# How to calculate and plot a cumulative distribution function with matplotlib in python ?

Daidalos May 10, 2020

Examples of how to calculate and plot a cumulative distribution function in python

### 1 -- Generate random numbers

Let's for example generate random numbers from a normal distribution:

import numpy as np
import matplotlib.pyplot as plt

N = 100000

data = 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)*dx

plt.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 norm

x = 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()