parametrized

Parametrized, or parameterised, is the adjective formed from parameterize. It denotes something described using one or more parameters. In mathematics, science, and computing, a parametrized object is expressed by a parameter that can be varied to generate a family of related objects.

In mathematics, a curve or surface can be parametrized by a parameter such as t (or a vector t). The coordinates are given as functions of the parameter, for example x = cos t and y = sin t parameterize the unit circle. Parameterizations can simplify analysis, differentiation, and integration and reveal structure not evident from a fixed description.

In statistics and modeling, a model is often described as parametrized by a set of parameters. A parametric model specifies a probability distribution as a function of parameter values, such as the normal distribution N(μ, σ^2). Parameter estimation aims to infer these values from data, contrasting with non-parametric approaches that do not assume a fixed form.

In computer science and software engineering, parametrization appears in several forms. Parametrized tests run the same logic with multiple input values; parametrized types or generics use type parameters to generalize code; and algorithms or templates may depend on parameters to control behavior. The core idea is that adjustable parameters define or modify the object’s structure or behavior.

Usage notes: the spelling varies by region. Parameterized is common in American English, parametrized in British English, but both denote the same concept. The related noun is parameterization.