Sigmoïde

SIGMOID CURVE

Sigmoid : sigma shaped.

A sigmoid curve is a curve having, not the shape of an S, but rather that of a stretched S. More precisely: curve located between two parallel asymptotes having a point of inflection, which is
also center of symmetry, located equidistant from the two asymptotes.

Examples of sigmoids normalized so that they are curves of an odd differentiable function f increasing from –1 to 1 on the reals and satisfying .

Function f Comments Outline

Correspond to a branch of the puntiform quartic : .

Connection of two portions of hyperbolas : .

for t > 0.

Generalization of the two previous ones; opposite, animation for t ranging from 0.2 to 8.

Hperbolic tangentoid

Tangentoid.

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Function f	Comments	Outline
	Correspond to a branch of the puntiform quartic : .
	Connection of two portions of hyperbolas : .
for t > 0.	Generalization of the two previous ones; opposite, animation for t ranging from 0.2 to 8.
	Hperbolic tangentoid
	Tangentoid.