Let the corresponding marginal cumulative distribution functions of the random variable be Then, if the marginal functions are continuous, there exists a unique copula C, such that Furthermore, if the distributions are continuous, the multivariate dependency structure and the marginals might be separated, and the copula can be considered independent of the marginals (Joe, 1997;Parsa and Klugman, 2011).
the copula does not have requirements on the marginal distributions, and any arbitrary marginals can be combined and their dependency structure can be modeled using the copula.