Assuming you have an array of number to which you need to
plot a histogram. Plot the histogram in python using the following code.
n, bins, patches = plt.hist(D, 40, histtype='bar')
plt.show()
plt.show()
The resulting plot looks like image 1. Once you have
histogram you know need transform the histogram such that sum of frequency of all the points is 1
Image 1
To do that just use the following code in
python. We are just diving each range by total number of data points.
n = n/len(A)
n = np.append(n, 0)
Now we have histogram whose sum of probability of all the
points of occurrence is 1.
The final Step:
If your histogram looks like a Gaussian distribution, plot
the mean and variance for the histogram.
mu = np.mean(n)
sigma = np.std(n)
Once you have the mean and variance plot the gaussian pdf
function. There might be problem in scale and you might get peak at a higher
value. To fix this just scale this to a factor it fits. A final image in shown
in image 2.
mu = np.mean(n)
sigma = np.std(n)
plt.bar(bins,n, width=(bins[len(bins)-1]-bins[0])/40)
y1= (1/(sigma*np.sqrt(2*np.pi))*np.exp(-(bins - mu)**2 /(2*sigma**2)))*0.03
plt.plot(bins, y1, 'r--', linewidth=2)
Image 2
Finally we have the probability distribution function as
1/(sigma*np.sqrt(2*np.pi))*np.exp(-(bins - mu)**2 /(2*sigma**2)))*0.03
PS : Imports
import numpy as np
import matplotlib
from matplotlib import pyplot as plt
