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Rayleigh Distribution

The Rayleigh distribution is used to model the magnitude of a vector that is the sum of two orthogonal components, such as wind speed or signal strength in communication systems.

Key Topics

Generating Rayleigh Distribution

NumPy's random.rayleigh() function generates random numbers following a Rayleigh distribution. The scale parameter determines the spread of the distribution.

Example

# Generating Rayleigh distribution
import numpy as np

# Scale parameter = 2, Size = 10
rayleigh_values = np.random.rayleigh(scale=2, size=10)

print("Rayleigh values:", rayleigh_values)

Output

Rayleigh values: [2.31 1.89 3.45 0.87 2.91 ...]

Explanation: The random.rayleigh() function generates random numbers representing magnitudes in a Rayleigh distribution.

Visualizing the Distribution

You can visualize the Rayleigh distribution using a histogram to observe its positively skewed shape.

Example

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

# Data
rayleigh_values = np.random.rayleigh(scale=2, size=1000)

# Plot
sns.histplot(rayleigh_values, kde=True, color="orange")
plt.title("Rayleigh Distribution")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.show()

Output

A histogram showing the positively skewed Rayleigh distribution.

Explanation: The histogram shows the Rayleigh distribution's characteristic shape, often used in signal strength analysis.

Key Takeaways

  • Rayleigh Distribution: Models magnitudes resulting from the sum of two orthogonal components.
  • Simulation: Use random.rayleigh() to generate data for wind speeds or signal strengths.
  • Visualization: Histograms and KDE plots highlight the skewed shape of the distribution.
  • Applications: Analyze wind speed, signal strength, and other magnitude-related phenomena.
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