Sklar's theorem

Sklar's theorem states that any joint probability distribution of multiple variables can be separated into two parts: their individual behaviors (marginal distributions) and how they are interconnected (copula). Essentially, it allows us to model each variable’s behavior separately and then combine them using a copula function to understand their dependency. This helps in accurately capturing how variables interact, especially in complex systems like finance or risk management, by focusing on their individual characteristics and their dependence structure independently.