Fit a gaussian function

Question

I have a histogram (see below) and I am trying to find the mean and standard deviation along with code which fits a curve to my histogram. I think there is something in SciPy or matplotlib that can help, but every example I've tried doesn't work.

import matplotlib.pyplot as plt
import numpy as np

with open('gau_b_g_s.csv') as f:
    v = np.loadtxt(f, delimiter= ',', dtype="float", skiprows=1, usecols=None)

fig, ax = plt.subplots()

plt.hist(v, bins=500, color='#7F38EC', histtype='step')

plt.title("Gaussian")
plt.axis([-1, 2, 0, 20000])

plt.show()

Answer 1

Take a look at this answer for fitting arbitrary curves to data. Basically you can use scipy.optimize.curve_fit to fit any function you want to your data. The code below shows how you can fit a Gaussian to some random data (credit to this SciPy-User mailing list post).

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

# Define some test data which is close to Gaussian
data = numpy.random.normal(size=10000)

hist, bin_edges = numpy.histogram(data, density=True)
bin_centres = (bin_edges[:-1] + bin_edges[1:])/2

# Define model function to be used to fit to the data above:
def gauss(x, *p):
    A, mu, sigma = p
    return A*numpy.exp(-(x-mu)**2/(2.*sigma**2))

# p0 is the initial guess for the fitting coefficients (A, mu and sigma above)
p0 = [1., 0., 1.]

coeff, var_matrix = curve_fit(gauss, bin_centres, hist, p0=p0)

# Get the fitted curve
hist_fit = gauss(bin_centres, *coeff)

plt.plot(bin_centres, hist, label='Test data')
plt.plot(bin_centres, hist_fit, label='Fitted data')

# Finally, lets get the fitting parameters, i.e. the mean and standard deviation:
print 'Fitted mean = ', coeff[1]
print 'Fitted standard deviation = ', coeff[2]

plt.show()