Week_05/Generating_Confidence_Interval.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval: [-7.7, 7.5]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "sorted_items = {-9.8: 0.001, -9.5: 0.001, -9.1: 0.001, -9.0: 0.001, -8.8: 0.004, -8.6: 0.002, -8.5: 0.001, -8.4: 0.001, -8.3: 0.003, -8.2: 0.002, -7.9: 0.002, -7.8: 0.006, -7.7: 0.001, -7.6: 0.001, -7.5: 0.007, -7.4: 0.002, -7.3: 0.001, -7.0: 0.002, -6.9: 0.002, -6.8: 0.003, -6.7: 0.006, -6.6: 0.002, -6.5: 0.002, -6.4: 0.003, -6.3: 0.008, -6.2: 0.002, -6.1: 0.009, -6.0: 0.003, -5.8: 0.006, -5.7: 0.005, -5.6: 0.002, -5.5: 0.001, -5.4: 0.005, -5.3: 0.011, -5.2: 0.006, -5.1: 0.009, -5.0: 0.013, -4.9: 0.004, -4.8: 0.006, -4.7: 0.005, -4.6: 0.004, -4.5: 0.004, -4.4: 0.005, -4.3: 0.008, -4.2: 0.008, -4.1: 0.007, -4.0: 0.008, -3.9: 0.002, -3.8: 0.008, -3.7: 0.001, -3.6: 0.014, -3.5: 0.006, -3.4: 0.008, -3.3: 0.005, -3.2: 0.01, -3.1: 0.004, -3.0: 0.005, -2.9: 0.007, -2.8: 0.004, -2.7: 0.009, -2.6: 0.006, -2.5: 0.007, -2.4: 0.009, -2.3: 0.005, -2.2: 0.005, -2.1: 0.006, -2.0: 0.011, -1.9: 0.007, -1.8: 0.008, -1.7: 0.004, -1.6: 0.011, -1.5: 0.008, -1.4: 0.009, -1.3: 0.001, -1.2: 0.007, -1.1: 0.006, -1.0: 0.004, -0.9: 0.012, -0.8: 0.004, -0.7: 0.013, -0.6: 0.012, -0.5: 0.008, -0.4: 0.009, -0.3: 0.01, -0.2: 0.007, -0.1: 0.014, 0.0: 0.014, 0.1: 0.008, 0.2: 0.014, 0.3: 0.012, 0.4: 0.01, 0.5: 0.011, 0.6: 0.014, 0.7: 0.008, 0.8: 0.008, 0.9: 0.008, 1.0: 0.013, 1.1: 0.017, 1.2: 0.005, 1.3: 0.004, 1.4: 0.007, 1.5: 0.01, 1.6: 0.006, 1.7: 0.006, 1.8: 0.008, 1.9: 0.015, 2.0: 0.016, 2.1: 0.006, 2.2: 0.006, 2.3: 0.011, 2.4: 0.01, 2.5: 0.006, 2.6: 0.006, 2.7: 0.005, 2.8: 0.009, 2.9: 0.006, 3.0: 0.001, 3.1: 0.01, 3.2: 0.002, 3.3: 0.005, 3.4: 0.005, 3.5: 0.008, 3.6: 0.005, 3.7: 0.004, 3.8: 0.007, 3.9: 0.008, 4.0: 0.002, 4.1: 0.009, 4.2: 0.002, 4.3: 0.006, 4.4: 0.004, 4.5: 0.007, 4.6: 0.004, 4.7: 0.001, 4.8: 0.001, 4.9: 0.003, 5.0: 0.007, 5.1: 0.006, 5.2: 0.005, 5.3: 0.003, 5.4: 0.006, 5.5: 0.006, 5.6: 0.005, 5.7: 0.009, 5.8: 0.007, 5.9: 0.004, 6.0: 0.007, 6.1: 0.005, 6.2: 0.004, 6.3: 0.006, 6.4: 0.007, 6.5: 0.004, 6.6: 0.001, 6.7: 0.004, 6.8: 0.004, 6.9: 0.005, 7.0: 0.006, 7.1: 0.002, 7.3: 0.003, 7.4: 0.001, 7.5: 0.003, 7.6: 0.001, 7.7: 0.002, 7.8: 0.001, 7.9: 0.001, 8.0: 0.002, 8.2: 0.002, 8.3: 0.002, 8.4: 0.002, 8.5: 0.001, 8.8: 0.003, 8.9: 0.002, 9.0: 0.001, 9.2: 0.001, 9.3: 0.002, 9.7: 0.002}\n",
    "cdf = []\n",
    "cumulative_prob = 0.0\n",
    "\n",
