Fitting a better gaussian to data points?

Question

I am trying to fit a gaussian to a set of data points that seem to follow a gaussian distribution. I have already checked a lot of possible ways to do that, but I don\'t really

Answer 1

I think there are two different things here:

seem to follow a gaussian distribution

→ If you think that the data are normally distributed, you are in the realms of statistics and probability distributions, and may want to make a test to see if they agree with a particular distribution (normal or other).

---

And work with your plot:

get a "better" gaussian plot

In your code, you can leave out the first estimation in curve_fit and plot the fitted curve against a continuous independent variable:

import numpy as np
import matplotlib.pyplot as plt
from scipy import asarray as ar, exp, sqrt
from scipy.optimize import curve_fit


angles = [-8, -6, -4, -2, 0, 2, 4, 6, 8]
data = [99, 610, 1271, 1804, 1823, 1346, 635, 125, 24]
angles = ar(angles)
data = ar(data)

n = len(data)  ## <---
mean = sum(data*angles)/n
sigma = sqrt(sum(data*(angles-mean)**2)/n)

def gaus(x,a,mu,sigma):
    return a*exp(-(x-mu)**2/(2*sigma**2))

popt,pcov = curve_fit(gaus,angles,data)#,p0=[0.18,mean,sigma])  ## <--- leave out the first estimation of the parameters
xx = np.linspace( -10, 10, 100 )  ## <--- calculate against a continuous variable

fig = plt.figure()
plt.plot(angles, data, "ob", label = "Measured")
plt.plot(xx,gaus(xx,*popt),'r',label='Fit')  ## <--- plot against the contious variable
plt.xlim(-10, 10)
plt.ylim(0, 2000)
plt.xticks(angles)
plt.title("$^{137}$Cs Zero Point")
plt.xlabel("Angle [$^\circ$]")
plt.ylabel("662 keV-Photon Count")
plt.grid()
plt.legend()
plt.savefig('normal.png')
plt.show()

---

In this example:

print( popt )

[  1.93154077e+03  -9.21486804e-01   3.26251063e+00]

Note that the first estimation of the parameter is orders of magnitude away from the result: 0.18 vs. 1931.15.