A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation
where
, the value of the function's midpoint;
, the supremum of the values of the function;
, the logistic growth rate or steepness of the curve.[1]
Standard logistic function where
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.[2] It is also sometimes called the expit, being the inverse of the logit.[3][4]
^Verhulst, Pierre-François (1838). "Notice sur la loi que la population poursuit dans son accroissement" (PDF). Correspondance Mathématique et Physique. 10: 113–121. Retrieved 3 December 2014.
^"Sigmoid — PyTorch 1.10.1 documentation".
^expit documentation for R's clusterPower package.
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