I know what the properties "grounded" and "2-increasing" means in copula functions definition but actually I can't understand the reason behind these two! I mean why it is necessary for copulas to be grounded and 2-increasing?
Any help would be appreciated!
One interpretation of the requirements is from Sklar's theorem which says the joint cumulative of two random variables can be expressed as a Copula whose arguments are the marginal distributions of either random variable. Then the grounded condition makes sure you assign 0 probability when one of the marginals is 0. The 2 increasing is a generalization of the requirement that a one dimensional cdf is increasing. Here's a nice summary of all this.