Maximal asymmetry of bivariate copulas and consequences to measures of dependence

作者：Florian Griessenberger, Wolfgang Trutschnig · 发表于：Dependence Modeling · 年份：2022 · DOI：10.1515/demo-2022-0115 · 被引用次数：3 · 研究领域：Financial Risk and Volatility Modeling、Statistical Distribution Estimation and Applications、Probability and Risk Models

Abstract In this article, we focus on copulas underlying maximal non-exchangeable pairs ( X , Y ) \left(X,Y) of continuous random variables X , Y X,Y either in the sense of the uniform metric d ∞ {d}_{\infty } or the conditioning-based metrics D p {D}_{p} , and analyze their possible extent of dependence quantified by the recently introduced dependence measures ζ 1 {\zeta }_{1} and ξ \xi . Considering maximal d ∞ {d}_{\infty } -asymmetry we obtain ζ 1 ∈ 5 6 , 1 {\zeta }_{1}\in \left[\frac{5}{6},1\right] and ξ ∈ 2 3 , 1 \xi \in \left[\frac{2}{3},1\right] , and in the case of maximal D 1 {D}_{1} -asymmetry we obtain ζ 1 ∈ 3