How does one define a sigmoidal function

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SUMMARY

A sigmoidal function is defined by its characteristic S-shaped curve, which typically includes an inflection point where the curve changes concavity. To classify a curve as a sigmoid, it must exhibit this S-shape and meet specific mathematical constraints, such as being bounded and having a horizontal asymptote. Skewed S-shaped curves do not qualify as traditional sigmoids unless they adhere to the defining properties of sigmoid functions. The discussion emphasizes the importance of understanding these constraints for accurate classification.

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Mathematicians, data scientists, and anyone involved in modeling functions or analyzing curves will benefit from this discussion on sigmoidal functions.

marellasunny
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I am trying to model a 'perturbation function' and I finally arrive at a S-shaped graph,which I later found was called a 'sigmoid'. Is a sigmoid defined based on its inflection point? How does one classify a curve as a 'sigmoid'?
Can i say that a certain function f is a sigmoid just because it has a S-shaped curve?What about skewed S-shaped curves?Are they sigmoids also?
What are the constraints?
 
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