The final solution of the Hitchhiker’s problem #5
arXiv:2506.20672v1 Announce Type: new
Abstract: A recent survey, nicknamed “Hitchhiker’s Guide”, J.J. Arias-Garc{i}a, R. Mesiar, and B. De Baets, A hitchhiker’s guide to quasi-copulas, Fuzzy Sets and Systems 393 (2020) 1-28, 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 (arXiv:2410.19339, accepted in Fuzzy Sets and Systems), we addressed the question of extreme values of the mass distribution associated with multivariate quasi-copulas. Using a linear programming approach, we were able to solve Open Problem 5 of the “Guide” up to dimension d = 17 and disprove a recent conjecture on the solution to that problem. In this paper, we use an analytical approach to provide a complete answer to the original question.
Abstract: A recent survey, nicknamed “Hitchhiker’s Guide”, J.J. Arias-Garc{i}a, R. Mesiar, and B. De Baets, A hitchhiker’s guide to quasi-copulas, Fuzzy Sets and Systems 393 (2020) 1-28, 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 (arXiv:2410.19339, accepted in Fuzzy Sets and Systems), we addressed the question of extreme values of the mass distribution associated with multivariate quasi-copulas. Using a linear programming approach, we were able to solve Open Problem 5 of the “Guide” up to dimension d = 17 and disprove a recent conjecture on the solution to that problem. In this paper, we use an analytical approach to provide a complete answer to the original question.
Matjav{z} Omladiv{c}, Martin Vuk, Aljav{z} Zalar
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