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Context: statistics, probability, dependence

To make things simpler, we shall first start off with two random variables. Later we can generalise this to n random variables.

Suppose you have two random variables, X and Y, which has the distribution function, F(x) and G(y), and has a joint distribution function H(x, y). Now by Sklar's Theorem, there exists a function C(a, b) (which satisfies the property of being a joint distribution function for two separate) random variables taking values in [0, 1]) such that

H(x, y) = C(F(x), G(y))

and the function C is called a copula. Its use is to couple two marginal distributions together to form a joint distribution.

Of course, when you replace the random variables X and Y with a random vector x, you get a n-dimensional form of Sklar's Theorem.

There is a more formal form of the definition of what a copula is, but the way described here should be sufficient for most practitioners.

Copulas are especially useful in studying dependence between random variables, something in which statisticians are always interested.

In linguistics, the copula is any word which links the subject and predicate of a sentence. Most frequently, it is a verb related to states of being, such as English 'is' and Spanish 'ser' and 'estar.' Sometimes, however, the copula takes a form more similar to pronouns and noun suffixes, as in the Inuit languages, Guarani, and Classical Chinese. Furthermore, many languages do not involve copulae at all, and are called 'zero copula' or 'null-copula' languages; Russian, Semitic languages like Arabic and Hebrew, Quechuan languages, and the conlang Dothraki are all null-copular.

Zero copula languages do not require a specific word or particle to unite the subject and predicate of sentences. Their verbs may intrinsically include states of being, such as saying "to be hungry" rather than "to hunger" in the base unmarked form of the verb. If a subject noun is placed adjacent to another word, it may be assumed that the quality of the other word (whether an action or a descriptive adjective) is being applied to the noun.

Copula languages treat verbs as separate from states of being: a person may hunger, as an action, or a person may be hungry, as a descriptive state of being. Zero copula languages either would not distinguish between these two states, or they would use a different way of indicating the difference, without the use of copulae.

In Romance languages such as Spanish, Italian, and Portuguese, there are two primary copulae. The first, derived from Latin 'sum, esse,' typically indicates that a state of being is permanent and ongoing for the subject it describes: "Jane is lonely" would indicate that Jane is intrinsically lonely, always. The second copula, derived from Latin 'sto, stare,' typically indicates that a state of being is temporary or situational for the subject: "Jane is lonely" would indicate that Jane is lonely right now, but she may not be lonely tomorrow.

The primary copulae in English are the various forms of 'be, was, am, being, been.' These words indicate states of being, such as "John is a cat" or "The book is open on the desk."
English has many words classifiable as 'pseudo-copulae,' because they simultaneously convey a state of being and an action. Seem, become, look, appear, feel, sound, stay, and many others can act as copulae within English, while most of these also have non-copular roles within the language.

Many vernacular forms of English frequently omit copulae, such as African American Vernacular English (AAVE or Ebonics). An AAVE speaker might say, "He crazy," rather than "He is crazy," and a non-AAVE English speaker would generally have little difficulty understanding the statement: typically copular languages have no difficulty understanding omissions of copulae, and they are mutually-intelligible with their own zero copula dialects. It is significantly rarer for a zero copula language to possess a copula dialect.

Cop"u*la (?), n. [L., bond, band. See Couple.]

1. Logic & Gram.

The word which unites the subject and predicate.

2. Mus.

The stop which connects the manuals, or the manuals with the pedals; -- called also coupler.

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