{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1fed6682-9224-4b54-81cf-c798d2522a38",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Base.Threads\n",
    "using Distributions\n",
    "using Random\n",
    "using StatsPlots\n",
    "default(fmt=:png, titlefontsize=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "abf341ae-6a11-479c-bed1-e8cb23c2fdb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pvalue_bayesian (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "safediv(x, y) = x == 0 ? x : x/y\n",
    "\n",
    "function pvalue_clopper_pearson(n, k, p)\n",
    "    k == 0 && return min(1, 2ccdf(Beta(k+1, n-k), p))\n",
    "    k == n && return min(1, 2cdf(Beta(k, n-k+1), p))\n",
    "    min(1, 2cdf(Beta(k, n-k+1), p), 2ccdf(Beta(k+1, n-k), p))\n",
    "end\n",
    "\n",
    "function pvalue_wilson_score(n, k, p)\n",
    "    2ccdf(Normal(), safediv(abs(k - n*p), √(n*p*(1-p))))\n",
    "end\n",
    "\n",
    "function pvalue_adjusted_wald(n, k, p; z = 2)\n",
    "    p̂ = (k + z^2/2) / (n + z^2)\n",
    "    2ccdf(Normal(), safediv(abs(p̂ - p), √(p̂*(1-p̂)/n)))\n",
    "end\n",
    "\n",
    "function pvalue_bayesian(n, k, p; a = 1, b = 1)\n",
    "    min(1, 2cdf(Beta(k+a, n-k+b), p), 2ccdf(Beta(k+a, n-k+b), p))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "47d0a625-d280-4ac9-899d-04ed8a71938d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function plot_pvalue_functions(; n = 20, k = 6, z = 2, a = 1, b = 1,\n",
    "        f = trues(4), kwargs...)\n",
    "    plot()\n",
    "    f[1] && plot!(p -> pvalue_wilson_score(n, k, p), 0, 1;\n",
    "        label=\"Wilson score\", c=1)\n",
    "    f[2] && plot!(p -> pvalue_bayesian(n, k, p; a, b), 0, 1;\n",
    "        label=\"Bayesian\", ls=:dashdot, c=2)\n",
    "    f[3] && plot!(p -> pvalue_adjusted_wald(n, k, p; z), 0, 1;\n",
    "        label=(z == 0 ? \"\" : \"adjusted \") * \"Wald\", ls=:dash, c=3)\n",
    "    f[4] && plot!(p -> pvalue_clopper_pearson(n, k, p), 0, 1;\n",
    "        label=\"Clopper-Pearson\", c=4)\n",
    "    plot!(; xtick=0:0.1:1, ytick=0:0.1:1)\n",
    "    title!(\"data: (n,k)=($n,$k)\" * \n",
    "        (f[2] ? \", prior: Beta($a, $b)\" : \"\") *\n",
    "        (f[3] && z !== 0 ? \", adjustment for Wald: z=$z\" : \"\"))\n",
    "    plot!(; xguide=\"rate parameter θ\", yguide=\"P-value\")\n",
    "    plot!(; kwargs...)\n",
    "end\n",
    "\n",
    "plot_pvalue_functions(; n = 20, k = 6, z = 2, a = 1, b = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fedfcde3-17db-4cd7-8cb1-2099431242cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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z56XFrVu39u3bl4hGjRp19uxZIlqyZMmXX35pq1JrF3sLQp4jA66VAQB7FBgYuG/fPun1vn379Hr9gQMHpMU9e/ZIF+pv3769okfAQkXsLQiLdNmFJVdtXQUAgOX16NHD+KCe2NjYmJiY0os9e/YkokWLFt26dav0p/Ly8qZNm9a5c+cuXbrMmTNHWnnt2rXRo0d37tz55ZdfTk5OllbOmDFjz549w4YNi4yMXLBggVhmlq4LFy4MHz68ffv20dHRP/30k7Ty6NGjI0aM6NChw4gRI6SnI2RnZ7/++uuRkZHDhg07ffq01Oyrr7768ccfp0yZ0r59+1u3bmVnZ8+YMaNLly6DBg06ceKEpXdV9dhbEOYUJTzI22LrKgAALK9nz54nTpzQarWFhYW3bt166aWXTp06ZTAY0tPTr1y5EhUVRUT79+/PyMgo/amFCxfm5ORs2bLlp59+6tq1KxHl5uZ27969a9eumzZt8vf3j46O1ul0RLR79+5333137ty533zzzYoVK7Zu3WpSwPPPP9+/f/+9e/cuWbLE19eXiE6cODF48ODRo0f/+uuvr776qpSdQ4YMKSkp2bBhw4gRI5588sk7d+4Q0enTp994443evXv/8MMPnp6eTz75pIeHx6ZNm1599dUhQ4ZIbWzF3q4aVTBOwA31AGAdH54X5p0x1My2Ml9Uej78iIUWLVq4u7ufOHFCp9N16dLFycmpSZMmf/zxR0JCQtOmTf39/cvtJz8/XxRFxlhQUFBQUBARbdmypXHjxtOmTSOif/3rX+vXr4+Nje3Tpw8RzZkzR3oWwsiRI0+ePGkyC3R+fn5JSYlarW7RooW0ZvHixdOnTx8+fDgRSc9OuHr16tmzZ3ft2qVWq4ODg3/99de1a9e+8847Up/SLJv79+/X6XTvv/8+ETVo0GDYsGE///zzP/7xD0vuvuqwtyDkGCs7nAcAsIi32nBvtbHZgTTGWFRU1OHDh3U6nTT+69Gjx+HDhxMSEnr16lXRp+bNm/fGG280a9ascePGM2fOHDNmzN27dxs3biy9y3FcWFjY3bt3pcUGDRpIL1xcXMpOcr169eq33norJiame/fuH374YevWrW/fvj1s2LDSbe7duxcQEKBWq6XFJk2aGDuX5tokops3b967d69Dhw7GT4WFhT3SLrEMewtCBceLYg39vQYAUMN69OixefNmnU63ZMkSIurevfvSpUsTEhLefvvtij7i5+e3YcOGkpKSHTt2jBkzpmvXrr6+vsarT4koMTHRz8/PzK3//vvvGRkZn3/++QsvvHDx4kV/f3+To5o+Pj6pqal6vV6hUEidG8PV+IBcPz+/oKCgM2fOVPPbW4u9nSPkiWGuUQCwV9Jpwvj4+FatWhFR165df/vtt8uXL/fo0aOij+zZsyc1NVWlUrVr106pVHIcN2jQoFOnTu3cuVMQhBUrVuTl5VXycSNRFDdt2qTVauvVqxceHi498HbChAlffPGFdBfH3bt3ExMTW7RoERQU9PHHH+v1+hMnTvzyyy+jRo0y6ap3794FBQWfffZZSUmJXq8/efKkdJWNrdjdiJDncCMhANir8PDwyMjI8PBw6cm0Go2mf//++fn50qUrUgMXFxciCggIkM4TnTt3bvr06YWFhS4uLl988YV0l8XWrVtjYmImTpzYpEmTnTt3ajQaImrRooX0goj8/PzKPhRo3bp1b7zxBs/zwcHBq1evJqL+/ft//PHH48ePv3//vr+//6pVqxo0aLBly5Zp06Y1bNjQ29t79erV0rMWgoODfXx8pH7UavW+ffvefPPNxYsXi6LYvHnzRYsWWXvXVaIWnFGbO3euh4dHTEyMOY2/vfDnj5e/jx31sbWrqq68vDzpX6esyLOq4uJijuOUSqWtCzElz90lz6q0Wq1KpZLbE+oFQdBqtcbf9VXy9/ePi4sz87AhWFVaWlpERIR00FWn0zk5OVmwc3s7NOqsdGOKcFtXAQAAtYa9BaGPxl9QjbZ1FQAAUGvYWxAqOdLhWhkAgL8YDAbjBDSl3bx589q1azVfjwzZWxAqGOnlftITAOBRPPHEE4cPH5Ze79+/PzQ0VJpfm4i2bNnSv3//cj+Vn5/fo0cPQTAdIqxdu/abb76xXrW1iL0FoYqnEtxGCAD2yGTSbSIqO+k2PAJ7C0KtLkeh327rKgAALE+aR0Z6HRsbO3fu3NKLvXr1unfv3pgxYyIiIjp27LhgwQK9Xm/SQ1ZW1tixY8PDw1966aUHDx7UaPUyZsX7CA8ePHjw4EFfX9/x48c7OzuXbXDmzJk9e/bwPP/CCy8EBgZaZKM6Q76DYT/RsKqbAgBUU4mhpNhQUna9ilc58CrjYpG+SCeYhhAROSocldzfv3ULdIWCWM5FDRqlhmOs7PqePXvOnDmzsLBQEIR79+6NHTv23XfflSbdvn79elRUlFarHTduXNu2bXNyciZMmODl5TV16tTSPYwZM6Zhw4ZHjhw5fvz4Cy+88NJLL5n/3e2YtYJw1apV8+bNmzlz5r59+1avXn3y5EmTO4o2bNgwc+bMf/zjHxkZGZ06dTp58qQ0G+xjUvEcYWYZALCO/8bvWnvhp7LrRzYbPC7i7/lTPj+97FjiqbLN3uo6s2tAJ+Pi9H3/TC0wnc+TiFb0X+yj8S67vnnz5vXq1Tt+/LhOp+vatauDg0Pz5s3PnTuXkJAQHh4u3a7u4eFx9uzZjIyMVq1aHThwoHQQpqamHjhwIDMz09nZecCAAf369avOV7dnVglCQRAWLly4bNmyQYMGGQyGZs2a7dy5c+DAgaXbzJ8//9NPPx0zZgwR5eXlLV68+LPPPnv8TTtwnFjeX1gAAI/v2WaDn202uMpmb3WZaU5vK/ovrm4B3bt3lybdliZFi4qKio2NvXnzpvQwwqNHj44ePbpv375eXl6JiYk5OTmlP5ucnFyvXj3j8bmQkBCtVlvdAuySVc4R3r179+bNm0899RQR8Tzfp0+fQ4cOmbRJTEw0Tn/epEkT4ynfx4QRIQDYsZ49e8bGxsbGxhqD8PDhw8an8i5dujQmJmb58uUfffRR9+7dTT7r6+ubmZlpDD/jQyHAKiPClJQUNzc34zx1Pj4+V65cMWnTokWLI0eOdO7cmYh+++034yOSyxIE4eeff46Pj5cWIyIiJk+eXFFjzqAjEoqKih73O1haUVGRDOcMk2dV0hRrBoPsLv+V5+6SbVWCIMhwirWioiK5VVUt0mlCd3d3aQLPyMjI33//PTc3V8pFV1fXs2fP6vX6y5cvL1261OR8k5+fX9euXd99990FCxacOHFi+/btte4cYVFRkTTFGivvHGq5VCqV8akXFbFKECoUitL3rBgMhrL/o3766afDhg07fvx4RkaGKIoODg5UsYCAgPbt20uvg4KCKvl3rFbwoijK8B86z/Ooykw8z3McJ8/CUJWZ+L/YupCHMMZkWFW1NGvWrF+/fk2bNpV+uavV6ueee66goMDb25uI3n333VdeeSU4OLh58+bvvvvuhQsXiEihUHTr1k1Kju+///7VV18NCwvr2LHj/PnzVSpV5ZuTG57nRVGs1t9Y5kSmVYLQz88vLy/POBdwcnJy2Vlru3Xrdv369bNnz/r5+R0+fPinn8o5/yzhOC4yMtLk2qeKODs6EAkKpdLcvxZqilKplOGf7fKsShAEeU66Lc/dJc+q9Hq9UqmUW+QIgiAVZutCHsuWLVtKL3799dfG1wEBATt37jRpr9FojE8f9PPzM/l47aJUKqVgs+wP0SrnCBs0aNCqVStpdxcWFu7evfuZZ54hory8vJMnTxqbubu7R0dHBwYGfv31188995xFNq1RqpMMwzDLGgAAmMlat08sWLBg/Pjxx44di4uLa9u2bVRUFBGdO3eud+/eOp2OiL799tsdO3Z4eXkdPnw4MjJy4sSJFtmuo8Ihh/oXG0hlb1MFAACAVVgrCAcMGHDy5Mnffvtt6NChTz75pDSYbd269cGDB6UGo0eP9vf3T01NnTx5cmRkpAU37cCJRQZyqd0HPwAAoIZYcWaZ0NDQ0NDQ0mvc3NyMV/S6urqa3FloKQ48KzaIRHI7SwgAAHJkhwcQHXkqkt2F9wAAIFP2FoQ6Qe8tfIggBAAAM1nx0KitqIQ/EIQAYBG5ubnGuUHAhnJzc63Xub0FIc84IkFbzrTvAADVM3z48K5du9bAhkRRNH+qlDorPDzcSj3bWxAyxohELUaEAPDYlixZsmTJkhrYkHH6EVkpKChQq9V1IaHt7RwhI0ZEWj3uqAcAALPYWxASERFXaEAQAgCAWewwCBlxhSUIQgAAMIs9BiFjBXrR1lUAAEDtYIdBGOb7VpFgbxcBAQCAldhhEPo4t9Dq7fB7AQCANdhhYDjxrBCHRgEAwDx2GIRqhViAG+oBAMA8dhiEGgUhCAEAwEx2GIQ7rr2RV5Rt6yoAAKB2sMOrK/UGrc6AISEAAJjFDkeEHOMKMcUaAACYxw6DUMFxuKEeAADMZIdByDGmRRACAIB57DAIlYwrwKFRAAAwjxUvljl16tRvv/3m5+c3cuRIlUpVtsGVK1f2799PRL1797bgExd5jtPq8EBCAAAwi7VGhOvWrRs4cGBOTs7y5cv79esniqbHKrds2dK1a9ekpKSkpKQnnnhiy5Ytltq0gnGFegHHRgEAwBxWGREKgjB//vxvv/12yJAhRUVFYWFhhw4dio6OLt1m1apV//jHP9555x0icnFxWbly5dChQy2y9c97/mvzzxqtntR2eG8IAABYmFVGhDdv3rxz506/fv2IyNHRsU+fPnv37jVpExQUlJSUJL1OTEwMCgqy1NY1SrWzksvTWao/AACwZ1YZNCUnJ3t6ejo4OEiLfn5+xswz+ve//z1y5Mh27doRkbe39+bNmyvqTRCEnTt3ZmRkSIvNmzd/4YUXKmqs0+kMBoOzQp1ZUOwupyuBiouLyz1RaluyrYrjOEGQ3RVPst1d8qxKFEWe521dyEMEQSguLlYoZHewSLY/RJ7nGWO2LuQher1ep9NxnLm/31UqVZVfwSpZwRgrfVJQFMWydaxatSolJeWDDz744IMP7t+/v3Llyko6dHR0dP+LRqOpsgBXJT0oebTaAQCgbrHKX0Z+fn7Z2dnFxcXSoPD+/ft+fn4mbT7++OPly5f379+fiHief/nll2fMmFFubxzHRUdHx8TEmLNpjuPSCjLcVMoi5uTgIKM/ZEpKSoxDZPmQZ1VExHGcUqm0dRWm5Lm75FmVIAgqlUqGI0JBEGS4u+T5Q9Tr9Q4ODnIbEfI8z3GcZXeXVUaEoaGhwcHBO3fuJKKioqJ9+/Y9/fTTRFRYWHjt2jWpjUajyczMlF5nZGQ4Oztbausfnlyk4RIelOC6UQAAqJpVRoSMsffff3/KlCmnTp36/fffw8PDe/ToQUTHjh0bPHhwQUEBEb355pszZ868ePEiEa1YseKjjz6y1NY5YmqFmIuLZQAAwAzWOmn8wgsvNG/ePDY29vXXXx86dKg0uG7Tps3GjRulBhMnToyMjDx69CgRxcbGtmzZ0lKb5jhOwwk4RwgAAOaw4tVT7dq1ky4KNapXr94zzzxjXGzZsqUF88+IY5yaF3IRhAAAYAY53WFgIRxxTkrxgQ7nCAEAoGr2GISMUyswIgQAALPYZxBqFEIOghAAAMwguxkWHp+Xk4eLUpVTjEOjAABQNTscEU5v+0ob3zYYEQIAgDnsMAiJyF1FCEIAADCHvQYhw6FRAAAwh70GIWVjRAgAAGawwyC8ln3jQXEaI9LqbV0KAADInh0G4baEPedSL7qrKBvzbgMAQFXsMAg5xgmi4OnAsottXQoAAMievQahwcOBEIQAAFAlOwxCnvEGUfB0YFm4cBQAAKpih0HIGBNF0dOBsjAiBACAqthhEHKMM4gCghAAAMxhj0FITBAFL0eWiUOjAABQFTucdDvMPcTT2TNTpHv5ti4FAABkzw6D8MmGPRwdHZNKhEwcGriFXbcAACAASURBVAUAgKrY4aFRiZcDyyjCoVEAAKiC/QahI2FECAAAVbLiodH79+/v3r3byclpwIABGo3G5N2rV68mJiYaFzmOi46OtuDWvR0JI0IAAKiStYLw0qVLUVFRgwYNSktLmz9//okTJ1xdXUs32Lt377Zt26TXN2/eVCgU165ds8imz6VdUCqVrXzaZBaRSMQs0ikAANgpax0a/eijj15++eVVq1Zt377dx8dn9erVJg2mT5++7y8NGzYcP368pTZ9Jev6H2mXVBw58pSLhzEBAEClrBWEO3bsGDZsGBExxoYOHbpz586KWt66devo0aPjxo2z1KY54gQSiMjbCdfLAABAFaxyaFSr1WZnZ/v7+0uLAQEBSUlJFTVeuXLl008/bWxcliAIhw4dMhgM0mLjxo2HDBlSUWOdTieKot6g1+l0Xg6Ukq9v6PSoX8OidDqdTqezdRWmZFsVx8nxMi7Z7i55VsUYEwTB1oU8RBAE2e4u2VbFmLzOL+n1ep1Op1CYG14KhaLKr2CVIJT+9Ru3zXGcMcbKtly7du2iRYsq71Cr1WZlZUmvHzx4UFFvRGQwGERBNAgGg8FQz4FLLRAMno/yFSzOYDBUUratyLYqURRlmIWy3V2oykyCIMizMDlXJbcgNPzFzPY8z