# Inverse of a six-parameter asymmetric sigmoidal curve

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• Jul 28th 2010, 01:39 AM
spiceman
Inverse of a six-parameter asymmetric sigmoidal curve
Dear Math-Helpers.

I'm having a really hard time to find the inverse of the following six-parameter sigmoidal function:

y = c + k*log(x) + (d-c)/(1+exp(b*(log(x)-log(e))))^f

k, c, d, e and f are parameters.

I need to solve the function to x.

Any hints on what transformations are necessary?
If I omit k*log(x) it's easy, but this term makes it hard somehow...

Thanks in advance,
ans
• Jul 30th 2010, 10:01 AM
Media_Man
Quote:

Originally Posted by spiceman
I'm having a really hard time to find the inverse of the following six-parameter sigmoidal function:

Not to sound sarcastic, but are you sure it exists? The inverse may not be expressible in closed form, yet a dozen different methods can be used to actually compute with it.
• Jul 31st 2010, 01:42 AM
HallsofIvy
exp(b(log(x)- log(e))= exp(log(x^b))e^{-blog(e)) (I am assuming here that the "e" is just some constant- NOT the base of the exponential function since you have written that as "exp(x)", not "e^x") and exp(log(x^b))= x^b. That equation will have "log(x)" and powers of x. Looks to me like you will need the Lambert W function.