    "for k, prob in sorted_items.items():\n",
    "    cumulative_prob += prob\n",
    "    cdf.append((k, cumulative_prob))\n",
    "\n",
    "confidence_level = 0.95\n",
    "lower_percentile = (1 - confidence_level) / 2\n",
    "upper_percentile = 1 - lower_percentile\n",
    "\n",
    "lower_bound = None\n",
    "upper_bound = None\n",
    "\n",
    "for k, cum_prob in cdf:\n",
    "    if cum_prob >= lower_percentile and lower_bound is None:\n",
    "        lower_bound = k\n",
    "    if cum_prob >= upper_percentile:\n",
    "        upper_bound = k\n",
    "        break\n",
    "\n",
    "print(f\"95% confidence interval: [{lower_bound}, {upper_bound}]\")\n",
    "\n",
    "# Plotting the histogram\n",
    "keys = list(sorted_items.keys())\n",
    "values = list(sorted_items.values())\n",
    "\n",
    "plt.bar(keys, values, width=0.1, align='center', color='lightblue', edgecolor='black')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Histogram with 95% Confidence Interval')\n",
    "\n",
    "# Marking the confidence interval\n",
    "plt.axvline(x=lower_bound, color='red', linestyle='--', label=f'Lower Bound ({lower_bound})')\n",
    "plt.axvline(x=upper_bound, color='green', linestyle='--', label=f'Upper Bound ({upper_bound})')\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval: [-7.5, 7.1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "sorted_items = {-9.0: 0.002, -8.8: 0.005, -8.3: 0.003, -7.9: 0.003, -7.6: 0.01, -7.5: 0.01, -7.0: 0.001, -6.6: 0.008, -6.5: 0.003, -6.3: 0.012, -6.1: 0.009, -5.8: 0.006, -5.7: 0.024, -5.6: 0.002, -5.4: 0.019, -5.3: 0.017, -5.2: 0.005, -5.0: 0.021, -4.9: 0.006, -4.8: 0.011, -4.7: 0.005, -4.6: 0.008, -4.5: 0.001, -4.3: 0.007, -4.2: 0.005, -4.1: 0.012, -4.0: 0.007, -3.9: 0.004, -3.8: 0.004, -3.6: 0.025, -3.4: 0.008, -3.3: 0.01, -3.0: 0.002, -2.9: 0.005, -2.8: 0.007, -2.7: 0.006, -2.6: 0.008, -2.5: 0.01, -2.4: 0.017, -2.3: 0.001, -2.2: 0.011, -2.1: 0.003, -2.0: 0.003, -1.9: 0.007, -1.8: 0.001, -1.7: 0.002, -1.6: 0.024, -1.5: 0.002, -1.4: 0.01, -1.2: 0.003, -1.1: 0.013, -1.0: 0.015, -0.9: 0.03, -0.7: 0.009, -0.6: 0.009, -0.5: 0.007, -0.4: 0.008, -0.3: 0.008, -0.2: 0.008, -0.1: 0.005, 0.0: 0.003, 0.1: 0.011, 0.2: 0.007, 0.3: 0.021, 0.4: 0.014, 0.5: 0.011, 0.6: 0.013, 0.7: 0.015, 0.8: 0.003, 0.9: 0.01, 1.0: 0.016, 1.1: 0.011, 1.2: 0.001, 1.3: 0.006, 1.4: 0.001, 1.5: 0.017, 1.6: 0.003, 1.7: 0.008, 1.8: 0.008, 1.9: 0.026, 2.0: 0.018, 2.1: 0.012, 2.3: 0.004, 