A multivariate distribution for a random vector contains a description of both the marginal distributions and their dependence structure. A copula approach to formulating a multivariate distribution provides a way to isolate the description of the dependence structure from the marginal distributions. A copula is a function that combines marginal distributions of variables into a specific multivariate distribution. All of the one-dimensional marginals in the multivariate distribution are the cumulative distribution functions of the factors. Copulas help perform large-scale multivariate simulation from separate models, each of which can be fitted using different, even nonnormal, distributional specifications.
The COPULA procedure enables you to fit multivariate distributions or copulas from a given sample data set. You can do the following:
estimate the parameters for a specified copula type
simulate a given copula
plot dependent relationships among the variables
The following types of copulas are supported:
normal copula
t copula
Clayton copula
Gumbel copula
Frank copula