import numpy as np
import matplotlib.pyplot as plt
 
# Function for Gaussian CI
def gaussian_ci(mu, sigma):
    lower_bound = mu - 2 * sigma
    upper_bound = mu + 2 * sigma
    return lower_bound, upper_bound
 
# Function for Lognormal CI
def lognormal_ci(mu, sigma):
    lower_bound = np.exp(mu - 2 * sigma)
    upper_bound = np.exp(mu + 2 * sigma)
    return lower_bound, upper_bound
 
# Example values for Gaussian and Lognormal distributions
mu_gaussian = 10  # Mean of Gaussian
sigma_gaussian = 2  # Standard deviation of Gaussian
 
mu_lognormal = np.log(10)  # Mean of lognormal (log-scale)
sigma_lognormal = 0.2  # Standard deviation of lognormal (log-scale)
 
# Calculate CI for Gaussian
gaussian_lower, gaussian_upper = gaussian_ci(mu_gaussian, sigma_gaussian)
 
# Calculate CI for Lognormal
lognormal_lower, lognormal_upper = lognormal_ci(mu_lognormal, sigma_lognormal)
 
# Print results
print(f"Gaussian CI: [{gaussian_lower}, {gaussian_upper}]")
print(f"Lognormal CI: [{lognormal_lower}, {lognormal_upper}]")
 
# Plot the results (for visualization)
x = np.linspace(mu_gaussian - 4 * sigma_gaussian, mu_gaussian + 4 * sigma_gaussian, 1000)
gaussian_pdf = (1 / (sigma_gaussian * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((x - mu_gaussian) / sigma_gaussian) ** 2)
 
# Create a figure
plt.figure(figsize=(10, 6))
 
# Plot Gaussian PDF
plt.plot(x, gaussian_pdf, label="Gaussian Distribution", color="blue")
 
# Plot CI for Gaussian
plt.axvline(gaussian_lower, color='red', linestyle='--', label=f'CI Lower (Gaussian): {gaussian_lower}')
plt.axvline(gaussian_upper, color='red', linestyle='--', label=f'CI Upper (Gaussian): {gaussian_upper}')
 
# Lognormal PDF (on the log scale)
x_lognormal = np.linspace(0, 30, 1000)
lognormal_pdf = (1 / (x_lognormal * sigma_lognormal * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((np.log(x_lognormal) - mu_lognormal) / sigma_lognormal) ** 2)
 
# Plot Lognormal PDF
plt.plot(x_lognormal, lognormal_pdf, label="Lognormal Distribution", color="green")
 
# Plot CI for Lognormal
plt.axvline(lognormal_lower, color='orange', linestyle='--', label=f'CI Lower (Lognormal): {lognormal_lower}')
plt.axvline(lognormal_upper, color='orange', linestyle='--', label=f'CI Upper (Lognormal): {lognormal_upper}')
 
# Add labels and legend
plt.title('Gaussian and Lognormal Confidence Intervals')
plt.xlabel('Value')
plt.ylabel('Probability Density')
plt.legend()
 
# Show the plot
plt.show()

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