What is "copula"

Copula \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.

linking verb, 1640s, from Latin copula "that which binds, rope, band, bond" (see copulate).

n. 1 (context linguistics grammar English) A word, usually a verb, used to link the subject of a sentence with a predicate (usually a subject complement or an adverbial), that unites or associates the subject with the predicate. 2 (context statistics English) A function that represents the association between two or more variables, independent of the individual marginal distributions of the variables.

1. n. an equating verb (such as `be' or `become') that links the subject with the complement of a sentence [syn: copulative, linking verb]

2. [also: copulae (pl)]

In linguistics, a copula (plural: copulas or copulae; abbreviated ) is a word used to link the subject of a sentence with a predicate (a subject complement), such as the word is in the sentence "The sky is blue." The word copula derives from the Latin noun for a "link" or "tie" that connects two different things.

A copula is often a verb or a verb-like word, though this is not universally the case. A verb that is a copula is sometimes called a copulative or copular verb. In English primary education grammar courses, a copula is often called a linking verb. In other languages, copulas show more resemblances to pronouns, as in Classical Chinese and Guarani, or may take the form of suffixes attached to a noun, as in Beja, Ket, and Inuit languages.

Most languages have one main copula, although some (such as Spanish, Portuguese and Thai) have more than one, and some have none. In the case of English, this is the verb to be. While the term copula is generally used to refer to such principal forms, it may also be used to refer to some other verbs with similar functions, like become, get, feel and seem in English (these may also be called "semi-copulas" or "pseudo-copulas").

In probability theory and statistics, a copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform. Copulas are used to describe the dependence between random variables. Their name comes from the Latin for "link" or "tie", similar but unrelated to grammatical copulas in linguistics. Copulas have been used widely in quantitative finance to model and minimize tail risk and portfolio optimization applications.

Sklar's Theorem states that any multivariate joint distribution can be written in terms of univariate marginal distribution functions and a copula which describes the dependence structure between the variables.

Copulas are popular in high-dimensional statistical applications as they allow one to easily model and estimate the distribution of random vectors by estimating marginals and copulae 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.

Copula may refer to:

• Copula (linguistics), a word used to link subject and predicate
  • Indo-European copula, this word in the Indo-European languages
• Copula (music), a type of polyphonic texture similar to organum
• Copula (probability theory), a function linking marginal variables into a multivariate distribution
• Copula (jellyfish), a genus of box jellyfish
• Copula linguae, an embryonic structure of the tongue
• Beatmania IIDX 23: Copula, the 23rd entry in the Beatmania IIDX rhythm game series.

Copula is a monotypic genus of box jellyfish in the family Tripedaliidae of the phylum Cnidaria. The only species in the genus is Copula sivickisi, a very small gelatinous, bell-shaped organism with four tentacles that is active only at night. It is unusual among box jellyfish in having a mating ritual and internal fertilisation. The specific name honours the Lithuanian zoologist Pranciškus Baltrus Šivickis.

With regard to early polyphony the term copula has a variety of meanings. At its most basic level, it can be thought of as the linking of notes together to form a melody. "A copula is a rapid, connected discant..." However, it is often considered to be a particular type of polyphonic texture similar to organum, but with modal rhythm. The music theorist Johannes de Garlandia favoured this description of copula. The term refers to music where the lower voice sings long, sustained notes (the chant or tenor) while the higher voices sing faster-moving harmony lines. This style is typical of what is referred to as Notre Dame Polyphony; examples of which can be found in the Magnus Liber Organi. Copula might have implied a strophic construction with much repetition in the various parts, which was characteristic of much of the music written in this idiom. The upper part consists of "antecedent-consequent" phrases, themselves featuring much melodic repetition. The rhythm is notated in copula, unlike in organum. It is, in essence, the "coming together" of these two (or more) parts at the cadence that led to the term copula being used, from the Latin meaning "that binds."

Franco of Cologne, a music theorist, considered copula to be one of the three categories of discantus - copula itself being the type that was "continuous." He further describes it as a fast, cadential passage that is similar to either the 2nd or 6th rhythmic mode, although it differs in tempo and notation.