parametrisch

Parametrisch (parametric) is an adjective used in Dutch and German to describe approaches, models, or representations that are defined by parameters. In English, parametric likewise refers to methods that rely on a parameter vector to describe a system or phenomenon. Parametric approaches are common across disciplines such as mathematics, statistics, computer-aided design (CAD), engineering, and data analysis.

In mathematics, a parametric representation expresses quantities as functions of one or more parameters. A curve is described by parametric equations x(t), y(t) (and z(t) in three dimensions). For example, x = r cos t, y = r sin t traces a circle as t varies. The choice of parameterization can affect properties like simplicity and numerical stability.

In statistics and econometrics, a parametric model assumes the data arise from a distribution determined by a fixed set of parameters. Examples include the normal distribution with mean μ and standard deviation σ. Parameter values are estimated from data, often by maximum likelihood or Bayesian methods, and inferences rely on the assumed distribution.

In design and computer graphics, parametric modeling defines shapes through parameters and constraints rather than fixed geometry. Adjusting a parameter propagates through the model, enabling rapid exploration of alternatives. CAD software often uses parametric features and constraints; nonparametric alternatives exist as well.

Parametric methods offer compact representation and easy adjustability but can suffer from mis-specification, parameter identifiability issues, or singularities if the parameterization is poorly chosen. The term traces to Greek roots meaning "measurements by parameters" and has a long history in mathematics, statistics, and engineering.