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.

中文翻译：

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多元混合离散连续模型中的 copula 变换

Copulas 允许对复杂的依赖结构以及各种边缘分布进行灵活且同步的建模。特别是如果密度函数可以表示为边际密度函数和 copula 密度函数的乘积，这会导致对条件分布的直观解释和方便的估计程序。然而，对于具有混合离散和连续边缘分布的 copula 模型，情况不再如此，因为相应的密度函数不能很好地分解。在本文中，我们介绍了一种 copula 变换方法，该方法允许将具有混合离散和连续边缘的分布的密度函数表示为边缘概率质量/密度函数和 copula 密度函数的乘积。