In probability theory and statistics, a **copula** is a function that couples multivariate distribution functions to their one-dimensional marginal distribution functions. It provides a way to describe the dependence structure between random variables, independent of their marginal distributions. ### Key Concepts: 1. **Marginal Distributions**: These are the probability distributions of individual random variables, ignoring the presence of others.
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A copula is a joint distribution function on a unit cube whose one-dimensional marginal distributions are uniform distributions. Applying each continuous marginal distribution to its random variable produces uniform marginals by the probability integral transform; their copula records the remaining dependence. Independent uniform coordinates and one common uniform coordinate give different copulas with the same marginals.