A Tractable Family of Smooth Copulas with Rotational Dependence: Properties, Inference, and Application

We introduce a new family of copula densities constructed from univariate distributions on $[0,1]$. Although our construction is structurally simple, the resulting family is versatile: it includes both smooth and irregular examples, and reveals clear links between properties of the underlying univariate distribution and the strength, direction, and form of multivariate dependence. The framework brings with it a range of explicit mathematical properties, including interpretable characterizations of dependence and transparent descriptions of how rotational forms arise. We propose model selection and inference methods in parametric and nonparametric settings, supported by asymptotic theory that reduces multivariate estimation to well-studied univariate problems. Simulation studies confirm the reliable recovery of structural features, and an application involving neural connectivity data illustrates how the family can yield a better fit than existing models.