mathematical-statistics/chebyshev_inequality.ipynb

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    "#### Chebyshev's Inequality\n",
    "\n",
    "**Basic Idea:**\n",
    "Bounds the proportion of values within $k$ standard deviations from the mean, regardless of distribution.\n",
    "\n",
    "**Conditions:**\n",
    "- Finite mean $\\mu$ and finite variance $\\sigma^2$.\n",
    "- $k > 0$.\n",
    "\n",
    "---\n",
    "\n",
    "**Version-1 (Upper Bound):**\n",
    "$$\n",
    "P(|X - \\mu| \\geq k\\sigma) \\leq \\frac{1}{k^2}\n",
    "$$\n",
    "\n",
    "**Version-2 (Lower Bound):**\n",
    "$$\n",
    "P(|X - \\mu| < k\\sigma) \\geq 1 - \\frac{1}{k^2}\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "**Example (for $k = 2$):**\n",
    "\n",
    "- **Version-1**:  \n",
    "  $$\n",
    "  P(|X - \\mu| \\geq 2\\sigma) \\leq 0.25\n",
    "  $$\n",
    "\n",
    "- **Version-2**:  \n",
    "  $$\n",
    "  P(|X - \\mu| < 2\\sigma) \\geq 0.75\n",
    "  $$\n",
    "\n",
    "\n",
    "At least 75% values are within ${\\pm2\\sigma}$ from mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e0c9ecf1-e406-4928-8470-87b2d69f32dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Parameters\n",
    "n_samples = 1000000\n",
    "k_std_dev = 2      \n",
    "np.random.seed(47)\n",
    "plt.style.use('dark_background')\n",
    "\n",
    "mean = 0\n",
    "std_dev = 1\n",
    "\n",
    "# Generate a random distribution (Normal)\n",
    "data = np.random.normal(loc=mean, \n",
    "                        scale=std_dev, \n",
    "                        size=n_samples)  \n",
    "\n",
    "# Compute the proportion of values within ±k std\n",
    "within_std_count = np.sum(\n",
    "    np.abs(data - mean) < k_std_dev * std_dev\n",
    ")\n",
    "empirical_probability = (\n",
    "    within_std_count / n_samples\n",
    ")\n",
    "\n",
    "# Theoretical bound by Chebyshev\n",
    "chebyshev_bound = 1 - 1 / k_std_dev**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5f9a8909-fc73-4131-bb7a-840e0f10da1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2700x1560 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2700x1560 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Empirical Probability within ±2σ: 0.9549\n",
      "Chebyshev's Bound within ±2σ: 0.7500\n"
     ]
    }
   ],
   "source": [
    "# Plot 1: Theoretical Area (Chebyshev's Bound)\n",
    "plt.figure(figsize=(9, 5.2), dpi=300)\n",
    "n, bins, patches = plt.hist(data, bins=1000, alpha=0.5, density=True, label='Data Distribution', color='yellow')\n",
    "\n",
    "# Color the histogram between ±2σ\n",
    "for i in range(len(bins) - 1):\n",
    "    if bins[i] >= mean - k_std_dev * std_dev and bins[i+1] <= mean + k_std_dev * std_dev:\n",
    "        patches[i].set_facecolor('magenta')  # Coloring the bins within ±2σ\n",
    "\n",
    "# Add vertical lines for ±2σ\n",
    "plt.axvline(mean + k_std_dev * std_dev, color='red', linestyle='--', label=f'+{k_std_dev}σ')\n",
    "plt.axvline(mean - k_std_dev * std_dev, color='red', linestyle='--', label=f'-{k_std_dev}σ')\n",
    "\n",
    "# Annotation for Chebyshev's bound\n",
    "plt.text(mean + k_std_dev * std_dev, 0.1, f\"AUC (Inequality based) ≥{chebyshev_bound:.2f}\", color='magenta')\n",
    "plt.title(f'Theoretical Area: Chebyshev\\'s Bound (Normal Distribution, ±{k_std_dev}σ)')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "\n",
    "# Plot 2: Empirical Area\n",
    "plt.figure(figsize=(9, 5.2), dpi=300)\n",
    "n, bins, patches = plt.hist(data, bins=1000, alpha=0.5, density=True, label='Data Distribution', color='yellow')\n",
    "\n",
    "# Color the histogram between ±2σ for empirical area\n",
    "for i in range(len(bins) - 1):\n",
    "    if bins[i] >= mean - k_std_dev * std_dev and bins[i+1] <= mean + k_std_dev * std_dev:\n",
    "        patches[i].set_facecolor('cyan')  # Coloring the bins within ±2σ\n",
    "\n",
    "# Add vertical lines for ±2σ\n",
    "plt.axvline(mean + k_std_dev * std_dev, color='red', linestyle='--', label=f'+{k_std_dev}σ')\n",
    "plt.axvline(mean - k_std_dev * std_dev, color='red', linestyle='--', label=f'-{k_std_dev}σ')\n",
    "\n",
    "# Annotation for empirical probability\n",
    "plt.text(mean + k_std_dev * std_dev, 0.1, f\"AUC (Empirically)={empirical_probability:.3f}\", color='cyan')\n",
    "plt.title(f'Empirical Area: Actual Probability (Normal Distribution, ±{k_std_dev}σ)')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n",
    "\n",
    "# Output results\n",
    "print(f\"Empirical Probability within ±{k_std_dev}σ: {empirical_probability:.4f}\")\n",
    "print(f\"Chebyshev's Bound within ±{k_std_dev}σ: {chebyshev_bound:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47fa78a3-e7c5-4449-bcd7-da92b08bec2c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c2b81b35-49d0-47b9-ace2-4428bfb5919a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "threads",
   "language": "python",
   "name": "threads"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}