Generating Random Numbers from Exponential distribution

Faisal Qureshi
faisal.qureshi@ontariotechu.ca

Copyright information

© Faisal Qureshi

License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

import numpy as np
import matplotlib.pyplot as plt

Using numpy's method

n = 100000
x = np.empty(n)
for i in range(n):
    x[i] = np.random.exponential()

plt.figure(figsize=(4,4))
plt.title(f'Exponential')
plt.hist(x, bins=np.linspace(0,10,100));

Using cdf inverse method

def inv_cdf_of_exponential(mu, u):
    return - mu * np.log( u )

def gen_samples_from_exponential_using_inv_cdf(n):
  mu = 1
  x = np.empty(n)
  for i in range(0,n):
    u = np.random.rand()
    x[i] = inv_cdf_of_exponential(mu, u)
  return x

Sample histogram

x_cdf = gen_samples_from_exponential_using_inv_cdf(n)
plt.figure(figsize=(4,4))
plt.title(f'Exponential')
plt.hist(x, bins=np.linspace(0,10,100), color='blue', alpha=0.2, label='builtin');
plt.hist(x_cdf, bins=np.linspace(0,10,100), color='red', alpha=0.2, label='inv cdf');
plt.legend()

<matplotlib.legend.Legend at 0x11419a7b0>