A copula transformation in multivariate mixed discrete-continuous models

Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and the copula density function, this leads to both an intuitive interpretation of the conditional distribution and convenient estimation procedures. However, this is no longer the case for copula models with mixed discrete and continuous marginal distributions, because the corresponding density function cannot be decomposed so nicely. In this paper, we introduce a copula transformation method that allows to represent the density function of a distribution with mixed discrete and continuous marginals as the product of the marginal probability mass/density functions and the copula density function. With the proposed method, conditional distributions can be described analytically and the computational complexity in the estimation procedure can be reduced depending on the type of copula used.