Parametric

Parametric describes models, equations, or designs defined by parameters—variables that control outcomes without altering their underlying structure. A parameter can be adjusted to change results, enabling systematic variation and analysis.

In mathematics, a curve can be expressed parametrically by x(t) and y(t). This form represents shapes that may be difficult to describe as a single function y=f(x). For example, a circle can be parameterized as x = R cos t, y = R sin t.

In statistics, a parametric model assumes the data arise from a distribution characterized by a finite set of parameters (such as the mean and variance of a normal distribution). Inference estimates these parameters; parametric methods are efficient when the model is correct but can be biased if the assumptions fail, with nonparametric methods offering alternatives.

In engineering and design, parametric design uses adjustable parameters to control geometry, enabling rapid variation, optimization, and constraint-driven modeling. Parametric CAD tools maintain relationships among features, allowing coordinated changes. In computer science, parametric concepts appear in polymorphism and generics, where code or types depend on parameters.

Etymology: from Greek para- "beside" and metron "measure." Related terms include nonparametric and semiparametric. Parametric concepts appear across many fields, often to enable systematic variation, analysis, and efficient modeling.