Plotting a probability density function by sample with Matplotlib

To plot a probability density function by sample with Matplotlib, we can use NumPy to generate data points and create a smooth curve. This is particularly useful for visualizing Gaussian distributions and other probability functions.

Steps

• Create x and p data points using NumPy
• Plot x and p data points using plot() method
• Scale the X-axis to focus on the relevant range
• Display the figure using show() method

Example

Here's how to create a probability density function plot ?

import numpy as np
from matplotlib import pyplot as plt

# Set figure size and layout
plt.rcParams["figure.figsize"] = [7.00, 3.50]
plt.rcParams["figure.autolayout"] = True

# Create data points
x = np.arange(-100, 100)
p = np.exp(-x ** 2)

# Plot the probability density function
plt.plot(x, p)
plt.xlim(-20, 20)
plt.xlabel('x')
plt.ylabel('Probability Density')
plt.title('Probability Density Function')
plt.show()

Enhanced Example with Normal Distribution

For a more realistic probability density function, let's create a proper normal distribution ?

import numpy as np
from matplotlib import pyplot as plt

# Parameters for normal distribution
mu = 0      # mean
sigma = 2   # standard deviation

# Create x values
x = np.linspace(-10, 10, 100)

# Calculate probability density function
pdf = (1 / (sigma * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((x - mu) / sigma) ** 2)

# Plot the PDF
plt.figure(figsize=(8, 5))
plt.plot(x, pdf, 'b-', linewidth=2, label=f'Normal(?={mu}, ?={sigma})')
plt.xlabel('x')
plt.ylabel('Probability Density')
plt.title('Normal Distribution PDF')
plt.grid(True, alpha=0.3)
plt.legend()
plt.show()

Key Points

• Data Generation: Use np.linspace() for smoother curves than np.arange()
• PDF Formula: For normal distribution: PDF = (1/(??(2?))) × e^(-0.5×((x-?)/?)²)
• Visualization: Add labels, title, and grid for better readability
• Range Selection: Use xlim() to focus on the meaningful range of the distribution

Output

Conclusion

Plotting probability density functions with Matplotlib helps visualize statistical distributions effectively. Use NumPy for mathematical calculations and Matplotlib's plotting functions for clear, informative graphs with proper labels and formatting.