Affine Rational Transformations of Copulas and Quasi-Copulas
Published in Thai Journal of Mathematics, 2022
The transformation-based methods are indeed the convenient ways for constructing a newcopula using known copulas. In this research, we characterize linear rational transformations for mul-tivariate copulas and multivariate quasi-copulas. This is an extension to the already known results inthe bivariate case. We found that this type of transformations extended naturally for the multivariatequasi-copulas. Yet, the only linear rational transformation of multivariate copulas is the identity functionwhich is different from the bivariate case. This means that the set of linear rational functions that trans-form a multivariate copula varies depending on the copula itself. As an example, we also characterizesuch sets in the case of the trivariate product copula.
Recommended citation: Lueangwitchajaroen, P., Tasena, S., Affine Rational Transformations of Copulas and Quasi-Copulas, Thai Journal of Mathematics, 20 (4) (2022) 1649 - 1660. https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1428