Random discrete copulas

TL;DR

This paper introduces the concept of bivariate random discrete copulas on equidistant meshes, analyzing their stochastic properties, distributions, and extensions to continuous fields over the unit square.

Contribution

It defines and explores the properties of random discrete copulas, including their distributions, expectations, variances, and bilinear extensions to continuous fields.

Findings

Distribution of the random variables at mesh points is characterized.

Expected value and variance of the copula values are calculated.

Bilinear extension to a continuous random field is developed.

Abstract

We introduce the notion of a bivariate random discrete copula on an equidistant mesh and explore its stochastic properties. A random discrete copula is a discrete random field, hence, its value at a given point on the mesh is a random variable. We determine the distribution of this random variable and calculate its expected value and variance. We also consider bilinear extension of a random discrete copula to a random field over the whole unit square.