2.4: 0.001, 2.5: 0.002, 2.6: 0.01, 2.7: 0.003, 2.8: 0.003, 2.9: 0.002, 3.2: 0.008, 3.3: 0.002, 3.4: 0.006, 3.5: 0.034, 3.6: 0.005, 3.8: 0.011, 3.9: 0.011, 4.1: 0.017, 4.2: 0.002, 4.3: 0.009, 4.5: 0.008, 4.7: 0.001, 5.0: 0.001, 5.1: 0.01, 5.4: 0.004, 5.5: 0.011, 5.6: 0.001, 5.7: 0.014, 5.8: 0.002, 5.9: 0.005, 6.0: 0.004, 6.2: 0.005, 6.3: 0.005, 6.4: 0.002, 6.5: 0.002, 6.6: 0.005, 6.7: 0.004, 6.8: 0.007, 6.9: 0.005, 7.0: 0.006, 7.1: 0.007, 7.8: 0.004, 8.0: 0.006, 8.3: 0.003, 8.4: 0.002, 8.5: 0.001, 8.8: 0.003}\n",
    "\n",
    "cdf = []\n",
    "cumulative_prob = 0.0\n",
    "\n",
    "for k, prob in sorted_items.items():\n",
    "    cumulative_prob += prob\n",
    "    cdf.append((k, cumulative_prob))\n",
    "\n",
    "confidence_level = 0.95\n",
    "lower_percentile = (1 - confidence_level) / 2\n",
    "upper_percentile = 1 - lower_percentile\n",
    "\n",
    "lower_bound = None\n",
    "upper_bound = None\n",
    "\n",
    "for k, cum_prob in cdf:\n",
    "    if cum_prob >= lower_percentile and lower_bound is None:\n",
    "        lower_bound = k\n",
    "    if cum_prob >= upper_percentile:\n",
    "        upper_bound = k\n",
    "        break\n",
    "\n",
    "print(f\"95% confidence interval: [{lower_bound}, {upper_bound}]\")\n",
    "\n",
    "# Plotting the histogram\n",
    "keys = list(sorted_items.keys())\n",
    "values = list(sorted_items.values())\n",
    "\n",
    "plt.bar(keys, values, width=0.1, align='center', color='lightblue', edgecolor='black')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Histogram with 95% Confidence Interval')\n",
    "\n",
    "# Marking the confidence interval\n",
    "plt.axvline(x=lower_bound, color='red', linestyle='--', label=f'Lower Bound ({lower_bound})')\n",
    "plt.axvline(x=upper_bound, color='green', linestyle='--', label=f'Upper Bound ({upper_bound})')\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval: [-7.5, 6.7]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "sorted_items = {-7.5: 0.039, -5.8: 0.002, -5.7: 0.03, -5.6: 0.01, -5.4: 0.002, -5.3: 0.016, -5.2: 0.005, -5.0: 0.017, -4.6: 0.024, -4.2: 0.013, -4.1: 0.014, -4.0: 0.001, -3.8: 0.004, -3.6: 0.031, -3.4: 0.016, -3.3: 0.028, -3.0: 0.04, -2.6: 0.002, -2.4: 0.021, -2.2: 0.002, -1.6: 0.009, -1.4: 0.008, -1.1: 0.005, -1.0: 0.008, -0.9: 0.048, -0.7: 0.006, -0.6: 0.002, -0.5: 0.011, -0.4: 0.005, -0.3: 0.002, -0.2: 0.029, -0.1: 0.001, 0.1: 0.002, 0.2: 0.039, 0.3: 0.002, 