The Poisson Distribution model the number of times an event happens within a fixed time or space when we know the average number of occurrences. It is used for events that occur independently such as customer arrivals at a store, Website clicks where events happen independently.

numpy.random.poisson() Method

In Python'sNumPylibrary we can generate random numbers following a Poisson Distribution using the numpy.random.poisson() method. It has two key parameters:

• lam : The average number of events (λ) expected to occur in the interval.
• size : The shape of the returned array.

Syntax:

numpy.random.poisson(lam=1.0, size=None)

Example 1: Generate a Single Random Number

To generate a single random number from a Poisson Distribution with an average rate of λ = 5:

import numpy as np

random_number = np.random.poisson(lam=5)
print(random_number)

Output :

5

Example 2: Generate an Array of Random Numbers

To generate multiple random numbers:

random_numbers = np.random.poisson(lam=5, size=5)
print(random_numbers)

Output :

[13 6 4 4 10]

Visualizing the Poisson Distribution

To understand the distribution better we can visualize the generated numbers. Here is an example of plotting a histogram of random numbers generated using numpy.random.poisson.

import numpy as np
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns

lam = 2  
size = 1000  

data = random.poisson(lam=lam, size=size)

sns.displot(data, kde=False, bins=np.arange(-0.5, max(data)+1.5, 1), color='skyblue', edgecolor='black')

plt.title(f"Poisson Distribution (λ={lam})")
plt.xlabel("Number of Events")
plt.ylabel("Frequency")
plt.grid(True)

plt.show()

Output:

The image shows a Poisson Distribution with λ=2 displaying the frequency of events. The histogram represents simulated data highlighting the peak at 0 and 1 events, with frequencies decreasing as the number of events increases.