9smCDUajaura1paWlBQEBHdv3+/ogHfnj17ioqKBgwYUElvHMf1798/JibGnE3zPO+octDqih0dHX3VhhxB4egoi9+nOp3O0dHR1lWYkmdVjDGO45RKpa0LMSXP3SXPqkRRVKlUPM/bupCHCIIgiqIMd5c8f4gGg8HR0VFuQajX63met+zuslZIREdH79q1S3q9e/fu3r17E5EoisnJyXq93ths5cqVY8eOteyvPEacIBqIqL4TpWkt2DEAANgha90+ERMT8/TTT+v1+vv37585c+a7774jotzc3ICAgMuXLzdv3pyIMjMzt23bdvbsWctumjEmiCIReTuyewW4WAYAACpjrRFhZGTksWPHlEplkyZN4uLivL29iUij0axevdp4mPTBgwcrVqwIDw+37KZb1mv2REAnIvLBiBAAAKpixZllWrRo0aJFi9JrlEpl6dskQkJCQkJCLL7dMPcQ6fBxfSeWqpXXRWsAACA3sriQxEp8nCityNZFAACAvNlzEPo6sVQtzhECAEBl7DkI6zlSTjHpcHAUAAAqZodBeC7twveXNhMRx8jLkdIxyxoAAFTMDoMwpzj3Zs4d6bWvE0vFhaMAAFAxOwxCjnGC+L/job5qul9o23IAAEDW7DwI/ZxYCq6XAQCAitlhEPKMMxiDUE0pGBECAEDF7DAIiZj4dxCylEKMCAEAoEJ2GIQPHRrFiBAAACplh0H48KFRlowRIQAAVMyKc43aSjPPxr5uPtLrADUlY0QIAAAVs8MgdFE5ezvWk177qVmqVhRE4uT1aEkAAJALOzw0WpqSIzcVpWPqbQAAqICdByER+eM0IQAAVMz+g7CBhhLxnHoAAKiAHQbh9eyE2QffMy420LDEAhuWAwAAsmaHQSiSmF/yd/QFqFkSRoQAAFABOwxCjjiB/n4IYQMNYUQIAAAVsccg5DhBKB2EDOcIAQCgIla8j/DmzZtxcXGBgYGRkZEVtTl//nx8fLy3t3dkZKSjo6NlNiySSH8nX6Az3cOIEAAAKmCtEeHGjRs7d+68bdu2F198cdq0aWUbGAyGsWPHDho0aPPmzfPnz1+/fr2lNl16ijUiCtSwewUihoQAAFAuq4wIBUGIiYlZvnz5kCFDUlNTw8LCpk+f3rhx49Jtli1b9scff1y6dMnFxYWIRMtFVelJt4lIrSAnnjKLqJ6FBpwAAGBPrDIi/PPPPzMyMgYMGEBEPj4+UVFR27ZtM2mzfv36GTNmZGVlnThxoqCggDGLzYHGGCeWCkIiCnJmd/MxJgQAgHJYZUSYmJjo6+urUPyv88DAwKSkJJM2CQkJGzduXLZsmaur69WrV7dv396mTZtyexME4cSJE8uWLZMWGzZs+NRTT1W0aYPB4OtUf2mfTwwGg3FloIbu5Blae9hyvlGDwVC6JJmQbVWiKHKc7K7kku3uQlVmEgRBnoXJuSoLjlIswvAXM9tzHFflV7BKEOp0Op7n/96GQlFSUmLSpqCgQKPR7Nq1izH29ttvz5o168CBAxV1mJSUdObMGel1cXFxr169Ktm0wWBwVDjqdDrjygZO3M1cUaez5aBQp9OVLkkmZFuVDFOQZLy75FkVY6z09dtyIAiCbHeXbKuSWxDq9XqdTmccaFVJpVLZJgj9/PzS09ONi2lpaWVHe/7+/r1795bq69Onz7fffltRbxzHDR8+PCYmxpxN8zxvMBhMLkANcRNStKKjI1/Rp2qATqez2GWxliPPqhhjHMcplUpbF2JKnrtLnlWJoqhSqUr/QSwHgiCIoijD3SXPH6L0u1SGQcjzvGV3V2V/d+fm5p4+fXrnzp3V7bRVq1aCIMTFxRFRSUnJ4cOHo6KiiMhgMBQV/e9JED169Lh9+7b0+tatW/7+/tXdivmCXeh2vvW6BwCAWqz8EWFJScnMmTO/++47nU4XEBCQmJhIRFOmTMnJydmwYUOVnarV6hkzZrz44oszZ87cvn17s2bNunXrRkRbtmyZMWOGdL5w1qxZPXr0cHd3d3V1Xbhw4eeff26prySIQmpBmo+mvnFNQ2d2O09eh2gAAEAmyh8Rvvnmm+vWrVu4cOHSpUuNK4cOHbp161bjkK5y77333nvvvXfp0qXo6GjjmLJNmzYffPCB9Lp58+ZHjhwpLCxMSkr65ZdfRo8e/Xhf5G8PSvIn755Vek2IC7udh6tGAQCgHOWMCEtKSpYvX/75559Pnjz58OHDxvURERFarfbevXsmdwSWizE2atSoUaNGlV4ZFhYWFhZmXGzatOmCBQseo/jycYwJD9+V6O1IxQLl6chFdmedAADAxsoZEaanpxcWFkpn9UpzdnYmopycnJqo6zGY3FAvaeiMQSEAAJSjnCB0d3fned54JYvR2bNniahBgwY1UNbjYMTKBmGIC91CEAIAQBnlBKFGo+ndu/c777yTnp5uvHA2JSVl1qxZkZGRfn5+NVthtZnMNSoJdma4cBQAAMoq/6rRJUuWdO/evUmTJk2bNs3JyRk4cOBvv/1GRLGxsTVa3SMpO8UaEYW4MIwIAQCgrPKvGm3SpMn58+fHjRuXl5enUqkuXbo0fPjwuLi4tm3b1nB9j6Dcc4SNXOlmnk3KAQAAWatwZhk/P79FixbVZCmWwjOu9E2EklAXlvAAtxICAIApOc7o+Jg4xn0/aJnJylBXdjMPTyUEAABT5Y8IX3nlldzc3HLf2rhxozXrsRa1glyVlFIo+qvlNW8eAADYVvlBeOfOnaysLONiXl7erVu3HBwcmjZtWlOFWV6oK0t4QP5qW9cBAAByUn4Q7t2712TN3bt3R44cOX78eKtXZDWhLizhgdjdFyNCAAD4m7nnCIOCghYvXjx79uy8vFpw8eWRe8cNouljG8PcWALuoAAAgIdV42KZ4ODgwsLC+Ph461VjKQuPfVFiMH3KZZgrxZd/3hMAAOquagThDz/8QESBgYFWK8Ziyr2VsLEri3+AESEAADzErKtGdTrdjRs3Ll68OHToUG9v75qq7dHxjC97aLSJG4vPFUUinCQEAAAjs64aVSqVzZo1mzFjxrhx42qqsMfCGBPL3DTopiJHnu4Xkh8uHAUAgL+Ye9Vo7VLuoVGSBoUPRD/cSggAAH+xw5llqIIHUBBRYzd2PRenCQEA4G9/jwgTExP/+OOPKj/wzDPPWLMeyyj3ARRE1BRBCAAAD/s7CPft2/fyyy9X+YGy595k6IkGnZS8suz6pm60uhbc/QEAADXn7yAcOnRox44dbViKBb3RcUq565u5s6s5eAYFAAD87e8gdHd3d3d3t2DXRUVFx48fd3R07NSpE8/zJu9qtdqUlBTjoo+Pj0ajseDWyxXmyu4ViCUCqezz3CgAAFRbhc8jfExJSUlRUVFBQUG5ublqtXrfvn1OTk6lGxw/frxfv34NGjSQFr/66qt+/fpZqRgjJUdBGpbwQGzujgtHAQCAqJIg3LNnz4YNG27evFlQUFB6/ZkzZ8zp9z//+c8TTzyxdu1ag8HQrVu3tWvXTp482aRNeHj4uXPnHqHox9HMnV3NQRACAMD/lH+I8P/+7//69u177ty5u3fvFhYWurm5Xb9+/erVqyEhIWb2+/PPP48ZM4aIeJ4fPXr0L7/8UraNwWD4888/7969a/ELcDZd3ZqlzS73rebudCXHslsDAIBarPwR4cKFCydMmLB8+fKXX345ICBgwYIFaWlpw4cPb9iwoTmdGgyGlJQUY+OgoKDExMSyzRITEydMmHD37t2GDRtu3rw5KCio3N5EUfzzzz+NDwT28/N74oknKtq0IAiCIOy+eaC1dwt3B7eyDZq50d4kQajxK2akwmp6q1WRbVXG/8qKbHeXbKtiTF6HXoS/2LoQU3Kuqrb/EDmu6ktCygnCvLy8e/fuTZkyhTHGGCsuLiai+vXrf/311+3bt583b56Hh0flnep0OoPBoFT+7wYGlUql1WpN2kRGRqalpSkUipKSkrFjx06fPv2///1vub0JgvDnn38WFRVJi+3atWvfvn3lmyaRioqLjB8pLUzNPs/ii4pKKv8KFldcXGzcIfIh26o4jjMYTGeLtTnZ7i4ZVlVUVCQIQtmr5GxLEISioiK5VUUy/iFyHCe3INTr9TqdzvyqHB0dq8zCcoKwpKREFEXpGs569eqlpqZK68PCwnQ63c2bNyvJIeOGPTw8MjIyGjVqREQZGRl+fn4mbdTq/834qVKpJk2aNHr06Ip643l+zJgxMTExlW9UIgUhz/MqB5VxE6W1VdGNPJ2Dk5qv2R+uwWAotx7bkmdVPM9zHCfD3wvy3F3yrIoxplKp5BY50vhGhrtLnj9EURTVarU8g9Dk6svHVE5Oenl5ubm53bp1i4iaN2++d+9eaQLuX3/9lYh8fHzM6bdLly6xsbHS69jY2C5dulTSOD4+vn79+tWsvDI844QKzjuqFeTjxG7hCb0AAEBEFZ0j7NOnz6ZNm/r37//cc8+9/fbbjRs3Dg4O/uOPP/r372+84aFys2bNGj58uKenZ1ZW1i+//HL27Fki0mq1bm5ucXFxERERH374oSAIISEh169fX7Ro0VdffWXBb1XRpNuSFh50KVsMc5XXnzkAAGAT5Qfh2rVrdTodETk5OR09enTZsmW3bt0aMWLEzJkzzew3Ojr6l19++eGHHxwdHY8cOSIdI1UqlW+//bY0+OvZs+eWLVv27Nnj6+u7Z8+eyMhIC30jIiKO8UKZ5xEatfBgF7NpsFnX/QAAgJ0rPwidnJyMR2BDQkI+/vjjR+i6V69evXr1emhjCsW7774rve7atWvXrl0foVtzcMQqGRFGeLBtd3FoFAAAiCq6j3Dq1Kk7duyQ4WV7ZhrUpJ+fc4XnMiM82YUsBCEAABBVFIQnTpwYMGBAYGDgm2++eenSpRqu6fH1btjdR1Ph1TfN3NntfLG4tqY8AABYUvlBGBcXd+TIkYEDBy5btqxly5YtWrT4+OOP09PTa7g4K1FxFOLCruLBhAAAUFEQchzXrVu3b7/9Njk5efXq1T4+Pm+99VZgYOCzzz5bw/VZSStP9ieOjgIAQEVBaOTs7Dxu3LiDBw8ePXrU19d306ZNNVOWtbX2ZH9kIggBAKCqICwqKvrpp5/69+/fvXv3pKSkgQMH1kxZj2nVnz9eSL9SSYPWXuw8ghAAACoJwri4uBkzZgQGBj733HO3b99euHDhvXv3tm7dWpPFPbKbObeziyp7xkRrTwQhAAAQVXQfYefOnU+dOuXl5fX888+PGzeuyslF5abymWWIyE9NCo6SCsQADeaXAQCo08oPwhYtWsTExAwYMEClUtVwQRbBM85QaRCSNCjMogBNzVQEAAAyVf6h0ZUrVw4bNkx6fNLWrVsfPHhQw2U9JsY4saogbFePnc3A0VEAgLquiotl0tPTBw8enJCQUDPVWEqVh0aJqK0XO4fThAAAdV7Vj+6tjcw5NNrWCyNCAACw0yBkjIkVPI/QKMyN5ZSIGeU8xB4AAOqQ8i+WMWKM8TwvtycUV+m55kM1yioe98z+OjraJ6CWfTsAALCgKoIwMDBQr9fXTCkW1NAt0JxmHeqxMxkIQgCAOs300Ojq1atbtWrl4OAQHBw8adKk/Px8m5RVMzp6szPpOE0IAFCnPRSEO3bseOmll1JSUnr16qVWq5cvXz516lRbVVYDOniz0whCAIC67aEgXLVqVaNGja5du7Z79+5Lly69+uqrGzZsKCqy2+tJQlxYoV5M1dq6DgAAsJ2HgvDGjRvPP/+8p6cnETHGpk6dqtfrb9++bZvSHsOKP77fcn1Hlc0YUUdvdiq9ihstAADAjj0UhDk5OVIKSurVq0dEWVlZNV3UY9MJuiJ9sTktO9dnJ9NwdBQAoO6y4n2E2dnZp06dSktLq7xZXl6exS/JMWdmGUlnb+4kThMCANRhpkE4b948z780a9aMiPr27etZipn9btmyJSws7M033wwPD//uu+8qanbt2jUfH5+hQ4c+8hcoVzWCsD47ky4KiEIAgLrqofsIn3nmmfT09MfvVK/Xv/7666tXrx44cOCZM2eio6NHjhzp5uZm0kwQhEmTJg0ePDgjI+PxN1oax5hQ1cwyEk8HqufIruSILTxwNyEAQF30UBAuXbrUIp0ePXrUYDAMGDCAiDp06BASErJz587Ro0ebNPvyyy/btm3bqFGjbdu2WWS7RuaPCImoqw87noYgBACoo6qYWebR3Lt3Lzg42DgxW0hIyN27d03a3L59e/ny5SdOnFi1alXlvYmieOPGjf3790uL3t7erVu3rvwjHON0grkT4nSpz46nihObmtkcAADsilWCsLCwsPQTfZ2cnAoLC0s3EEVx0qRJH330kYuLS5W9CYJw6NAh46OgOnfuHBoaWlFjnU5nMBj0JfoiQ5GZ1+C0dmFfXFDm51v3dsKCggIZTtkqz6qKi4s5jlMqlbYuxJQ8d5c8q9JqtSqViud5WxfyEEEQioqKqpyRv+bJ84dYWFgoCILcCtPr9dLveTPbq9VqjqvislCrBKGvr2/pmy4yMjKioqJKN9i7d+/lvxw7duz27dufffbZrFmzyu2N5/lXXnklJibGnE1LO2hM65EikQOvqvoDRJ00lFqkK1Y6ezmY0/wRiaLo7OxsxQ08EnlWpVQq5RmE8txd8qyK53l5BiHP8xqNxtaFmJLnD5Explar5RmETk5OFuzTKrdPtG3bNj4+XroEpqSk5PTp0x07dizdwN/ff8yYMdnZ2dnZ2YWFhXq9Picnx4IFqHiVmSlIRDyjzt7sWCpuqwcAqIusEoRBQUFDhgwZO3bsnj17XnrppdatW3fo0IGIVq9eHR0dTUQREREf/WXgwIFhYWEffPCBNSox0xO+3O+psjtaAgAANcBaN9SvWrWqU6dO33zzTYMGDf773/9KK5s2bSpdSlpahw4dRo0aZaUyzNTNhx29jyAEAKiLrHKOkIjUavX7779vsrJLly5dunQxWdm1a9euXbtadusFukK9oHdzcDWzfef67I8sUasnJ2vtDwAAkCkrTrFmQ/tvH17xx/fmt9coqJUnO45JRwEA6h77DEJGTKTqpVpPP3Y4BdfLAADUOfYZhNWaWUbS04+LTcGIEACgzrHPIOQZZ6hmED7hw85mioXmTkcDAAB2wj6D8BFGhGoFtcZpQgCAusc+g5AxTqxmEBJOEwIA1En2GYSPcGiUiHr6cYdwmhAAoI6xzyDUqNRuDlVP522iqw/7I1PM01mjIgAAkCn7vIE80r9DpH+H6n5KraCO3iw2RRgYZJ9/HwAAQFn4jf+QPgHcviQcHQUAqEMQhA95KoAhCAEA6hQE4UPaeLGsYvFuPrIQAKCusM8gzNJm/5l26RE+yDGK9sfRUQCAOsQ+gzAh5/baixsf7bM4OgoAUKfYZxA+wswyRk83YPuTBD1urAcAqBsQhKb81ayhC+ZaAwCoKxCE5XgmkO24hyEhAECdgCAsxzOB3I67GBECANQJ9hqETBAfPck6erP0IvF2HrIQAMD+2WsQPtaIkGPUtwG38x6CEADA/lkxCEVRvH79elpaWkUNCgsLr127lpycLD7G6K1cbg6ubX0iHqeHZ4LYtrs4TQgAYP+sFYTJycmtW7cePHhwRETEq6++Wjbqli9f7u/vP3z48Hbt2rVt2/b27dsW3Lq/s+/ktuMep4d+DbhjqWJOiaUqAgAAmbJWEL7//vvt27e/cuXKlStXtm/ffuDAAZMGQ4cOTU9Pv3jxYnJycvPmzd955x0rVfJonJUU5cd24dpRAAB7Z5UgFEXxxx9/nDJlChF5enqOGjXqxx9/NGlTr149pVJJRBzHhYeHFxYWWqOSxzE0mNtyG6cJAQDsnFWeR5iZmZmfnx8WFiYthoaGnjt3rmyzpKSkdevW3blz59y5cytWrKioN1EUk5KS4uLipEV3d/fQ0FBrlG1icENu1gldkYF35GtgawAAYBtWCcL8/HwicnR0lBbVavWDBw8qaiyKYnp6enJycosWLcptIAjCzz//fPToUWmxW7duH374YUW96XQ6g8GQVZi97+7h4WEDHv07EDkQtXRXbk/Q9vU3PE4/koKCAsbY4/djWfKsqri4mOM46YCBrMhzd8mzKq1Wq1KpeF5ef0UKglBUVGTxq/Menzx/iIWFhYIgyK0wvV4v/Z43s71area4Ko59WiUIfXx8iCg7O1uj0RBRVlaWr69v2WYBAQFz584lorVr106bNu3q1avl9sbz/PTp02NiYszZ9P+CUJ+z+87BcW2ee/TvQEREz4YKO++LI5pY4H9mURSdnZ0fvx/LkmdVSqVSnkEoz90lz6p4npdnEPI8L/1ekhV5/hAZY2q1Wp5B6OTkZME+rXKO0MnJqVmzZsePH5cWjx8/3rZt20rae3t7W/YcISP2OPcRGo0I4bbeEYotMCAEAACZssqIkIimT58+b968+vXrx8fH7969+z//+Q8RJSUl9ezZ89ixY97e3p9++mmDBg0CAwPv3Lkzf/78sWPHWnDrHONEssDRDz81tfRke5OEgUH2OfMAAABYKwinTJkiCMK//vUvDw+P3bt3BwUFEZGjo2NUVJRKpSKikJCQzZs3p6SkeHt7z5s374UXXrDg1nnGGSwxIiSiUY24n26KA4Ms0hkAAMiOtYKQMfbaa6+99tprpVd6eXkZrw4dPnz48OHDrbT1x5xirbQRIdy8Mzqtnney1q4CAABbss8jfoxxgmCZIPR2pA712E7cWQ8AYKfsMwh5xglksegaHcp9nyC7660BAMAi7DMIHRUO41o+7r0TRsNDuEPJQkaRpfoDAAAZsc8gVPGqEc0GWqo3VyX1C+Q23cLRUQAAO2SfQWhxL4Zx6+IRhAAAdghBaJY+Aex2vhifizOFAAD2BkFoFgVHL4Ryq65jUAgAYG/sMwhFEmcdfNeyfU5sxq2OF3SIQgAA+2KfQciIxaX8Ydk+m7qxRi54VC8AgL2xzyAkIsZIsPTDViY05VZcx2lCAAC7YrdBaMFZ1oyebcQdvS8kFyILAQDsh90GISNOtHQQahT0XCi3/CqCEADAfthtEPKcxR5AUdrr4dz/XcUlMwAA9sNug9Aah0aJqLk7a+pGW24jCQEA7ITdBiEjZpFn85b1Wji39DKCEADATthtEH7Y820H3sEaPQ9uyN3Moz+ycKYQAMAe2G0QtqnfUsHx1uhZwdHr4dznFzAoBACwB3YbhFY1uTm37a6QWIBBIQBArYcgfBTuKnoxjPsaZwoBAGo/BOEjeqMl9901IV9n6zoAAODxWDcIHzx4kJWVVUmD3NzcvLw8a2x6ws4ZqQXp1uhZEuzCevhxK/E8CgCAWs5aQSgIwiuvvNKwYcNmzZoNHDiwsLDQpMGuXbsaN24cFBQUFBTUpUuXhIQEyxZQqNMaRINl+zQxrw336Z9CsXU3AgAA1mWtINy0adORI0fu3LmTnJxcUFDwxRdfmDTQaDTff/99bm5uWlpa06ZNX3vtNcsWYKUb6ktr48UiPGkNnlwPAFCbWSsI169f/9JLL7m6uioUitdee+377783aRAVFdWpUyciUiqVQ4YMiY+Pt2wBNRCERPROW/7jPwQ9ohAAoNayVhDevHmzSZMm0uumTZvevHlTrPihSBs2bOjTp08lvWVlZd38y/37980pgGPM4o9hKiuyPgt2oR8SkIQAALWVwkr95uXlOTk5Sa81Gk1xcXFxcbGjo2PZll999dWpU6dOnz5dUVd6vX7lypUbN26UFnv16vXll19W1Fin0xkMBr1eTyLlF+Tn8/mP9z2qNrsZN+20YpBPiaLSPyoKCgoYY9YuprrkWVVxcTHHcUql0taFmJLn7pJnVVqtVqVS8bxVJrV4ZIIgFBUVVfJHua3I84dYWFgoCILcCtPr9dLveTPbq9VqjqtiyGetIPT29s7NzZVeZ2dnu7m5lZuCq1at+uSTT2JjY728vCosUaGIiYmJiYkxZ7vSDnJ0dFTwSkcnB2dn50er33z9nKnRNf2mZPUrzSrb16Io1kAx1SXPqpRKpTyDUJ67S55V8TwvzyDkeV6j0di6EFPy/CEyxtRqtTyD0DjQsghrHRpt1aqVcZB3+vTpiIiIsm02btz49ttv79mzp1GjRhYvgGdWeQxTuT7syM8/J2j1NbM1AACwJGsF4ZQpU1auXLlnz55Tp0599NFHxotCBwwYcODAASLavn37Cy+8MHny5IsXL27atOmXX36xbAGLnlwY5hFi2T4r0qEe6+TNll3FmUIAgNrHWodGO3fu/O233y5cuLC4uHj27NnPb8KAHwAAIABJREFUPfectD4gIECtVhNRfn7+0KFDL168ePHiRSJSqVTDhg2zYAFqpSUHzlX6oD3Xe6f+5Sacm6omNwsAAI+LyfC8sYm5c+d6eHhU9xyhtasqa+IRg5cDfdyp/JMieXl5Li4uNVxSleRZlWwvlpHn7pJnVbK9WEar1crwHKE8f4gFBQU4RwjV82EHfuV14cYDuf9hAQAApdltEGZqs4sNJTW5xfpONKMF/9ZpnCkEAKhN7DYIFx77/GL6lRre6KwI7mS6ePQ+BoUAALWG3QZhzUyxZsJJQZ915qb+btBhWAgAUEvYbRAyZpvrgEaEcEHOtBTP7AUAqCXsNghr8oZ6E4u78B+eNyQV4AApAEAtYLdByIgTyTZBGObKpjbnZpzAoBAAoBaw2yDkOc4g2CyK3mrDX80Rf76FLAQAkDu7DUKbXCxj5MDTiu7868cM6UW2KgEAAMxit0Ho5eThoLDldGed67PnQrlZJ8x9VggAANiE3QbhjA6TI/072LaGBR34k+k4QAoAIGt2G4RyoFHQD734V48Z7uEKUgAAuUIQWlf7euy1cP6VIwYkIQCAPCEIre6t1ly+jhZftdYTrwAA4HHYbRBey7yRkp9q6yqIiBQcbYjml17jMQcpAIAM2W0Qbr2xO+7+eVtX8T8NNGxpJ/0LsYYM3E0BACAzdhuEPONtNcVauZ7yM4wJYyMP6DEfNwCArNhtENr2hvpyfdCed1WxyUdxZyEAgIwgCGsOx+j7nvyZDPErPJsCAEA27DgImWCLxzBVzllJW/vwC88Zdt2TXW0AAHWTdYNQp9Pp9XqrbqIiMhwRSoJd2IZoxUu/6a/kIAsBAGzPWkGo1+snTJjg5eXl6en5+uuvC2UeBJGamjp+/PiIiAhPT88HDx5YvADZBiER9fBj/+nM991tuJOPLAQAsDFrBeF3330XFxeXlJR09+7dgwcP/vDDDyYNBEFo06bNe++9l52dbY1HyYd5hDRw8bd4t5byYhgX04p7cqfhvtbWpQAA1G3WCsI1a9a8/vrrLi4u7u7ukydPXrNmjUkDPz+/mTNndu3a1UoFPBnco3tgpJU6t4hXw7kxYdzTu/TZxbYuBQCgDrNWEN64caN58+bS6/Dw8ISEhMfpTavVZv8lPz/fEgXKwnvtuJ5+bNA+fb7O1qUAANRV1poAMzc319nZWXrt7OycnZ39yF3p9fpPPvlk8eLF0mKfPn1WrFhRUWOdTmcwGHQ62QVLRfn9QUuaeUbZe7vh5x46N2VNnzKU518VxcXFHMcplUpbF2JKnrtLnlVptVqVSsXzvK0LeYggCEVFRWUvWbA5ef4QCwsLDQYDY8zWhTxEr9dX6zJMtVpd5b9DawWhl5dXbm6u9DonJ6d+/fqP3JVCoXjvvfdiYmLMaSwFoaOj4yNvznpcXFzKXb+iF80+aRh0mN/TT+Fd44VXVJUNqVQqeQYhyXJ3kSyrUigU8gxChUKh0WhsXUg5ZPhD5DhOrVbLMwidnJws2Ke1Do22aNHi7Nmz0utz584ZD5PWmPOpF04ln63hjT4aRvRZZ35UIy5quz4JTy4EAKhZ1grCyZMnL1q06OLFi+fOnVu6dOnkyZOl9X379r1w4QIRiaK4f//+I0eOEFFsbOzBgwctW8CVzPizqX9atk+rimnNjWvM9dhhuJaLLAQAqDnWOjQ6cuTIO3fujBo1iuO4t956q1+/fiYNRFH8+OOPiejJJ5/86quvHBwcoqOjLVgAY8wad2VY1dzWnK8T9diu/6GXItpfXocjAADslRWfFjt79uzZs2ebrNy9e7f0guO4ffv2WW/rcr6hvhLjm3CN3djIA/p32vJTm9vtBHgAAPJht79qOeIEqn1BSERP+LDYZxRfXBTmnDToa+U3AACoTew3CGvniFDSxI2dGKS4lCP22onLZwAArMtug5DnOIP87hYyn6cD7XhaMSKY6/irHo+qAACwHrsNQkZMpNqdH4xoRkvup2jF5KOGt04bSmpxrAMAyJfdBmF4vabdG8h6rlEzdfdlcUMVl3Oow3/1cRm1O9oBAGTIboMwzCOkk387W1dhGd6O9N8+/DttuQF79HNPG4oNti4IAMCO2G0Q2p+RIdz5Ycr4XGq3RX8oBUNDAADLQBDWJj5O9POT/IIO3ITfDCMPGG7nIQ4BAB4XgrD2GRrMXR6haO3JOv6qfy/OgEc4AQA8DrsNwvNpF9de/MnWVViLI09vt+XODVUk5FHjjbrPLwhac59JAgAAD7HbIMwpyk3Ivm3rKqyrgYat78nv6684liY23qT/6rKA62gAAKrLboOQZ5yh1s4sUy0tPdjm3vy2p/i9iWLDDbq3zxgwGQ0AgPnsNgg5xgtiHRoftfViW5/ijw5U6EVqs0U/cK9+fxLiEACganYchLV4rtFHFubKPurI3xylHBjEzTxhaLtF/39XhUKcPgQAqJgdByETatvzCC3FRUmTmnEXhis+7sRvuysEb9BNOWo4mCwa6uj+AACojBWfR2hbdXNEWBojeiqAPRWguJMvbrolzj1tuJMvDgvmnm3ERfkyHs/9BQAgIgRhXdDQmc2OYLMjuFt54uZb4psnDfcKxGHB3PAQrpWaXGxdHgCAbdltEDbxDJ3cdpytq5CXEBc2pxWb04q7lSduuiW+c8ZwIcuhc319tD8X7c861GMKuz1SDgBQIbsNQheVc1PPMFtXIVMhLuzNVuzNVlxKdn5cnuZgsjDlqHA7X+zuy6L9uV5+rKUHQhEA6gq7DUIwh7NCHBDEBgTxRJRRRIdShIPJ4v9dFe7lixGerF091r4ea+fFWngwJXIRAOwUghD+p54jjQzhRoYQET3Q0flM8WyGGJssfvancDtfDHdn7eqxlh6ssRtr7EoNnTFkBAA7Ya0gTE5OHj9+/LFjx/z9/RctWtS/f3+TBoIgzJkzZ/Xq1RzHTZo0acGCBYzhQka5cFVSlC+L8v3fT6RAT39kiucyxcs54ra7QvwDul8oBjmzJm7UxI01dmVhrqyxG/mrMXAEgNrHWkH42muvNWrUaPv27QcOHBg1atSdO3c8PDxKN1izZs2uXbuuXLmi1+ujoqLatGkzcuRICxZwI/vWkrjvFj+50IJ91lkaBXX1YV19/v5LpdhACXni9VwxPpfOZoobbwo3HlCqVvR0ID81C9BQgJr5a1gDDfk6sUAN1XNk7ipywgEIAJAfq/xmSk9P3759++3bt1UqVb9+/dq0abNhw4apU6eWbrNq1app06bVr1+fiKZOnbpy5UrLBiGRmF9SYNEO4W8OPIW7s3D3hwbxIlGqlpILxKRCMamAUgrFo/fpvla4l08ZRWJOCRGRu4o8HJi7itwdyEPF3B3+XuOhIncH5q4iDSNPB/JWEg4RAEANsEoQJiQkuLq6BgQESIsRERHXr183aXPt2rWIiAjpdcuWLb/++mvL1sAYJ+I+wprFiHydyNeJtasgwrR6yimh7BIxp5hySii7WMwpoexiul8oXs2h7GLKKRFySiiriMvVUU6xTiRyVxFj5KFiROThQIzIXfqvinGM3FQk/ZeIlBw5K/63XUf+79Gns5KMB2zdVMx47FbBkYuy/G/h7lD+FywoYBoSNQqmss4RYI8KtgsAVmWVIMzKynJ2djYuurq6JiUlmbTJzs52cXExNsjMzKyoN71eP3fu3Llz50qLzzzzzI8//lhRY51OZzAYdDodK6G7DxJ7fD9IWu/h6L7uqaXGZqdTz88/+Z+yH+/o0+a9znOMiz9c+/mHa7+UbfZ80+HPNx1mXPzg1Gcn758t2+ydTrM6+7aTXufn54/bNy3z/9s707AmsnSPnxASAiKQgIRFVtkUN8hVsFtl03HBhwkKjIPYqKi42+Pj6Fy6VWZwwV3pxm67m1Z5FBVHBWRXERABwSgICIjIvkRQtkASstT9cHpqMgmkGTWFXs7vU9XJW3X+lXOq3qqzvfx3imaXFn6nr8mA212C7tWZWxVtVKSfx+ONUD8A4KPo1wZAmwza+0qODqd/3l+FQqGamhqFQvm3frhcqhgAAAb7wRxTvymGK6QY6BWRJBjIazje2c9RPJsRY8842v/wRECMkQAAXe9CpdIh9PM0zktJv+knYd3jhRsUbSQkvRbSLxhGIZFEAxKggT21UjusaNaHOddJw/Bdplo8kxSvaMaVBnCxAHzXUi1Sh/RE0axi8H/fSv4H33WhbdAgDaH/seBnIUaD21TQ5aq5XtFmENAL+b/guww1zlSNIfS/k7LKhf/Wb0G5bqE+hP4G0Z8axP/W70g9ok/+QP0MpB/pH7n+Qy6nZzANFQ8ZEi0tLTKZrNyGhKlgQc6ioqLFixe/e/eb6M2bN2tpaZ08eVLWxtjYOD4+ft68eQCA9PT07du319TUDHm2v/3tb3Q6fe/evSPJGjpCGo32YVfw8enr68Md/6fDp6kKd4SjLUSeT/Pv+jRV8fl8KpX6uw8ggpFKpXw+f9y4caMtRJ5PsxD7+/u1tLQ+tWGMYrFYJBJpamp+xHOqpInH2tqax+M1NTXB3bKyMnt7ezkbe3v758+fw+3nz58rGiAQCAQCQQAqcYQGBgY+Pj4HDhzo7++/detWeXl5QEAAAODZs2dr1qyBNiEhIWfPnm1qaqqrqzt37lxISIgqlCAQCAQCoRxVjWc/d+5caGiohYWFqanpzZs39fT0AAB8Pr+xsREaBAUFvXz5cs6cOSQSafPmzb6+vipSgkAgEAiEElQ1/9nQ0PD27dudnZ2lpaVeXl4w8YsvvsjKyoLbJBIpIiKiubm5qakpLCxs+DP9d5w/f/7AgQMf62wfi7q6Otgb+qnh5eVVXV092irkOXToUFRU1GirkKeoqOjTfF2bOXOmkrFmo8WuXbvi4uJGW4U8aWlpn2Djk0QisbKyGm0VQxAcHJyZmTnaKuSJjY0d4ZCRkfP/bYazQCDg8/mjrUIeqVTa29s72iqGoK+vTyKRjLYKeQQCgYbGJzeTQCwWw0G2nxo9PT2qGPL2gfD5fKFQONoq5BkcHBwYGBhtFUPQ3d092hKGoL+/XyQSjbYKeYRC4UcvRLQiFgKBQCDGNMgRIhAIBGJMo5J5hB+X06dPx8TEGBsbj8S4ra1NKBRaWlqqWNR/h1AorKysnDlz5mgLkae0tNTOzu7jzsj5cBobG9XV1U1MTEZbyH/A4/EaGhocHR1HW4g8HA5nxowZ6uqfVjcHXF5qwoQJoy3kP+jq6uro6LCzsxttIf8BhmHFxcWzZ88ebSHyVFdXM5lMONTx04HL5fb391tbW4/Q/scff5w0aZJym8/AEUqlUnyIDQKBQCAQI8fFxeV3Fyv4DBwhAoFAIBCqA/URIhAIBGJMgxwhAoFAIMY0yBEiEAgEYkyDHCECgUAgxjTk8PDw0dbw/jx8+DArK4tCocBI94rU1tYmJSV1dHRYWVkRFkyEy+UmJCTU1dVZWVkNOahdJBI9f/68urqayGkeIpEoPT29sLBQX19fR0dH0aC1tfXu3bslJSVaWloMBoMwYbAQqVTqkIXY2Nj44MGDgoKCvr4+c3NzwgqxpKQkLS1NIBCYmZkpMSsqKuJyuSOc2/Ph8Hi8pKSk0tLSiRMnKk564fP5OTk5r/8FmUwmZuA7XrUMDAyGrFoAgN7e3pSUlOLiYgzDjIyMCFAFAKiqqrpz505PT4+FhYVizSkoKKiursb/rp6eHmLKsb29PSEhob6+3tLScsjnQ3d3d1paGofD0dTU1NfXJ0ASAEAoFKamphYVFRkaGg45xlIqlWZnZ+fm5mpoaBA2K0YkEpWVlVVWVipZgq64uDgzM1MqlX7QhCvss2Xbtm22trahoaFMJjMmJkbRIDk5WV9ff/369U5OTmw2mxhVpaWl+vr6X331lbu7O4vFGhgYkDPIysqi0WgGBgZ6enrESMIwTCQSubm5zZkzZ926dQwG49GjR3IGaWlpdDqdzWYHBgbq6OicO3eOGGFbtmyxs7PbtGkTk8n89ddfFQ1YLNaKFStCQkLs7e09PT2FQiEBqqKiooyNjUNDQ62trffu3Tuc2aNHjzQ0NDw9PQmQhGFYZ2enjY2Nt7d3QECAiYlJfX29nEFtba26uvqCfxEfH0+AKpFINH/+fCVVC8MwDofDZDIXLVoUHBw8ffp0AlRhGBYXF2dgYBAaGjplypS1a9cqGqxduxb/rxgMxvr16wlQ9fTpUwaDERwc7ObmNnv2bD6fL2dQWVlpYGAQEBCwdetWAwODn376iQBVfD5/9uzZ8+bNW7Nmjb6+/tOnT+UMRCKRl5eXq6vrtm3bjI2NL1y4QICqnJwc+KjU1tYezuYf//iHubl5aGiomZlZZGTke+f1uTrC2tpaLS2ttrY2DMOysrKMjIwGBwflbGbMmHHx4kUMw/r6+oyNjR8+fEiAMH9//7CwMAzDJBLJ7NmzFT00nNJbUFBApCO8deuWvb099CInTpzw8vKSM2hvb+/t7YXbCQkJurq6UqlU1apevXqlpaXV3t6OYdi9e/eMjY0VCxGHx+PR6fQHDx6oWtXAwACdTi8oKMAwrKGhgUajtbS0KJoJBAInJ6etW7cS5ggPHjzo7e0Nt0NCQrZv3y5nUFtbS2Slgty8edPBwQFWrePHjy9YsEDOQCwW29raRkdHE6lKIpFYWlomJiZiGPb27VsdHZ3y8vLhjAcGBvT09PLy8ggQ5uvru3//fgzDxGIxi8W6dOmSnMGePXv8/f3h9uXLlx0cHAhQdenSJScnJ5FIhGFYeHi44mfD5cuX7ezsoEFRURGTySTglbS7u/vNmzfFxcXDOcK3b99qaWlVVlZiGFZeXq6trd3d3f1+eX2ufYSpqalz5syBbSzu7u5isbi4uFjWoLGx8fnz5ytWrAAAaGtrL1q0KDk5WdWqMAxLTk728/MDAKipqfn6+ipmqqenZ2BgoGolciQnJ/v4+FCpVACAn59fVlaW3Kq1TCYTbw8xNjYWi8VSqVTVqlJSUr788ksmkwkA8PDwEAqFHA5nOOPBwUGpVEpAS9GjR4/GjRvn6uoKADA3N3dyckpPT1c0Cw8P9/f3d3BwULUenOTkZFifAQB+fn5D1me4+kReXh5h64PLVa379+/LrXrP4XA6OzuDgoJyc3NLS0uJUVVeXt7R0bF06VIAAIPB8PDwSElJGc44Pj7e0NDwiy++ULUqDMNSU1NhIZLJZDabrViIBgYG+L3Z399PzLMiOTmZzWbDdlo/P7/U1FS527+6utrJyQkasFiszs7OwsJCVavS1dVV3gZ7//79SZMmwXvQ0dFx4sSJDx48eL+8PldH2NLSMnHiRLhNIpGMjY1bWlpkDVpbW/X09LS1teGuqampnIEq6Orq4vP5pqamRGY6ElpaWnBVsCW9tbV1SEsMwyIiItasWUMmkwlQhReimpqaYiFCIiIiFixY4OjoePz48WnTphGpCgxTiCUlJZmZmbt371a1GDlhclULU1gNg8FgnDlzZufOnTY2Nrm5ucSrAgpVq7a2dvz48e7u7tHR0QEBAWw2m4B3rJaWFiaTiffAKb8TY2JiQkJCCOh+7uzsFAqFeO0aUtW2bdsYDMbcuXPZbPbPP//8yy+/qFoVUCjEwcHBjo4OWQMLC4uKigpY3168eCGRSD6FJ1tzc/Pv3qoj5HN1hBKJRLbiqquri8ViJQZkMlnOQEWqAAB4vsRkOhIkEoma2m9lraamRiKRhhO2d+/e9vb2yMhIYlQpL0QIm83etWvX6tWrDx48OJz/VqkquUhVYrF4w4YN33//PYVCUbUYOWF4IZLJZNh2LWtgaWn5+vXrpKQkDoezc+dOYgLvyaqC/5tcIcJw3FFRUdevXy8pKXn69Ont27cJUDXC27+mpqawsHD16tWqlgRG9nwoKirKzc3905/+FBAQQCaTr1y5Qoww2aoFFAoxMDAQAODt7R0eHh4cHGxoaKj4EkY8I3yAjITP1REaGxu/efMG3+VyuXJDhoyMjLq7uwcHB3EDAoaE6evrUygU/GVKUdVoIft3dXR0DDfCav/+/RkZGenp6fiXNGGqwPB/17Rp05YuXXr06FEHB4fLly8TrKq9vV2u5qSlpbW2tl68eDE0NPTatWtVVVVbt25VtSo5YVwu18jICH94QeArDtwODAx89eoVAQ2kclULwzC5QjQxMVFXV//yyy8BAJqami4uLmVlZQSo6uzsxB/WSm7/X3/9denSpcSMF50wYQKZTFb+fDh06NCWLVu2b98eGBh46dKlw4cPE1yIXC6XTCbDDgscTU3NoqKitWvXmpqa3rp1SyKRjHzNa9UxwgfISPhcHaG7u3teXh5sTC8rK+PxeCwWCwAwMDAA642VlZW5ufm9e/cAABKJ5P79+x4eHqpWpaam