How can I fit a copula for a bivariate vector of negative binomial and Bernoulli margins?
I would prefer a Frank or Clayton copula.
$\begingroup$
$\endgroup$
1
-
$\begingroup$ It will probably be worth looking at the copula package $\endgroup$– mnelCommented Oct 30, 2012 at 5:05
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
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.
$\begingroup$
$\endgroup$
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.
