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.
Bibliographical noteFunding Information:
We thank Woojoo Lee and Ruodu Wang for helpful comments and discussion. We also would like to thank the anonymous Reviewers for several helpful comments and suggestions which helped to improve the presentation of the paper. Jae Youn Ahn was supported by an National Research Foundation of Korea (NRF) grant funded by the Korean Government ( 2020R1F1A1A01061202 ). Sebastian Fuchs gratefully acknowledges the support of the WISS 2025 project ‘IDA-Lab Salzburg’ ( 20204-WISS/225/197-2019 and 0102-F1901166-KZP ). Rosy Oh was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2019R1A6A1A11051177 and 2020R1I1A1A01067376 ).
© 2020 Elsevier B.V.
- Collective risk model
- Copula density function
- Copula transformation
- Mixed discrete-continuous variable