Copula Models

Copula models describe how random variables depend on one another while allowing each variable to have its own marginal distribution. Approaches range from Gaussian, Archimedean, and Student copulas to vine constructions, rank-based inference, and neural density or diffusion models. They are used to generate tabular data, forecast multivariate time series, estimate information, and assess joint extremes in settings where correlations alone may miss tail or conditional dependence. A central challenge is balancing expressive dependence modeling with valid marginal behavior, computational scalability, and reliable evaluation; no single estimator works best across all distributions and benchmarks.