for my project I found that my data roughly follows a certain shape. See below. (They are from three different but similar experiments.) I was wondering if any of you know a good fit. I already tried something like $f(x) = ax + b/x$, which is a hyperbola symmetric wrt the origin with asymptotes $y = ax$ (for $a > 0$) and $x = 0$. ($a$ and $b$ have to be fitted.)
However, with these $f$ I find the following fits:
It's good, but I believe it could be better. For example, the bottom bump shouldn't be as sharp. Also, I'd like to incorporate a second "bump".
I was wondering if any of you could recommend some functions which would work better. (One with (not too many) parameters which still need to be fitted.) Thanks in advance!
Without clue about the kind of physical model one can imagine a lot of models equations. For example the combination of a linear function with a damped sinusoidal function :
Even with a simple polynomial equation the fitting isn't worse than with the above more sophisticated model :