Random discrete copulas

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.

Figures (3)

• Figure 1: Mass distribution of discrete copula $C_\pi$ from Example \ref{['ex:permutation']}.
• Figure 2: The densities of the random variables $Y_4(u,v)$ for all $(u,v) \in \Delta_4$ with $u,v \notin \{0,1\}$.
• Figure 3: Heat-maps of the densities of random variables $Y_4(u,v)$ for all $(u,v) \in \Delta_4$.

Theorems & Definitions (18)

• Definition 2.1
• Definition 2.2
• Definition 3.1
• Proposition 3.2
• proof
• Example 3.3
• Theorem 3.4
• proof
• Proposition 3.5
• proof