I also tried a polynomial fit and also a fit with two gaussians which both look very similar and good if the goal is a smooth curve. Ofcourse they are far away from those ouliers(if they are?) and I guess you would need more data points to decide which are outliers or not. A fit using a special function like logarithms, exponatial functions or combinations of them makes sense if you are searching the parameters of the underlying physics, but then you would have to provide the general form of the function derived from the physics.
As it seems that you just have the data and no more information about it I guess a polynomial fit or s spline interpolation (which runs exactly through all your datapoints) is as good as any.
Genfit() won't find the type of curve which fits best automatically but you will have to provide it, genfit() will only find the "optimal" parameters and very often is VERY sensible concerning the initial guess values you also have to provide. There are specialized programs which try to find the best type of function, one of them is "CurveExpert Professional". Not sure if they offer a trial version to download.
And yes, you can integrate and differentiate "functions" derived by interpolation routines - numerically only, of course.
See if the attached sheet helps. Think f1 is what you want to use but maybe you are even happy with linear interpolation (f0).
