How to match a Gaussian normal to a histogram?

Question

I'm wondering if there is a good way to match a Gaussian normal to a histogram in the form of a numpy array np.histogram(array, bins) .

How can such a curve been plotted on the same graph and adjusted in height and width to the histogram?

Answer 1

You can fit your histogram using a Gaussian (ie normal) distribution, for example using scipy's curve_fit. I have written a small example below. Note that depending on your data, you may need to find a way to make good guesses for the starting values for the fit (p0). Poor starting values may cause your fit to fail.

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

def fit_func(x,a,mu,sigma,c):
    """gaussian function used for the fit"""
    return a * norm.pdf(x,loc=mu,scale=sigma) + c

#make up some normally distributed data and do a histogram
y = 2 * np.random.normal(loc=1,scale=2,size=1000) + 2
no_bins = 20
hist,left = np.histogram(y,bins=no_bins)
centers = left[:-1] + (left[1] - left[0])

#fit the histogram
p0 = [2,0,2,2] #starting values for the fit
p1,_ = curve_fit(fit_func,centers,hist,p0,maxfev=10000)

#plot the histogram and fit together
fig,ax = plt.subplots()
ax.hist(y,bins=no_bins)
x = np.linspace(left[0],left[-1],1000)
y_fit = fit_func(x, *p1)
ax.plot(x,y_fit,'r-')
plt.show()