Give an example of what you want to achieve.
Some parameters and the result you expect to get.
I see that maxima has least squares curve fitting , would that be a good method to fit the sigmoidal curve ?
I wrote an interface to Maxima and you could use that to fit the curve you need.
Oh btw, I just found found a java applet that does what you want here. Here is the .jar for it(here's a mirror for the jar just in case). Also here's a Java decompiler that worked for me. The next step is pretty obvious, just take all the Java source code and conver it to Perl. Not very hard, but it will take some time.
Does this solve your problem ?