Created
December 31, 2023 16:38
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Fit a curve to a binned distribution
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# %% | |
from typing import Iterable | |
import numpy as np | |
from matplotlib import pyplot as plt | |
from scipy import integrate | |
from scipy.optimize import curve_fit | |
from scipy.stats import beta | |
if __name__ == "__main__": | |
rng = np.random.default_rng(123456) | |
# %% generate a skewed beta distribution with a=2, b=8 | |
X = rng.beta(2, 8, size=1000) | |
plt.hist(X) | |
# %% bin random values into NON-equidistant bins | |
y, bins = np.histogram( | |
X, bins=[0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 1] | |
) | |
x = (bins[1:] + bins[:-1]) / 2 | |
plt.plot(x, y) | |
# %% default fitting w/o accounting for the integral | |
def f_distr(x: Iterable[float], a: float, b: float, c: float) -> float: | |
"""Beta function with area normalisation `c`""" | |
_y = c * beta.pdf(x, a, b) | |
return _y | |
popt, pcov = curve_fit(f_distr, x, y) | |
print(f"Fit WITHOUT bin width: {popt[0]:.3f}, {popt[1]:.3f}") | |
_ = plt.plot(x, y, marker="o") | |
_ = plt.plot(x, f_distr(x, popt[0], popt[1], popt[2]), ls="--", c="red") | |
# %% fitting using integrals in bins | |
def f_integral(x: Iterable[float], *args) -> float: | |
"""Integral of the beta distribution""" | |
result = [ | |
integrate.quad(f_distr, v_min, v_max, args=args) | |
for v_min, v_max in zip(bins[:-1], bins[1:]) | |
] | |
return [v[0] for v in result] | |
popt, pcov = curve_fit(f_integral, x, y, p0=(1, 2, 3)) | |
print(f"Fit WITH bin width: {popt[0]:.3f}, {popt[1]:.3f}") | |
_ = plt.plot(x, y, marker="o") | |
y_fitted = f_integral(x, *popt) | |
_ = plt.plot(x, y_fitted, ls="--", c="red") |
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