I'm not a mathematician, so apologies beforehand as the vocabulary/expertise I might display in this enquiry might be a bit sketchy.
I have the following data for a reaction describing the growth of a compound:
The first derivative of this S-shaped curve describing the reaction seems to resemble an F-distribution curve. In my understanding, a cumulative distribution function (CDF) is an integral of a distribution curve, thus I was hoping to fit a CDF like F (10,10) to fit and model my reaction 1 (resembling the bottom right function of the image attached below).
Thus, I wanted to ask: what kind of formula could I use in i.e. python to model and obtain parameters of such an S-shaped curve? In this case, what would be the physical meaning of such a reaction with a CDF F-distribution behaviour compared to a reaction with a general logistic function behaviour?
Thanks a lot for the help!!