Sklar's theorem in finite settings
This paper deals with the well-known Sklar's theorem, which shows how joint distribution functions are related to their marginals by means of copulas. The main goal is to prove a discrete version of this theorem involving copula-like operators defined on a finite chain, that will be called discrete copulas. First, the idea of subcopulas in this finite setting is introduced and the problem of extending a subcopula to a copula is solved. This is precisely the key point which allows to state and prove the discrete version of Sklar's theorem.
sklar's theorem distribution function discrete copula discrete subcopula permutation matrix