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How can I fit a copula for a bivariate vector of negative binomial and Bernoulli margins?

I would prefer a Frank or Clayton copula.

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It will probably be worth looking at the copula package – mnel Oct 30 '12 at 5:05

With one margin being Bernoulli, it looks to me like the general form of copula for that bivariate discrete case would specify a $p$ (probability that the Bernoulli variable is 1) for each value taken by the negative binomial. I'd probably be inclined to write a function for those conditional $p_i$ (how $p_i$ changes with $i$ -- note that they don't themselves form a probability function; they don't add to 1, for example - as long as they're all probabilities). You are probably after something where the $p_i$ are monotonic (which suggests the possibility of using a cdf for that function). You might be able to use the CLayton or Frank copulas to come up with a suitable conditional cdf for the $p$'s.

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If your marginal distribution function has a closed form (or is limited sum of mass probabilities) you should write log-likelihood function and maximize it.

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