A metric space of subcopulas — An approach via Hausdorff distance

Abstract

© 2019 In this work, we define a distance function on the set of bivariate subcopulas to generate a compact metric space. Moreover, the copula space equipped with the uniform distance is essentially a metric subspace of this subcopula space. We also characterize the convergence in this space, and provide the interrelationship with the convergence of the distribution functions.