Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $f$ is a positive continuous real-valued function defined on $\mathbb{R}$ such that $f$ has a continuous derivative on $\mathbb{R}\setminus\{0\}$ and $\int_{-\infty}^{\infty}f(x)dx < \infty$, and if $g(x) = \int_{-\infty}^xf(t)dt$, then what are necessary and sufficient conditions on $f$ that $g$ be a sigmoid?

In particular, is it sufficient for $f’$ to be increasing on the set of negative numbers, and decreasing on the set of positive numbers?

Also: is the situation pretty much the same if we restrict the domain of $f$ to $[-1,1]$?

share|cite|improve this question
Sigmoid is not in general a technical term with a precise definition. It just means S-shaped. – Rahul Jan 14 '12 at 20:21

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.