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On a Measure of Tail Asymmetry for the Bivariate Skew-Normal Copula
Version 1
: Received: 22 June 2023 / Approved: 23 June 2023 / Online: 23 June 2023 (10:48:01 CEST)
A peer-reviewed article of this Preprint also exists.
Yoshiba, T.; Koike, T.; Kato, S. On a Measure of Tail Asymmetry for the Bivariate Skew-Normal Copula. Symmetry 2023, 15, 1410. Yoshiba, T.; Koike, T.; Kato, S. On a Measure of Tail Asymmetry for the Bivariate Skew-Normal Copula. Symmetry 2023, 15, 1410.
Abstract
Asymmetry in the upper and lower tails is an important feature in modeling bivariate distributions. This article focuses on the log ratio between the tail probabilities at upper and lower corners as a measure of tail asymmetry. Asymptotic behavior of this measure at extremely large and small thresholds is explored with particular emphasis on the skew-normal copula. Our numerical studies reveal that, when the correlation or skewness parameters are around at the boundary values, some asymptotic tail approximations of the skew-normal copulas proposed in the literature are not suitable to compute the measure of tail asymmetry with practically extremal thresholds.
Keywords
Measure of asymmetry; Skew-normal copula; Tail dependence; Tail order
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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