copule

Copula, sometimes spelled copule, is a term used in different disciplines to denote a linking element that connects components within a structure. In linguistics, the copula is a word or verb that links the subject of a sentence to a predicate, typically a predicative adjective, noun phrase, or other complement. The English copula is most often the verb to be, as in "The sky is blue." In other languages, the copula may be a different verb, a suffix, or may be omitted entirely in present-tense statements (a phenomenon known as a zero copula). Copular constructions can express identity, classification, or property ascription, and some languages have dedicated copula forms for tense, aspect, or mood.

In probability theory, a copula is a function that couples multivariate distribution functions to their one-dimensional margins. The use of copulas separates the modeling of marginal behavior from the dependence structure among variables. Sklar's theorem states that any multivariate distribution can be expressed in terms of its marginals and a copula, and conversely any copula combines with given margins to form a joint distribution. Copulas are widely used in finance, hydrology, and risk assessment to model correlated risks. Common families include Gaussian, Clayton, Gumbel, and Frank copulas, each with different tail dependence properties.

The term derives from Latin copula, meaning a bond or link. See also: Sklar's theorem, dependence modeling, copula families.