Examples of how to calculate and plot a cumulative distribution function in python
Table of contents
1 -- Generate random numbers
Let's for example generate random numbers from a normal distribution:
import numpy as npimport matplotlib.pyplot as pltN = 100000data = np.random.randn(N)
2 -- Create an histogram with matplotlib
hx, hy, _ = plt.hist(data, bins=50, normed=1,color="lightblue")plt.ylim(0.0,max(hx)+0.05)plt.title('Generate random numbers \n from a standard normal distribution with python')plt.grid()plt.savefig("cumulative_density_distribution_01.png", bbox_inches='tight')#plt.show()plt.close()
3 -- Option 1: Calculate the cumulative distribution function using the histogram
dx = hy[1] - hy[0]F1 = np.cumsum(hx)*dxplt.plot(hy[1:], F1)plt.title('How to calculate and plot a cumulative distribution function ?')plt.savefig("cumulative_density_distribution_02.png", bbox_inches='tight')plt.close()
4 -- Option 2: Sort the data
X2 = np.sort(data)F2 = np.array(range(N))/float(N)plt.plot(X2, F2)plt.title('How to calculate and plot a cumulative distribution function ?')plt.savefig("cumulative_density_distribution_03.png", bbox_inches='tight')plt.close()
4 -- Using the function cdf in the case of data distributed from a normal distribution
If the data has been generated from a normal distibution, there is the function cdf():
from scipy.stats import normx = np.linspace(-10,10,100)y = norm.cdf(x)plt.plot(x, y)plt.title('How to calculate and plot a cumulative distribution function ?')plt.savefig("cumulative_density_distribution_04.png", bbox_inches='tight')plt.close()
