A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation
- , the value of the sigmoid's midpoint;
- , the curve's maximum value;
- , the logistic growth rate or steepness of the curve.
For values of in the domain of real numbers from to , the S-curve shown on the right is obtained, with the graph of approaching as approaches and approaching zero as approaches .
The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. A generalization of the logistic function is the hyperbolastic function of type I.
The standard logistic function, where , is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse of the logit.