Sigmoid Function question

[Guest]

Hi, I'm looking for the equation of a sigmoid function with the following properties,
* it is differentiable.
* the upper limit is asymptotic to 1
* the lower limit is asymptotic to 0
* with the inflection point at a specified location, (p,q) : where 0<q<1
* and the specified gradient at (p,q) is g : where -1<g<+1

ie the function has p,q,g as coefficients.

I'm guessing there will be many such equations, but will the information I have select a unique curve within each equation form?

[Guest]

I have come up with this, which seems to work, but I would have liked something simpler.

[tex]y=(1-
((1-q*EXP(-W(q*LN(q))))*EXP(g/(q*LN(q))*W(q*LN(q))*p))*
EXP(-g/(q*LN(q))*W(q*LN(q))*x)
)^{(LN(q)/(LN(q)-W(q*LN(q))))}[/tex]

[Guest]

sorry, tex didn't work. In long hand,

y=(1-
((1-q*EXP(-W(q*LN(q))))*EXP(g/(q*LN(q))*W(q*LN(q))*p))*
EXP(-g/(q*LN(q))*W(q*LN(q))*x)
)^
(LN(q)/(LN(q)-W(q*LN(q))))

[Guest]

www.mathsisfun.com