Hi there

The Sigmoid function 1/1+e(-x) has the behavior of "S" shape curve,
but it runs from -ve values to +ve values.

1. I am looking for a variation of sigmoid function which can give me
the same "S" shape behavior on positive side. One has to shift the "S"
towards positive side. My range is 0 to 1, so I need the complete "S"
behavior between the range of 0 and 1.

2. I am not looking for some formula out of the blue (like
((1/1+e(-x)))-.5)*x which can generate the similar shape. Whatever
formula you want to answer should have valid references from
literature, (from any where, like Neural Networks, Marketing, IEEE,
ACM etc) and/or previously used somewhere.


Just to clarify it a little more, think of an example of Depth of
promotion on sales, if there is .1 to .3 (10 to 30%) off on particular
item, the curve seems stabilize in start and then (at 30%) starts
moving exponentially (from not-buying to Buy decision) and when the
sale amount reaches (70%+) the behavior again stabilize, means 70% and
99% are attracting the similar no of customers.

Good luck , I need it urgently