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Apologies beforehand, since I'm relatively new to Python.

I have the following data for a reaction describing the growth of a compound:

data

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).

cdf

The formula to describe such curve shape is written as follows:

Formula CDF F-distribution

Thus my question is: How can I write this formula in a pythonic way? NOTE: I've tried fitting different types of logistic functions, but none are fitted correctly. The CDF like F, however, seems to properly describe reaction 1.

Thanks a lot for the help!!

Dory
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  • Does this answer your question? [Calculate the Cumulative Distribution Function (CDF) in Python](https://stackoverflow.com/questions/24788200/calculate-the-cumulative-distribution-function-cdf-in-python) – Chris Jan 12 '22 at 15:28
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    @Chris not at all. I'm not asking how to calculate the CDF of my data – Dory Jan 12 '22 at 16:09
  • Would using the python implemented version of the [incomplete beta](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.betainc.html) do the trick? – mikuszefski Jan 13 '22 at 13:29

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