Parametrizes

Parametrizes is the third-person singular present tense of the verb parameterize (American English) or parameterise (British English). In mathematics, computer science, statistics, and related fields, to parametrize means to express an object, equation, or model in terms of parameters rather than fixed constants.

A parametric representation uses one or more parameters to describe a set, function, or geometric entity. For example, a curve in the plane can be parametrized by a parameter t, with coordinates given as x(t) and y(t). A line through a point p with direction v is parametrized by x(t) = p + t v, where t varies over the real numbers.

In statistics and modeling, a family of distributions or models is parameterized by a parameter vector θ; parametrization specifies how the probability distribution or model depends on θ. The choice of parameterization can affect interpretability, identifiability, and computational properties such as optimization and sampling.

Related terminology includes parameterization and parametrization (spelling variants), parameterize and parameterise, and the noun parameterization or reparameterization. The act of transforming a model to a different parameterization is sometimes called reparameterization.

In practice, parametrizes appears in technical writing when describing how a particular object or model is represented using a set of parameters. It is most common in contexts discussing the structure, representation, or transformation of mathematical objects, algorithms, or statistical models.