The sigmoid curve is the curve whose formula is the sigmoid function
The sigmoid curve shows early exponential growth which slows to linear growth then decelerates until it reaches a saturation level at y = 1.
The conversion from the log-likelihood ratio of two alternatives to a probability takes the form of a sigmoid curve.
Members of the family of curves with obtained by linear scaling and translation of the sigmoid curve are called logistic curves, and are found in a range of fields, from biology to economics.
See also: Hubbert curve, Logistic regression, Generalised logistic curve, log-likelihood ratio