Normality Test

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

# Generate sample data
np.random.seed(42)
normal_data = np.random.normal(loc=0, scale=1, size=1000)
skewed_data = np.random.exponential(scale=1, size=1000)

# Perform normality tests
def test_normality(data, name):
    shapiro_stat, shapiro_p = stats.shapiro(data)
    ks_stat, ks_p = stats.kstest(data, 'norm')
    anderson_result = stats.anderson(data, dist='norm')
    
    print(f"--- {name} ---")
    print(f"Shapiro-Wilk test: statistic = {shapiro_stat:.4f}, p-value = {shapiro_p:.4f}")
    print(f"Kolmogorov-Smirnov test: statistic = {ks_stat:.4f}, p-value = {ks_p:.4f}")
    print(f"Anderson-Darling test: statistic = {anderson_result.statistic:.4f}")
    print("Critical values:", anderson_result.critical_values)
    print()

test_normality(normal_data, "Normal Distribution")
test_normality(skewed_data, "Skewed Distribution")

# Visualize the distributions
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))

ax1.hist(normal_data, bins=30, density=True, alpha=0.7)
ax1.set_title("Normal Distribution")
ax1.set_xlabel("Value")
ax1.set_ylabel("Density")

ax2.hist(skewed_data, bins=30, density=True, alpha=0.7)
ax2.set_title("Skewed Distribution")
ax2.set_xlabel("Value")
ax2.set_ylabel("Density")

plt.tight_layout()
plt.show()

# Q-Q plots
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))

stats.probplot(normal_data, dist="norm", plot=ax1)
ax1.set_title("Q-Q Plot: Normal Distribution")

stats.probplot(skewed_data, dist="norm", plot=ax2)
ax2.set_title("Q-Q Plot: Skewed Distribution")

plt.tight_layout()
plt.show()