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I don't know if it is a good idea to post my question in MathOverflow instead of Mathexchange. But it seems to me that it is more appropriate to post my question in MathOverflow.

By definition, copula is a special case of subcopula, in which the domain of the function is $[0;1]^n$.

So, as for me, subcopula is more general and it can be used to model a wider variety of type of variables whereas copula is mainly used to model continuous random variables.

However, in the literature, I have seen very little article that talk about subcopula modelling as well as its inference/estimation from the data.

Could you please explain me why sub copula is very less used while it is more general ? And what is the main technical constraint in the inference/estimation of sub copula ?

Thank you very much for your help!

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The complication when using subcopulas to model estimations is that the domain of the subcopula depends on the marginal distribution functions, it is unknown and has to be estimated from data. In contrast, the domain of copulas is known.

The benefit of using subcopulas is that the subcopula associated with a joint distribution function is always unique, while the copula is only unique for a continuous distribution.

For a detailed exposition see On subcopula estimation for discrete models, Santi Tasena (2021).

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