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maximenc / pycop

Python library for multivariate dependence modeling with Copulas
https://pypi.org/project/pycop/
MIT License
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Can I specify the marginal distribution as one type of distribution and the copula as another type of distribution when estimating parameters？ #8

Open piper0124 opened 1 year ago

piper0124 commented 1 year ago

Can I specify the marginal distribution as one type of distribution and the copula as another type of distribution when estimating parameters？(For example, in binary distribution, two variables are designated as normal distribution, and copula is designated as student t distribution)

maximenc commented 11 months ago

Hi @piper0124,

The Canonical Maximum Likelihood Estimation (CMLE) estimates the copula parameters without requiring the specification of the marginals (during the estimation, the marginals are replaced by scaled ranks).

For the Maximum Likelihood Estimation (MLE) (If the parameters of the marginals are known or not). The Likelihood function is derived from the joint PDF:

$$ h(x,y) = c \left( F_X(x), F_Y(y) \right) f_X(x) f_Y(y) $$

where here we would need $f_X(x)$ and $f_Y(y)$ the PDF of the marginals.

In your case, you can estimate the Student t copula using the CMLE estimation without the need to specify the marginals. The development of the MLE is still in progress but is coming soon.

I hope this helps.

M.

PavelRechkalov commented 3 months ago

Greetings @maximenc , sir

Is there any update regarding "MLE is still in progress but is coming soon"?

Regards