Zweiparametrige

Zweiparametrige is a German term used in mathematics, statistics, and related fields to describe models, distributions, or equations that depend on exactly two independent parameters. As a descriptive category, it signals that the behavior of the object is governed by two degrees of freedom, rather than a single parameter or many parameters.

In probability and statistics, a zweiparametrige distribution is one whose probability law is determined by two parameters, often interpreted as shape and scale, location and scale, or other paired characteristics. Common examples include two-parameter families such as the two-parameter Weibull distribution (shape and scale) and the two-parameter gamma distribution (shape and scale). The two-parameter logistic model in psychometrics, known in German as zweiparametrisches logistisches Modell, uses two item parameters—discrimination and difficulty—to describe the probability of a correct response as a function of ability.

From a modeling perspective, zweiparametrige formulations are more flexible than one-parameter models while remaining simpler and more interpretable than higher-parameter ones. They are often estimated by maximum likelihood, Bayesian methods, or method of moments, with attention to identifiability and parameterization choices. Location-scale families are another common instance where two parameters (location and scale) define the distribution.

The term is primarily descriptive rather than denotes a single canonical model. It contrasts with einparametrige (one-parameter) models and mehrparametrige (multi-parameter) models, and is used across disciplines wherever two independent parameters govern the system under study.