Fit a simple S-curve and find the midpoint in python

Question

Let's say I have S-curved shaped data like below :

S-Curved data

I would like too find the simplest way to fit this kind of curves AND use this fit to find the midpoint (aka the point where y=0.5). The fact is that I don't know beforehand where the midpoint.

Thanks a lot for your answers,

Cheers

Answer 1

This is clearly a case of fitting a logistic curve with L=1:

import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit

data = np.loadtxt(r"\data.txt", delimiter=",")

x = data[:, 0]
y = data[:, 1]


def f(x: np.ndarray, k: float, x0: float):
    return 1 / (1 + np.exp(-k*(x - x0)))


popt, pcov = curve_fit(f, x, y, p0 = [1, 120])

fig, ax = plt.subplots(figsize=(8, 5.6))

plt.scatter(x, y)
plt.plot(x, f(x, *popt), color="red")
plt.show()

x0 is given by popt[1], i.e. 121.18.