0.4: 0.002, 0.5: 0.004, 0.6: 0.029, 0.7: 0.004, 0.9: 0.008, 1.0: 0.002, 1.1: 0.01, 1.3: 0.018, 1.4: 0.019, 1.5: 0.04, 1.8: 0.013, 1.9: 0.101, 2.0: 0.005, 2.1: 0.007, 2.8: 0.007, 3.2: 0.001, 3.3: 0.011, 3.4: 0.004, 3.5: 0.005, 4.1: 0.044, 4.3: 0.044, 4.5: 0.01, 5.1: 0.018, 5.4: 0.018, 5.5: 0.01, 5.7: 0.025, 6.4: 0.001, 6.6: 0.014, 6.7: 0.024, 7.8: 0.004, 8.0: 0.003, 8.4: 0.001}\n",
    "cdf = []\n",
    "cumulative_prob = 0.0\n",
    "\n",
    "for k, prob in sorted_items.items():\n",
    "    cumulative_prob += prob\n",
    "    cdf.append((k, cumulative_prob))\n",
    "\n",
    "confidence_level = 0.95\n",
    "lower_percentile = (1 - confidence_level) / 2\n",
    "upper_percentile = 1 - lower_percentile\n",
    "\n",
    "lower_bound = None\n",
    "upper_bound = None\n",
    "\n",
    "for k, cum_prob in cdf:\n",
    "    if cum_prob >= lower_percentile and lower_bound is None:\n",
    "        lower_bound = k\n",
    "    if cum_prob >= upper_percentile:\n",
    "        upper_bound = k\n",
    "        break\n",
    "\n",
    "print(f\"95% confidence interval: [{lower_bound}, {upper_bound}]\")\n",
    "\n",
    "# Plotting the histogram\n",
    "keys = list(sorted_items.keys())\n",
    "values = list(sorted_items.values())\n",
    "\n",
    "plt.bar(keys, values, width=0.1, align='center', color='lightblue', edgecolor='black')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Histogram with 95% Confidence Interval')\n",
    "\n",
    "# Marking the confidence interval\n",
    "plt.axvline(x=lower_bound, color='red', linestyle='--', label=f'Lower Bound ({lower_bound})')\n",
    "plt.axvline(x=upper_bound, color='green', linestyle='--', label=f'Upper Bound ({upper_bound})')\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dcZv2YouLizOioqKsyytXrjQkGdOmTbPpd++99xomk8nYv3+/tU2S4ePjY9P2448/GpKM1157Ld++AJReeefSyx9ms9lYuHChTV9HzyO7du0yJBkPPfSQTb8xY8YYkoyvvvrK2tawYUOb81qepk2bGt26dbMb+9ChQ42C3orm5b7g4GDj1KlTNusuXbpkZGZm2rT99ddfRkREhDF48OB82/Dz8zP++OMPa/vWrVsNScbo0aOtbXFxcYYkY/jw4da23Nxco1u3boaPj481x3z99deGJOO9996z2f+aNWts2k+dOmX4+PgY3bp1M3Jzc639xo0bZ0gqMD/804ULF4y6desakoyoqChj0KBBxvz5842UlJQC+17u/fffz/deJC9/PvLII9a2S5cuGdWrVzdMJpPx/PPPW9v/+usvw8/PzybOouTAy/OXo8fto48+uuL7gsJ07NjRaNiwYaHr87ZtL1e76jVb0Hs5R19zecf98vdgBW2zsNgMw8j3HrZXr16Gj4+PceDAAWvb8ePHjaCgIOOWW26xtuWdX2JiYmxey6NHjza8vLyMs2fPFrg/AMVHXi97ed0w/j4PDx061Dhz5ozh4+Nj/Pe//zUMwzBWrVplmEwm4/Dhw9ZcnRdfbm6uUadOHSM2NtZmvxcuXDCio6ON22+/3abtcgV9tnf0vE5OJiejcEztglLj/PnzkqSgoCC7/fLWWywWm/bHHnvsivvIm/ri8ccft2kfPny4w3E2aNDA5or5sLAw1a1bVwcPHrS2mc1m6800cnJydPr0aeu0JDt37nR4X0URGBhoPYaSbK4cy87O1unTp3X99derQoUKDsfwz22cP39ef/75pzp06KALFy7o999/d3rMl6tQoYKkv6eYKe6NOc1ms+Lj4x3uP3DgQJvX4L333quqVavqs88+K9b+HfXZZ5/Jy8tLI0aMsGl/4oknZBiGVq9ebdMeExOj2rVrW5ebNGmi4OBgm9chgLJjzpw5Wrt2rdauXatFixapc+fOeuihh2yuHHL0PJJ3PktISMjXT1KBv/q6XIUKFfTLL79o3759xX5OvXv3zjeNm5eXl3U+1dzcXJ05c0aXLl1Sy5YtC8xdvXr1UrVq1azLrVq1UuvWrQs8Zw8bNsz6/3lTZGVlZenLL7+UJC1btkwhISG6/fbb9eeff1ofLVq0UGBgoPVn6F9++aWysrI0fPhwmyvCR40a5dDz9vPz09atW/Xkk09K+vvXX0OGDFHVqlU1fPhwm5/h/zMPZ2Rk6M8//1SbNm0kqcDj8dBDD1n/38vLSy1btpRhGBoyZIi1vUKFCvnet+QpTg509Ljl5fRPP/1U2dnZdo9RUQUGBkrSFd9TuOI1a8+VXnOukJOToy+++EK9evWyuZ9Q1apV9cADD+ibb77J9x76kUcesXktd+jQQTk5OUpOTnZZnMC1jrxedvL6P1WsWFFdunTR+++/L0lavHixbr75Zuuv0f5p165d2rdvnx544AGdPn3aGl96erpuu+02bdq0yfoZuKif7a90Xicnk5NROArpKDXyPrjZO+H+c/3lBffo6Ogr7iM5OVnlypXL1/f66693OM6aNWvma6tYsaLNPGu5ubl6+eWXVadOHZnNZlWuXFlhYWH66aefbOYKc6a0tDSbY3Lx4kVNmDDBOp9eXgxnz551OIZffvlFd999t0JCQhQcHKywsDDrzw2d8Twuj/lyffv2Vbt27fTQQw8pIiJC999/vz744IMiFdWrVatWpJvc1KlTx2bZZDLp+uuvzzf/nLMlJycrMjIy3/HIm2bn8sTpyOsQQNnRqlUrxcTEKCYmRv3799eqVavUoEED64cAyfHzSF4uvDz3ValSRRUqVHDojfqUKVN09uxZ3XDDDWrcuLGefPJJ/fTTT0V6ToXl7XfeeUdNmjSxzpkZFhamVatWFZh3Lj9nS9INN9yQ75xdrly5fDcpv+GGGyTJ2nffvn06d+6cwsPDFRYWZvNIS0vTqVOnJP3fcbx832FhYapYseKVn7j+vknXiy++qMOHD+vw4cOaP3++6tatq9mzZ2vq1KnWfmfOnNHIkSMVEREhPz8/hYWFWY9bQcfj8twQEhIiX19fVa5cOV97QfmiODnQ0ePWsWNH9e7dW5MnT1blypXVs2dPJSUl2XxxUFxpaWmS7F+M4crXbEEcec25Qmpqqi5cuKC6devmW1e/fn3l5ubmm/f+8tdN3uuY9xSA65DXy1Ze/6cHHnhAa9eu1ZEjR7Ry5cp8NxbPk1dEjouLyxff22+/rczMTOsxKupn+yud18nJ5GQUjjnSUWqEhISoatWqVzyB/vTTT6pWrZrNzbgkFWn+6qvh5eVVYLvxj3nZp0+frvHjx2vw4MGaOnWqQkNDVa5cOY0aNarYV1bbk52drb1799rcwGT48OFKSkrSqFGj1LZtW4WEhMhkMun+++93KIazZ8+qY8eOCg4O1pQpU1S7dm35+vpq586d+ve//33Vz+OPP/7QuXPn7H6J4efnp02bNmn9+vVatWqV1qxZo6VLl+rWW2/VF198Uejf4vJtOFth89nm5OQ4FJMzOPI6BFB2lStXTp07d9Yrr7yiffv2We/RURT25ua+kltuuUUHDhzQxx9/rC+++EJvv/22Xn75Zc2bN8/mqmh7Cjo/L1q0SIMGDVKvXr305JNPKjw8XF5eXkpMTLTepNNVcnNzFR4ervfee6/A9UW56qkooqKiNHjwYN1999267rrr9N5772natGmSpPvuu0+bN2/Wk08+qWbNmikwMFC5ubnq0qVLgXm4oNzg6nzh6HEzmUxavny5vvvuO/3vf//T559/rsGDB2vGjBn67rvvrFewFUfejejsvadw1Wv2ath7P1GSeE8BuB953fncldfvuusumc1mxcXFKTMzU/fdd1+h8UnSSy+9lG+u+Dx5ubGon+2vdF4nJ+dHTkYeCukoVbp376633npL33zzjdq3b59v/ddff63Dhw/r0UcfLdb2o6KilJubq0OHDtl847x///5ix1yQ5cuXq3Pnzpo/f75N+9mzZ/NdFeas/V28eFGxsbE2bXFxcZoxY4a1LSMjQ2fPnrUZW1jC2LBhg06fPq0VK1bY3Izs0KFDTok578