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A copula is a multivariate distribution with uniform marginal distributions. Copulas are mostly used to represent or to model the structure of dependence between random variables, separately from the marginal distributions.
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Fitting copula for discrete margins
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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How to simulate a hidden Markov chain?
Each state corresponds to a bivariate data with known marginals that the dependence between them is modeled by a copula. What is the best algorithm? Is there any function in R for such work? …