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.

This is based on Sklar's theorem which shows that all multivariate distributions contain a copula, and how joint distributions are formed by coupling together marginal distributions with a copula. If you take a continuous multivariate distribution and apply the Probability Integral Transform to each margin, the resulting multivariate distribution has uniform margins and will be a copula.

Copulas are widely used in many application areas including finance, insurance, actuarial science, biostatistics, hydrology and weather research.

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