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Best-possible bounds on the set of copulas with a given value of Gini's gamma (2501.06915v1)

Published 12 Jan 2025 in math.ST, math.PR, and stat.TH

Abstract: In this note, pointwise best-possible (lower and upper) bounds on the set of copulas with a given value of the Gini's gamma coefficient are established. It is shown that, unlike the best-possible bounds on the set of copulas with a given value of other known measures such as Kendall's tau, Spearman's rho or Blomqvist's beta, the bounds found are not necessarily copulas, but proper quasi-copulas.