Copula (probability Theory)
In probability theory and statistics, a copula is a kind of distribution function. Copulas are used to describe the dependence between random variables. They are named for their resemblance to grammatical copulas in linguistics.
The cumulative distribution function of a random vector can be written in terms of marginal distribution functions and a copula. The marginal distribution functions describe the marginal distribution of each component of the random vector and the copula describes the dependence structure between the components.
Copulas are popular in statistical applications as they allow one to easily model and estimate the distribution of random vectors by estimating marginals and copula separately. There are many parametric copula families available, which usually have parameters that control the strength of dependence. Some popular parametric copula models are outlined below.
Read more about Copula (probability Theory): The Basic Idea, Definition, Sklar's Theorem, Fréchet–Hoeffding Copula Bounds, Empirical Copulas, Monte Carlo Integration For Copula Models