Fitting half a Gaussian curve/ normalization to Data points

Question

So I have two lists of data, which I can plot in a scatter plot, as such:

from matplotlib import pyplot as plt
x = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
y = [22.4155688819,22.3936180362,22.3177538001,22.1924849792,21.7721194577,21.1590235248,20.6670446864,20.4996957642,20.4260953411,20.3595072628,20.3926201626,20.6023149681,21.1694961343,22.1077417713,23.8270366414,26.5355924353,31.3179807276,42.7871637946,61.9639549412,84.7710953311]

plt.scatter(degrees,RMS_one_image)

This gives you a plot that looks like a Gaussian distribution, which is good as it should-

My issue is however I am trying to fit a Gaussian distribution to this, and failing miserably because a. it's only half a Gaussian instead of a full one, and b. what I've used before has only ever used one bunch of numbers. So something like:

# best fit of data
num_bins = 20
(mu, sigma) = norm.fit(sixteen)

y = mlab.normpdf(num_bins, mu, sigma)

n, bins, patches = plt.hist(deg_array, num_bins, normed=1, facecolor='blue', alpha=0.5)
# add a 'best fit' line
y = mlab.normpdf(bins, mu, sigma)
plt.plot(bins, y, 'r--')

Does this approach work at all here, or am I going about this in the wrong way completely? Thanks...

Answer 1

It seems that your normal solution is to find the expectation value and standard deviation of the data directly instead of using a least square fit. Here is a solution using curve_fit from scipy.optimize.

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

x = np.array([0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19])
y = [22.4155688819,22.3936180362,22.3177538001,22.1924849792,21.7721194577,21.1590235248,20.6670446864,20.4996957642,20.4260953411,20.3595072628,20.3926201626,20.6023149681,21.1694961343,22.1077417713,23.8270366414,26.5355924353,31.3179807276,42.7871637946,61.9639549412,84.7710953311]

# Define a gaussian function with offset
def gaussian_func(x, a, x0, sigma,c):
    return a * np.exp(-(x-x0)**2/(2*sigma**2)) + c

initial_guess = [1,20,2,0]
popt, pcov = curve_fit(gaussian_func, x, y,p0=initial_guess)

xplot = np.linspace(0,30,1000)
plt.scatter(x,y)
plt.plot(xplot,gaussian_func(xplot,*popt))

plt.show()