A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation where , 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 standard logistic function, where , is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse of the logit.
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