continuous and discrete variables with a copula?

[bradyj2]

Hi,

I have 3 correlated variables that I wish to model with a copula function. 2 of the variables are continuous and 1 is discrete.

My question is, generally speaking can you model continuous and discrete variables with a copula?

Thanks

[BGM]

Yes you can, as all random variables should have their own CDF which serve as the "input" of the copula.

Sklar's theorem will also states that for each joint CDF, you can uniquely induce the corresponding copula given that the marginal is continuous. When you are dealing with the discrete case it may not be unique (or unique up to certain rules).