Overview
Grounded
A function {% G(u,v) %} is grounded if
{% G(0,v) = G(u,0) = 0 %}
2-Increasing
A function {% G:A \times B \rightarrow \mathbb{R} %} is 2-increasing if for every rectangle {% [u_1,u_2] \times [v_1,v_2] %} whose vertices are contained within {% A \times B %}, then
{% G(u_2,v_2) - G(u_2,v_1) - G(u_1, v_2) + G(u_1,v_1) \geq 0 %}
Subcopula
A 2-demnsional sub-copula is a real function
{% C:A \times B \rightarrow \mathbb{R} %}
where {% A %} and {% B %} are subsets of {% I = [0,1] %} each containing both
{% \{ 0,1 \} %}.
- {% C %} is grounded and 2-increasing
- {% C(u,1) = u %} and {% C(1,v) = v %}
Copula
A 2-dimensional copula {% C %} is a 2-dimensional subcopula where {% A = B = I = [0,1] %}