Setting a Gaussian to a histogram using MatPlotLib and Numpy - incorrect scaling of Y?

Question

I wrote the code below to fit the Gauss histogram. This seems to work though the scaling of Y is different. What am I doing wrong?

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.mlab as mlab

list = [0,1,1,2,2,2,3,3,4]

plt.figure(1)
plt.hist(list)
plt.xlim((min(list), max(list)))

mean = np.mean(list)
variance = np.var(list)
sigma = np.sqrt(variance)
x = np.linspace(min(list), max(list),100)
plt.plot(x,mlab.normpdf(x,mean,sigma))

plt.show()

Thanks!

Answer 1

You need to normalize the histogram, since the normalized distribution also normalizes:

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.mlab as mlab

arr = np.random.randn(100)

plt.figure(1)
plt.hist(arr, normed=True)
plt.xlim((min(arr), max(arr)))

mean = np.mean(arr)
variance = np.var(arr)
sigma = np.sqrt(variance)
x = np.linspace(min(arr), max(arr), 100)
plt.plot(x, mlab.normpdf(x, mean, sigma))

plt.show()

Pay attention to normed=Truethe call plt.hist. Also note that I changed your sample data because the histogram looks weird with too few data points.

, , , , , .. , .

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.mlab as mlab

arr = np.random.randn(1000)

plt.figure(1)
result = plt.hist(arr)
plt.xlim((min(arr), max(arr)))

mean = np.mean(arr)
variance = np.var(arr)
sigma = np.sqrt(variance)
x = np.linspace(min(arr), max(arr), 100)
dx = result[1][1] - result[1][0]
scale = len(arr)*dx
plt.plot(x, mlab.normpdf(x, mean, sigma)*scale)

plt.show()

scale, , .