In mathematics, a univariate object is an

expression Expression may refer to: Linguistics * Expression (linguistics), a word, phrase, or sentence * Fixed expression, a form of words with a specific meaning * Idiom, a type of fixed expression * Metaphorical expression, a particular word, phrase, o ...

equation In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

involving only one

variable Variable may refer to: * Variable (computer science), a symbolic name associated with a value and whose associated value may be changed * Variable (mathematics), a symbol that represents a quantity in a mathematical expression, as used in many ...

. Objects involving more than one variable are

multivariate Multivariate may refer to: In mathematics * Multivariable calculus * Multivariate function * Multivariate polynomial In computing * Multivariate cryptography * Multivariate division algorithm * Multivariate interpolation * Multivariate optical c ...

. In some cases the distinction between the univariate and multivariate cases is fundamental; for example, the

fundamental theorem of algebra The fundamental theorem of algebra, also known as d'Alembert's theorem, or the d'Alembert–Gauss theorem, states that every non- constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomia ...

and

Euclid's algorithm for polynomials In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous to the greatest common di ...

are fundamental properties of univariate polynomials that cannot be generalized to multivariate polynomials. In

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, a univariate

distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations * Probability distribution, the probability of a particular value or value range of a vari ...

characterizes one variable, although it can be applied in other ways as well. For example, univariate data are composed of a single

scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...

component. In

time series analysis In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in m ...

, the whole time series is the "variable": a

univariate time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Ex ...

is the series of values over time of a single quantity. Correspondingly, a "multivariate time series" characterizes the changing values over time of several quantities. In some cases, the terminology is ambiguous, since the values within a univariate time series may be treated using certain types of

multivariate statistical analyses Multivariate may refer to: In mathematics * Multivariable calculus * Multivariate function * Polynomial#Number of variables, Multivariate polynomial In computing * Multivariate cryptography * Multivariate division algorithm * Multivariate interp ...

and may be represented using multivariate distributions. In addition to the question of scaling, a criterion (variable) in univariate statistics can be described by two important measures (also key figures or parameters): Location & Variation. * Measures of Location Scales (e.g. mode, median, arithmetic mean) describe in which area the data is arranged centrally. * Measures of Variation (e.g. span, interquartile distance, standard deviation) describe how similar or different the data are scattered.

References

Mathematical terminology Theory of probability distributions {{math-stub

See also

References