114
• DOI: 10.1016/j.fss.2025.109698
• COBISS.SI-ID: 259332611
• Publication date in RUL: 01.12.2025

Record is a part of a journal

• Title: Fuzzy sets and systems : international journal of soft computing and intelligence
• Shortened title: Fuzzy sets syst.
• Publisher: Elsevier
• ISSN: 0165-0114
• COBISS.SI-ID: 25498624

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: porezdelitev mase, d-kvazi-kopula, volumen, Lipschitzev pogoj, meje