LAUSR

We consider one-parametric families of copulas for which the complement function for independence satisfies an anti-symmetric property. The Spearman rank correlation and Kendall’s tau of an anti-symmetric family of copulas are necessarily odd functions of the parameter. Extending the parameter range of the FGM copula to the whole real line and truncated it from above and below using the Hoeffding-Fréchet bounds generates a comprehensive anti-symmetric extension of the FGM copula. The detailed analytical representation of the extended FGM copula, the absolutely continuous and singular components, as well as the Spearman rank correlation and Kendall’s tau dependence functions are derived. Several additional examples illustrate the anti-symmetric copula construction.