Gaussian Curve fitting

Question

[satyam85cool]

I have data where my x column corresponds to the residue position and the y axis corresponds to the entropy value. I want to do a curve-fitting on the data obtained. I was trying to fit a Gaussian curve but the curve is not fitting according to what it should look like. Can anyone suggest to me what should be an optimal way to do so?

from scipy.optimize import curve_fit

x = [18,23,95,142,154,156,157,158,258,318,367,382,484,501,522,574,681,832,943,1071,1078,1101,1133,1153,1174,1264]
y = [0.179,0.179,0.692,0.574,0.669,0.295,0.295,0.295,0.387,0.179,0.179,0.462,0.179,0.179,0.179,0.179,0.179,0.179,0.179,0.179,0.179,0.462,0.179,0.387,0.179,0.295]
x = np.asarray(x)
y = np.asarray(y)

amp1 = 100
sigma1 = 10
cen1 = 50

def Gauss(x, A, B):
    y = A*np.exp(-1*B*x**2)
    return y

parameters, covariance = curve_fit(Gauss, x, y)

fit_A = parameters[0]
fit_B = parameters[1]


fit_y = Gauss(x, fit_A, fit_B)
plt.figure(figsize=(18,10))
plt.plot(x, y, label='data')
plt.plot(x, fit_y, label="fit")
plt.legend()
plt.show()

Answer 1

[galen.seilis]

First of all, you should clarify for yourself (and us) on whether you are trying to fit a Gaussian function or a Gaussian distribution. These are not the same thing.

You code is attempting to fit a Gaussian function, but your data hardly looks anything like a Gaussian function. Perhaps consider a different model.

If you want to fit a Gaussian distribution to your data, I recommend you use maximum likelihood estimates with Bessel-corrected variance.