Python Code to Plot F-distribution Density Function

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

def plot_f_distribution(df1, df2, alpha=0.05):
    # Create x values for the plot
    x = np.linspace(0, 5, 1000)
    
    # Calculate F-distribution values
    y = stats.f.pdf(x, df1, df2)


    
    # Calculate critical F-value
    f_crit = stats.f.ppf(1 - alpha, df1, df2)
    
    # Create the plot
    plt.figure(figsize=(10, 6))

        # Add solid black line at y=0 (x-axis)
    plt.axhline(y=0, color='black', linewidth=1.5)
    
    # Plot F-distribution curve
    plt.plot(x, y, 'b-', lw=2, label=f'F({df1}, {df2})')
    
    # Fill the rejection region
    x_fill = x[x >= f_crit]
    y_fill = stats.f.pdf(x_fill, df1, df2)
    plt.fill_between(x_fill, y_fill, color='red', alpha=0.3)
    
    # Add vertical line at critical value
    plt.axvline(x=f_crit, color='r', linestyle='--', label=f'F-critical = {f_crit:.2f}')
    
    # Add arrow and annotation for alpha
    max_y = max(y)
    plt.annotate(f'α = {alpha}',
                xy=(f_crit+1, stats.f.pdf(f_crit, df1, df2)),
                xytext=(f_crit + 1.85, max_y * 0.8),
                arrowprops=dict(facecolor='black', shrink=0.05))
    
    # Add x=2.711 label on x-axis
    plt.text(2.75, -max_y * 0.01, 'x = 2.71', 
            horizontalalignment='center',
            verticalalignment='top')
    plt.axvline(x=2.711, color='green', linestyle=':', alpha=0.5)
    
    # Customize the plot
    plt.title('F-Distribution')
    plt.xlabel('F-value')
    plt.ylabel('Probability Density')
    plt.legend()
    plt.grid(True, alpha=0.3)
    
    # Show the plot
    plt.show()

# Example usage
plot_f_distribution(df1=5, df2=20)