On Asymmetric Structures of FGM Copulas: Measures of Association and Properties

Abstract

This paper introduces a generalization of the asymmetric Farlie–Gumbel–Morgenstern (FGM) copula family, along with several new extensions. General formulas for association measures of these copulas are derived. Necessary and sufficient conditions for certain dependence concepts within this family are also investigated. Since the original FGM copula has a limited correlation range, extending this domain is essential. The proposed generalized FGM family successfully improves the correlation coefficient, offering a broader range of dependence modeling. This key feature enhances the family’s applicability across various scientific disciplines.