fourparameter

Fourparameter is a term used in statistics and applied sciences to refer to a class of models described by four parameters. The most well-known example is the four-parameter logistic model (4PL), which is used to fit sigmoidal dose–response data and similar curves.

The 4PL model typically has the form y = A + (D − A) / [1 + (x / C)^B], where A is the lower asymptote, D is the upper asymptote, C is the inflection point (often corresponding to the EC50, the dose producing half-maximal response), and B is the slope factor that controls the curve’s steepness. The independent variable x is usually a dose or concentration, and the dependent variable y is the measured response.

Applications of the 4PL model are common in pharmacology, biochemistry, and analytical chemistry. It is widely used to model calibration curves, ELISA and other immunoassay data, and various dose–response analyses. Parameter estimation is typically accomplished through nonlinear regression or specialized software, providing estimates of the asymptotes, inflection point, and slope.

Related models include the five-parameter logistic (5PL) model, which adds an asymmetry parameter to capture deviations from symmetry around the inflection point. The four-parameter framework is valued for its balance of interpretability and flexibility in modeling sigmoidal relationships, and it serves as a standard baseline in many biological and analytical applications.