manujajay / poisson-distribution

Poisson Distribution

This repository focuses on the Poisson Distribution, a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, assuming these events occur with a known constant mean rate and independently of the time since the last event.

Prerequisites

• Python 3.6 or higher
• Libraries: numpy, matplotlib

Installation

To use the code examples in this repository, you will need to install the necessary Python libraries:

pip install numpy matplotlib

Example - Poisson Distribution Calculation and Visualization

This example demonstrates how to compute and visualize Poisson probabilities using NumPy and Matplotlib.

poisson_example.py

import numpy as np
import matplotlib.pyplot as plt

# Probability of k events in a fixed interval
lambda_ = 4  # average number of events per interval
k_values = np.arange(0, 10)  # possible number of events
poisson_probabilities = np.exp(-lambda_) * np.power(lambda_, k_values) / np.factorial(k_values)

# Plotting the distribution
plt.bar(k_values, poisson_probabilities, color='blue', alpha=0.7)
plt.title('Poisson Distribution - $\lambda=4$')
plt.xlabel('Number of Events')
plt.ylabel('Probability')
plt.show()

Contributing

Contributions that improve the clarity of explanations, extend the range of examples, or enhance the visualization of data are welcome. Please fork this repository, create a new branch for your changes, and submit a pull request.

License

This project is licensed under the MIT License. See the LICENSE file for more details.