python code to describe a generalized logistic function, useful for curve fitting and understanding when a transition happens

logistic.py

import numpy as np
from scipy.optimize import curve_fit

def logistic_fit(alpha, Q, b, v, alpha_N):
    # Implements a more general logistic function (solution of Richards's DE with K=1)
    return 1 / ((1 + Q * np.exp(-b*v*(alpha - alpha_N))) ** (1/v))

def generalized_logistic_threshold(alpha_N, b, Q, v):
    # Calculate the threshold value of alpha_N given as the argument where the above generalized logistic function equals 0.5
    correction_term = (np.log(2**v - 1) - np.log(Q)) / (-b*v)
    return correction_term + alpha_N
  
# Example fit with scipy
popt, _ = curve_fit(logistic_fit, x, p_curve, p0=[1., 1., 1., 3.5], bounds=([0., -np.inf, 0., 3.], [np.inf, np.inf, np.inf, 6.]), maxfev=5000)