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Chi-Square Distribution in NumPy
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Poisson Distribution in NumPy

Last Updated : 22 Apr, 2025
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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:

Python 
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:

Python 
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.

Python 
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:

poisson-distribution

Poisson Distribution

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.




Next Article
Chi-Square Distribution in NumPy

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Article Tags :
  • Python
  • Python numpy-Random
  • Python-numpy
Practice Tags :
  • python

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