import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import chi2

# More "paper-like" style
plt.rcParams.update({
    'font.size': 18,
    'axes.titlesize': 18,
    'axes.labelsize': 16,
    'legend.fontsize': 14
})

# Parameters
alpha = 0.05
df = 10
chi2_emp = 12.1

chi2_crit = chi2.ppf(1 - alpha, df)
p_value = 1 - chi2.cdf(chi2_emp, df)

x = np.linspace(0, 30, 500)
y = chi2.pdf(x, df)

# Create figure and axes (better control than plt.figure)
fig, ax = plt.subplots(figsize=(6, 5))

# Plot
ax.plot(x, y, color='black', label=r'$\chi^2$ distribution')

# Critical region
x_alpha = x[x >= chi2_crit]
ax.fill_between(x_alpha, chi2.pdf(x_alpha, df),
                color='red', alpha=0.3, hatch='///',
                label=r'$\alpha$ (critical region)')

# p-value region
x_p = x[x >= chi2_emp]
ax.fill_between(x_p, chi2.pdf(x_p, df),
                color='blue', alpha=0.3, hatch='\\\\',
                label='p-value')

# Vertical lines
ax.axvline(chi2_crit, color='red', linestyle='--',
           label=rf'$c_{{\alpha}} = {chi2_crit:.2f}$')

ax.axvline(chi2_emp, color='blue', linestyle='--',
           label=rf'$\chi^2_{{emp}} = {chi2_emp}$')

# Title
ax.set_title(
    rf'$\chi^2$ distribution (df={df})'
    f'\n$\\alpha = {alpha}$, p-value = {p_value:.4f}'
)

# Axis labels
ax.set_xlabel(r'$\chi^2$ value')
ax.set_ylabel('Probability density')

# Legend and grid
ax.legend(loc='upper right')
ax.grid(True)

# MANUAL margins
fig.subplots_adjust(
    left=0.12,
    right=0.98,
    bottom=0.18,
    top=0.88
)

# Save as clean SVG
fig.savefig(
    "Chi-square distribution — test statistic below critical value.svg",
    format="svg",
    bbox_inches='tight',
    pad_inches=0.1
)

plt.show()
plt.close(fig)