Yc/4y5IOXKldNtt92m2267TTNnztT06dP1zDPPaP369YqJibmqN4wFufznZYZhaP/+/WrSpIm1rWLFivmOo/T31Qz//Ka7KLFFRUXpyy+/1Pnz522+vc+bQqegnwMCuLZdunRJ0v9d+ePoeSQvF+7bt896VZskpaSk6OzZszbnG3vnsdDQUMXHxys+Pl5paWm65ZZbNGnSJOsHoOKcn5cvX67rrrtOK1assBk/ceLEAvsX9JPgvXv3qlatWjZtubm5OnjwoPXqo7x+kqx9a9eurS+//FLt2rWz++Es7/js27fP5pyfmpp6VVcLVaxYUbVr17Z+AP3rr7+0bt06TZ48WRMmTLD2u5qfQV+JIznwco4etzxt2rRRmzZt9Nxzz2nx4sXq37+/lixZ4vAH58vl5ORo8eLF8vf3L/C94z+54jVbGEdec3lXmV3+nqKgq0cdjS0sLEz+/v7as2dPvnW///67ypUrpxo1aji0LQAli7xeNvK6n5+fevXqpUWLFqlr166Ffv7Pm6YzODhYMTExdrfp6Gf7oiInk5ORH1O7oFR58skn5efnp0cffVSnT5+2WXfmzBk99thj8vf3t84rWlR5RdvXX3/dpv21114rXsCF8PLyyveN4bJly3Ts2DGn7keSfvzxR40aNUoVK1bU0KFD7cbw2muv5ftGNSAgQFL+hJH3Teg/t5GVlZXv2BXHV199palTpyo6Olr9+/cvtN+ZM2fyteV9W5/3s7PC4i+uvDvF51m+fLlOnDihrl27Wttq166t7777zuYu7p9++mm+n2UVJbY777xTOTk5mj17tk37yy+/LJPJZLN/AMjOztYXX3whHx8f64dmR88jd955pyRp1qxZNv1mzpwpSerWrZu1LSAgoMBz2OU5OjAwUNdff73NT4KLc34uKPds3bpVW7ZsKbD/ypUrbXLr999/r61btxZ4zvzncTEMQ7Nnz1b58uV12223Sfr76u+cnBybqVXyXLp0yfo8YmJiVL58eb322ms2cV5+PAvz448/6s8//8zXnpycrF9//dX689+CjkVR9lMcjuTAyzl63P766698z+XynF5UOTk5GjFihH777TeNGDEi368V/8lVr1l7rvSai4qKkpeXlzZt2mQzrqD3Wo7G5uXlpTvuuEMff/yxzc/VU1JStHjxYrVv397ucQLgHuT1v5XGvF6QMWPGaOLEiRo/fnyhfVq0aKHatWvrP//5j/XLk39KTU21/r+jn+0dRU4mJ6NwXJGOUqVOnTp655131L9/fzVu3FhDhgxRdHS0df7QP//8U++//77NTRaLokWLFurdu7dmzZql06dPq02bNtq4caP120hnfevZvXt3TZkyRfHx8br55pv1888/67333ss3L1dRff3118rIyLDewPTbb7/VJ598opCQEH300UeqUqWKTQz//e9/FRISogYNGmjLli368ssvValSJZttNmvWTF5eXnrhhRd07tw5mc1m3Xrrrbr55ptVsWJFxcXFacSIETKZTPrvf/9b5J8UrV69Wr///rsuXbqklJQUffXVV1q7dq2ioqL0ySefyNfXt9CxU6ZM0aZNm9StWzdFRUXp1KlTev3111W9enXrN9y1a9dWhQoVNG/ePAUFBSkgIECtW7cu0pxp/xQaGqr27dsrPj5eKSkpmjVrlq6//no9/PDD1j4PPfSQli9fri5duui+++7TgQMHtGjRonyvy6LE1qNHD3Xu3FnPPPOMDh8+rKZNm+qLL77Qxx9/rFGjRhX7NQ+gbMg7l0rSqVOntHjxYu3bt09PP/209Q24o+eRpk2bKi4uTm+++aZ1Gq/vv/9e77zzjnr16qXOnTtb99uiRQvNnTtX06ZN0/XXX6/w8HD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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def bootstrap_samples(data, n_bootstrap_samples):\n",
    "    \"\"\"\n",
    "    Generate bootstrapped samples from the initial data.\n",
    "\n",
    "    Parameters:\n",
    "    data (list or np.array): Initial list of samples.\n",
    "    n_bootstrap_samples (int): Number of bootstrapped samples to generate.\n",
    "\n",
    "    Returns:\n",
    "    list of np.array: A list containing the bootstrapped samples.\n",
    "    \"\"\"\n",