5ubmhsd0zszMdHd3BwDAfl0CWoSGw93dPTMzEz4XMjMznZ2d4TD33t5egUAAbY4fPx4fH5+RkUHYiG1YiLBLqbS0lM/nOzs7A5lClAX+h7q6uqpW5eLi0tra+urVKwBAT09PUVERLEShUNjT0wMAcHZ2PnPmDBxtaG9vz2AwPD09Va0K/KsQ4TZetQAAXV1ditFTORwOg8Eg4IVGrmqxWCzY2YxXLVdXVw0Njfr6emhfU1OjfEbKR2Hq1KkUCgX2YwmFwpycHHj7Dw4OdnV14WZisTg2NnbdunWq1gMhk8nz5s3LyMiAu3ghSqVS/PlAJpPx13e4QUAnhbu7u6yquXPnwlblnp4e/Pmgqanp7++/YcMGDoejoaEBb9VRAa9a8+fPLysr43K5AIC2trbKysq5c+e+50nfb4zNp4C3t7eHh8fp06cnT54MB2JhGPaXv/wFH3N1/vx5U1PTkydP+vr6Ojs7i8ViAlTdv39fT0/v8OHDoaGhpqamb9++xTAMNujB8e4dHR0bN25ks9lUKnXjxo379u0jQFV/f7+NjU1QUNCxY8cMDAxu3rwJ093d3Q8fPoxh2J07dwAAPj4+G/9FV1cXAcKWLFni6el5+vRpBweHAwcOwMSdO3cGBARgGFZVVbVw4cLw8PAjR454enra2dkRo2rXrl3Tpk07c+bM3LlzoRIMw3788cdp06bJWX733XeEjRqtq6tjMBi7d+/ev3+/rq7us2fPYLqhoWFCQgKGYadPn163bt2xY8e+/vprwubA8Hi8SZMmrV69GlatW7duwXQ3N7cjR47A7W+++cbJySk6OjooKMje3p7H4xEgLDIyctKkSadOnVq8eLGHhwdMvHXrFpPJxG2SkpKYTKaSscofnYyMDD09vSNHjmzYsMHMzAzW58bGRgBAU1MTVKijoxMeHh4VFTVlypSQkBACVHV1dZmZmYWEhERGRtLp9PT0dJjOYrGioqLgtp+fX2Rk5I4dO/T09FJTUwlQ9e7du40bN/r6+lIolI0bN37zzTcw3dXV9eTJk3B77dq1s2bNOnPmDIvF2rRp03vn9RlHnxAKhbGxsa9fv549e7avry9MLCws7O/v9/Lygrv37t178OCBkZHRmjVrfjcSx8eCw+EkJiZqa2t/9dVXcFwrn8+/fPnyn//8Z21t7b6+vqtXr+LGenp6AQEBBKh6+/btxYsXu7q6li5dig+QS0lJmThx4owZM6qrq3NycmTtV61aNW7cOFWrwgvRxcWFzWbDxMLCwoGBAU9Pz8HBwbS0tJKSEolEYmtr6+fnR0zoRAzD/vnPf3I4HHt7+9WrV8O346qqqhcvXixfvlzWsqKioq6ubtmyZQSoAgDU19dfuXJFLBYHBARMnjwZJl65cmXu3LkWFhYNDQ0pKSlNTU10On3hwoVOTk7EqFJeteBuYmLi48ePzc3Ng4KCiGl4BwAkJyfn5+ebm5sHBwfDmtPQ0JCXl7dq1SpokJ+fz+fz8ccFMTx58iQxMXH8+PHBwcGwBbK/vz8uLi4wMBDecaWlpampqQKBwNnZ2cfHh5hFJLhcbmxsbG9vr4+Pz6xZs2BiQkKCra0tjMEZFxdXUVExbtw4f39/W1tbAiTxeLy4uDh8V0dHZ+XKlQCApKQka2vrqVOnAgAkEgkUNn369JUrV8p1Foycz9gRIhAIBALx4XyufYQIBAKBQHwUkCNEIBAIxJgGOUIEAoFAjGmQI0QgEAjEmAY5QgQCgUCMaZAjRCAQCMSYZoiwkAgEAkEMNTU1aWlpUql04cKFcL4aAkE86IsQgfh9Wltbf/rpJ7iY0xgkJSVFSRij9+bChQuOjo6xsbHXrl2bPn362bNnP3oWCMRIQBPqEYjfJzs728PDIz8/f86cOaOtZRRYsGABiUS6e/fuRzxnTU3N1KlTv/3223379gEATp48uWfPnqKiIrhoMAJBJOiLEDGmGRwcbG9vl43e8vbtW7nQssqRSqVcLheuxz0SJBIJl8sVCoVD/gpD1ik5vK+vTzZWnFgsfvPmjZL13KVS6Zs3b2RX5RaLxe/evRvOvqOjQ8mvigwMDLS3tyuu+j2cYJzvv/9eQ0MDj+m4c+dOBoMRFRU18qwRiI/GB66LikB8jhgZGR08eHDXrl1aWloAgJycnK6uruXLl8OgHCQSydbW9urVq9A4KSkJLlQ7fvx4Op1Op9Pz8/MxDJNKpceOHcMD1rBYrOLi4uFyXLVq1YIFCy5cuACDbmtpaYWFhcGYghiGtbS0LFu2DC41qaamNmXKlOTkZPzY+Ph4Op2elZUFgxnZ2NhgGJaSkjJr1iy4uCKNRlu8eDFc1R0SHBzs7u5+48YNGGBo/PjxP/zwg0QiOXDgAFzq09LSsqCgQFbhzz//bG5uDq9l8uTJ9+7dg+nz589XV1enUCjw2pctWwbTq6qqFi1aBGMjaGtr7969WyQSyQmG0QCgYDmmTJmyZMkS2RRfX18TE5ORFB8C8XFBjhAxFqHRaIaGhl5eXsnJydnZ2c3Nza2trevWrUtJSXnx4sWjR48CAgLU1NQKCwsxDOORU/U8AAAHOUlEQVRyuSdOnAAAnD179u7du3fv3oVBA/bu3UulUiMiIp49e5aXl+fp6amnpwdjCCjCZrPpdLqVldWdO3eeP3++Z88eAEBkZCT8tbKycsuWLRkZGZWVldnZ2d7e3lQqtbKyEv4KozCampru37//4cOHMDhATEzM0aNH8/LyKisr4+PjraysZsyYgXtWPz8/BoMxderUhISEwsLC5cuXq6mphYSELFmyJCsrKysra+rUqVZWVrjrOn36NIlE+utf//rkyZPHjx8vX75cQ0OjrKwMw7DCwkInJydnZ2d47U+ePMEwrLm5ecKECSwWKzU1taKiIjo6ety4cV9//bUSwbJIpVIKhbJ161bZxL179wIA+vr6PrBwEYj/FuQIEWMRGo1mZmYmEAiGMxCLxVZWVviT/cGDBwAA+CEIaW5uVldXDw8Px1N6enr09fWHi6sFY2vk5eXhKX/84x8ZDMaQMYAEAoG+vn5ERATchX4lLCxMyRXBDjzoujAM8/PzI5PJuCvt6OggkUjm5uZ8Ph+mJCYmAgCgV+vr69PR0QkNDcXPJhQKra2t169fD3e9vLwWLFggm922bdvodDqMxAs5cuQIlUqFbux3Bff39w/XRtXc3KzkMhEIVYCmTyDGKEuWLNHQ0JBN4fF4169fr6mpgbFbRSJRbW3tcIdnZWWJxWJDQ0MY/BliZmZWXl4+3CFMJhO2bUJWrFiRmJjY0NBgY2MDAOjp6bl69WptbW1vby8AQE1NDQYHxvHx8ZE7YVVVVUJCQmtrq1AohK7l1atXMDwNAMDCwsLBwQFuGxgYMBgMNzc3Go0GU+zs7AAATU1NLBaroKCgt7fXzMxM9losLS2VXEtmZqadnV1JSQmeoqmpOTg4+PLlSzxkq6JgHNigymazAwMD8cSEhIS4uDgC4tAiEHIgR4gYo+B9e5CKigoPDw8KhbJw4UJ9fX0KhUKlUpUMgYFTKcLCwuTCxcEuwCGBwSlxTExMAADNzc02NjaPHz9etGiRnp6ep6cng8GAfXLQIw4n+PDhw/v27XN1dZ0+fTqdTqdQKAAAWcF0Ol3WnkqlyqZQqVQAAByYA6/l2LFjck5ISSh5Lpfb0NAgF0qTTqd3dnYOJ1gWDQ0NHR0dOp3u7++PJ+bn56urqzMYjOGOQiBUBHKEiDGKXAzP7777jkqlvnjxAo6XAQDIfh4poqurCwDIzc2dNm3aCHOUdRIAgDdv3gAA4GCWEydOmJiYPH36FP9iu379uhLBYrE4IiJi586dp06dgiklJSXR0dEjVCIHvJYbN2784Q9/GOEhOjo67u7uCQkJSmyUR0mdPn36y5cvZVMqKysdHBygh0YgiARNn0AgAACgrq7Ozs4O94KNjY2yDYNwpKVAIMBT5s+fTyKRbty4MfIsWltby8rK8N309HRtbW1LS0uYu6OjI+4Fy8vLGxsblZyqvb1dIBDITrlLTU0duRI5XF1dqVSqkmvR1taWm1Li5uaWk5MDffn7wWazCwsLm5ub4e67d++ys7NhTyoCQTDIESIQAAAwc+bM/Pz8lJQUoVBYUlLi5+cHGxshkyZNotFo58+fz8vL43A4PB7P3t5+zZo1R48ePXbsWFNTE5/Pf/HixYkTJ27evDlcFpqamsHBweXl5X19fT/88ENcXNymTZtgP+XMmTMzMjKys7OFQmFhYeHKlSs1NTWVqDUxMZkwYcK5c+fq6+v7+vouXbr0ITPwJkyYsHv37piYmLCwsLq6Oj6f//Lly+jo6JiYGGjg6Oj47Nmz69evP3nyBH7Gffvtt2KxeNmyZQ8fPuzv729ra8vMzFy/fv3IMw0NDTU1NfX3929sbGxtbQ0ODtbV1d2xY8d7XwUC8f6M9mgdBGIUoNFoBw4ckE3p7u52c3ODNwWVSt23b5+3t/f8+fNxg9jYWBsbG9hwl5ubi2GYUCjcs2cPnIkIsbW1VZwqAGGz2S4uLn//+9+hfyWRSEFBQUKhEP7a1tY2a9YseBIajXbq1ClXV1dfX1/4KxyE2dDQIHvCtLQ0AwMDeIiFhcXt27cBABcvXoS/+vn5sVgsWXtjY+MdO3bgu3Ac0LVr1+CuRCI5dOgQbCOFmJubx8XFwV87OjrYbLa+vj4AwN3dHSbKrQJDo9GWL1+uRLAiFRUVM2bMgIc7ODhwOBzl9giEikBLrCEQv4FhWH19fWdnp52dnaxLUI5AIKiurhaJRKamprDDb0h8fX3b2toKCwu7urpqampMTEwmTpwoayCVSl+/ft3T02Nvbw9bYn8X+Ommrq4+efJk5R1yI0QkElVWVgoEAlNTUxMTE7lxQEPS1NTU1tY2fvx4KysrvGn3v6Kurk4qlVpbW48kOwRCFSBHiEAQAe4IR1sIAoGQB/URIhAIBGJMg6ZPIBBEsHnz5oGBgdFWgUAghgA1jSIQCARiTIOaRhEIBAIxpkGOEIFAIBBjGuQIEQgEAjGm+T/uR8dP1Ci9KwAAAABJRU5ErkJggg=="
