2023•arXiv (Cornell University)Open access

Exact upper bound for copulas with a given diagonal section

Damjana Kokol Bukovšek, Blaž Mojškerc, Nik Stopar

Abstract

We answer a 15-year-old open question about the exact upper bound for bivariate copulas with a given diagonal section by giving an explicit formula for this bound. As an application, we determine the maximal asymmetry of bivariate copulas with a given diagonal section and construct a copula that attains it. We derive a formula for the maximal asymmetry that is simple enough to be used by practitioners.

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Key concepts: Diagonal, Bivariate analysis, Copula (linguistics), Upper and lower bounds, Mathematics, Asymmetry, Section (typography), Simple (philosophy)