    "    bootstrapped_samples = []\n",
    "    n = len(data)\n",
    "    \n",
    "    for _ in range(n_bootstrap_samples):\n",
    "        # Generate a bootstrapped sample by sampling with replacement\n",
    "        sample = np.random.choice(data, size=n, replace=True)\n",
    "        bootstrapped_samples.append(sample)\n",
    "    \n",
    "    return bootstrapped_samples\n",
    "\n",
    "# Example usage\n",
    "if __name__ == \"__main__\":\n",
    "    \n",
    "    # Initial list of samples\n",
    "    initial_samples = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
    "\n",
    "    # Number of bootstrapped samples to generate\n",
    "    n_bootstrap_samples = 1000\n",
    "    \n",
    "    # Generate bootstrapped samples\n",
    "    samples = bootstrap_samples(initial_samples, n_bootstrap_samples)\n",
    "    \n",
    "    # Calculate the means of the bootstrapped samples\n",
    "    bootstrapped_means = [np.mean(sample) for sample in samples]\n",
    "    \n",
    "    # Plot the distribution of the original data\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    \n",
    "    plt.subplot(1, 3, 1)\n",
    "    plt.hist(initial_samples, bins=10, edgecolor='k', alpha=0.7)\n",
    "    plt.title('Original Data Distribution')\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Frequency')\n",
    "    \n",
    "    # Plot the distributions of the bootstrapped samples\n",
    "    plt.subplot(1, 3, 2)\n",
    "    for sample in samples:\n",
    "        plt.hist(sample, bins=10, alpha=0.1, color='gray')\n",
    "    plt.title('Bootstrapped Samples Distribution')\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Frequency')\n",
    "    \n",
    "    # Plot the distribution of the bootstrapped means\n",
    "    plt.subplot(1, 3, 3)\n",
    "    plt.hist(bootstrapped_means, bins=30, edgecolor='k', alpha=0.7)\n",
    "    plt.title('Bootstrapped Means Distribution')\n",
    "    plt.xlabel('Mean Value')\n",
    "    plt.ylabel('Frequency')\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def bootstrap_samples(data, n_bootstrap_samples):\n",
    "    \"\"\"\n",
    "    Generate bootstrapped samples from the initial data.\n",
    "\n",
    "    Parameters:\n",
    "    data (list or np.array): Initial list of samples.\n",
    "    n_bootstrap_samples (int): Number of bootstrapped samples to generate.\n",
    "\n",
    "    Returns:\n",
    "    list of np.array: A list containing the bootstrapped samples.\n",
