Zhang, X., Sheng, N. and Borzooei, R.A. (2023) Partial Residuated Implications Induced by Partial Triangular Norms and Partial Residuated Lattices. Axioms, 12, Article 63.
https://doi.org/10.3390/axioms12010063

has been cited by the following article:

• TITLE: A Class of Copulas Derived from Residual Implications and Its Applications

  AUTHORS: Yihua Liang

  KEYWORDS: Copula, Residual Implication, Archimedean Copulas, Dependence Measures

  JOURNAL NAME: Open Journal of Statistics, Vol.15 No.2, March 31, 2025

  ABSTRACT: Copulas are multivariate distribution functions with uniform marginal distributions. In this paper, we study a class of copulas called radial copulas, which is derived from residual implications where the extensions of level curves intersect at a point. This class of radial copulas is a comprehensive and asymmetric extension of a class of Archimedean copulas. We derive analytical formulas for key concordance measures, including Spearman’s rho and Kendall’s tau, and demonstrate that these formulas cover the entire range of positive and negative correlations. Furthermore, we estimate the parameters of radial copulas and evaluate their performance through a simulation study under various dependence structures. Finally, using two datasets, we compare the performance of the class of radial copulas to that of several well-known copula models.