Prev Next

Pareto Distribution

The Pareto distribution, also known as the power law distribution, is used to model phenomena where a small number of events account for a large proportion of the effect, such as wealth distribution or city populations.

Key Topics

Generating Pareto Distribution

NumPy's random.pareto() function generates random numbers following the Pareto distribution. You specify the shape parameter (alpha) and the size of the dataset.

Example

# Generating Pareto distribution
import numpy as np

# Shape parameter (alpha) = 2, Size = 10
pareto_values = np.random.pareto(a=2, size=10)

print("Pareto values:", pareto_values)

Output

Pareto values: [0.45 0.31 1.23 0.78 0.89 ...]

Explanation: The random.pareto() function generates random numbers representing a Pareto distribution with a shape parameter of 2.

Visualizing the Distribution

You can use a histogram to visualize the Pareto distribution and observe its long tail.

Example

# Visualizing Pareto distribution
import seaborn as sns
import matplotlib.pyplot as plt

# Data
pareto_values = np.random.pareto(a=2, size=1000)

# Plot
sns.histplot(pareto_values, kde=True, color="purple")
plt.title("Pareto Distribution")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.show()

Output

A histogram showing the long-tail Pareto distribution.

Explanation: The histogram demonstrates the Pareto distribution's characteristic long tail, with a small number of large values.

Key Takeaways

  • Pareto Distribution: Models scenarios where a small number of events have a large impact.
  • Simulation: Use random.pareto() for scenarios like wealth distribution or city populations.
  • Visualization: Histograms highlight the long-tail behavior of the distribution.
  • Applications: Analyze wealth inequality, traffic patterns, or natural phenomena.
Prev Next