Certain constructions of copulas can be interpreted as an eigendecomposition of a kernel. We study some properties of the eigenfunctions and their integrals of a covariance kernel related to a bivariate distribution. The covariance between functions of random variables in terms of the cumulative...

This paper introduces a one-parameter bivariate family of distributions whose marginals are arbitrary and which include Fréchet bounds as well as the distribution corresponding to independent variables. Some geometrical and statistical properties on the stochastic dependence parameter are...