    "    \"\"\"\n",
    "    bootstrapped_samples = []\n",
    "    n = len(data)\n",
    "    \n",
    "    for _ in range(n_bootstrap_samples):\n",
    "        # Generate a bootstrapped sample by sampling with replacement\n",
    "        sample = np.random.choice(data, size=n, replace=True)\n",
    "        bootstrapped_samples.append(sample)\n",
    "    \n",
    "    return bootstrapped_samples\n",
    "\n",
    "# Example usage\n",
    "if __name__ == \"__main__\":\n",
    "    \n",
    "    # Initial list of samples\n",
    "    initial_samples = []\n",
    "\n",
    "    with open('delta_theta_uniform_initial.txt', 'r') as file:\n",
    "        for line in file:\n",
    "            num_strings = line.strip().split()\n",
    "            nums = [round(float(num), 25) for num in num_strings]\n",
    "            initial_samples.extend(nums)\n",
    "    \n",
    "    # Number of bootstrapped samples to generate\n",
    "    n_bootstrap_samples = 1000\n",
    "    \n",
    "    # Generate bootstrapped samples\n",
    "    samples = bootstrap_samples(initial_samples, n_bootstrap_samples)\n",
    "    \n",
    "    # Calculate the means of the bootstrapped samples\n",
    "    bootstrapped_means = [np.mean(sample) for sample in samples]\n",
    "    \n",
    "    # Plot the distribution of the original data\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    \n",
    "    plt.subplot(1, 3, 1)\n",
    "    plt.hist(initial_samples, bins=3, edgecolor='k', alpha=0.7)\n",
    "    plt.title('Original Data Distribution')\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Frequency')\n",
    "    \n",
    "    # Plot the distributions of the bootstrapped samples\n",
    "    plt.subplot(1, 3, 2)\n",
    "    for sample in samples:\n",
    "        plt.hist(sample, bins=3, alpha=0.1, color='gray')\n",
    "    plt.title('Bootstrapped Samples Distribution')\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Frequency')\n",
    "    \n",
    "    # Plot the distribution of the bootstrapped means\n",
    "    plt.subplot(1, 3, 3)\n",
    "    plt.hist(bootstrapped_means, bins=10, edgecolor='k', alpha=0.7)\n",
    "    plt.title('Bootstrapped Means Distribution')\n",
    "    plt.xlabel('Mean Value')\n",
    "    plt.ylabel('Frequency')\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.show()\n"
   ]
  }
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