import numpy as np
import matplotlib.pyplot as plt

mu = 3.5
sigmas = [0.1, 0.3]
size = 100000
rng = np.random.default_rng(42)

fig, axes = plt.subplots(1, 2, figsize=(16, 6))

for sigma in sigmas:
    samples = rng.lognormal(mean=mu, sigma=sigma, size=size)
    
    # lognormal → normal 변환
    log_samples = np.log(samples)
    
    # Lognormal 플롯
    axes[0].hist(samples, bins=200, density=True, alpha=0.5, label=f"sigma={sigma}")
    axes[0].set_xlim(0, 200)
    axes[0].set_title("Lognormal Distribution")
    axes[0].set_xlabel("Weight")
    axes[0].set_ylabel("Density")
    axes[0].legend()
    
    # Normal 플롯
    axes[1].hist(log_samples, bins=200, density=True, alpha=0.5, label=f"sigma={sigma}")
    axes[1].set_title("log(samples) → Normal Distribution")
    axes[1].set_xlabel("log(Weight)")
    axes[1].set_ylabel("Density")
    axes[1].legend()

plt.suptitle("Lognormal vs Normal (μ fixed)")
plt.tight_layout()
plt.show()