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_pvalue_functions(; n = 20, k = 0, f = Bool[1,0,1,0], z = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1346638b-25d3-4ddb-b76c-844f9333d123",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_pvalue_functions(; n = 20, k = 6, f = Bool[1,1,1,0], a=0.5, b=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4f095165-9258-4274-b276-9bf2cd18c6f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Roots\n",
    "using StatsFuns\n",
    "using DataFrames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "896f97f3-4a32-455c-af5c-67f627df3c6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "confint_clopper_pearson (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function confint_clopper_pearson(n, k; α = 0.05)\n",
    "    p_L = k > 0 ? quantile(Beta(k, n-k+1), α/2) : zero(α)\n",
    "    p_U = k < n ? quantile(Beta(k+1, n-k), 1-α/2) : one(α)\n",
    "    [p_L, p_U]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a4351f08-6cfb-4cca-a85b-8c0fe7c0151f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "confint_sterne (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x ⪅ y = x < y || x ≈ y\n",
    "_pdf_le(x, (dist, y)) =  pdf(dist, x) ⪅ y\n",
    "\n",
    "function _search_boundary(f, x0, Δx, param)\n",
    "    x = x0\n",
    "    if f(x, param)\n",
    "        while f(x - Δx, param) x -= Δx end\n",
    "    else\n",
    "        x += Δx\n",
    "        while !f(x, param) x += Δx end\n",
    "    end\n",
    "    x\n",
    "end\n",
    "\n",
    "function pvalue_sterne(dist::DiscreteUnivariateDistribution, x)\n",
    "    Px = pdf(dist, x)\n",
    "    Px == 0 && return Px\n",
    "    Px == 1 && return Px\n",
    "    m = mode(dist)\n",
    "    Px ≈ pdf(dist, m) && return one(Px)\n",
    "    if x < m\n",
    "        y = _search_boundary(_pdf_le, 2m - x, 1, (dist, Px))\n",
    "        cdf(dist, x) + ccdf(dist, y-1)\n",
    "    else # x > m\n",
    "        y = _search_boundary(_pdf_le, 2m - x, -1, (dist, Px))\n",
    "        cdf(dist, y) + ccdf(dist, x-1)\n",
    "    end\n",
    "end\n",
    "\n",
    "function pvalue_sterne(n, k, p)\n",
    "    pvalue_sterne(Binomial(n, p), k)\n",
    "end\n",
    "\n",
    "# 大きな n についてもうまく行くように\n",
    "# Sterneの信頼区間の実装は難しい.\n",
    "function confint_sterne(n, k; α = 0.05)\n",
    "    a, b = confint_clopper_pearson(n, k; α = α/10)\n",
    "    ps = find_zeros(a-√eps(), b+√eps()) do p\n",
    "        logistic(0 < p ≤ 1 ? pvalue_sterne(n, k, p) : zero(p)) - logistic(α)\n",
    "    end\n",
    "    # 次の行は稀に区間にならない場合への対策\n",
    "    [first(ps), last(ps)]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cb070b65-840b-4293-8d8b-1cdd785bbfc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11×2 adjoint(::Matrix{Float64}) with eltype Float64:\n",
       " 0.0        0.290865\n",
       " 0.0051162  0.446489\n",
       " 0.0367714  0.553511\n",
       " 0.0872644  0.619411\n",
       " 0.150028   0.709135\n",
       " 0.222441   0.777559\n",
       " 0.290865   0.849972\n",
       " 0.380589   0.912736\n",
       " 0.446489   0.963229\n",
       " 0.553511   0.994884\n",
       " 0.709135   1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hcat(confint_sterne.(10, 0:10)...)'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "216860d3-d525-4ed0-9d0c-e4671493b79e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "probabilities_of_type_I_error (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function probabilities_of_type_I_error(; n = 100, z = 2, a = 1, b = 1, α = 0.05, L = 10^6)\n",
    "    c_clopper_pearson = 0\n",
    "    c_wilson_score = 0\n",
    "    c_adjusted_wald = 0\n",
    "    c_bayesian = 0\n",
    "    c_sterne = 0\n",
    "    for i in 1:L\n",
    "        p = rand()\n",
    "        k = rand(Binomial(n, p))\n",
    "        c_clopper_pearson += pvalue_clopper_pearson(n, k, p) < α\n",
    "        c_wilson_score += pvalue_wilson_score(n, k, p) < α\n",
    "        c_adjusted_wald += pvalue_adjusted_wald(n, k, p; z) < α\n",
    "        c_bayesian += pvalue_bayesian(n, k, p; a, b) < α\n",
    "        c_sterne += pvalue_sterne(n, k, p) < α\n",
    "    end\n",
    "    DataFrame(\n",
    "        method = [\n",
    "            \"Clopper-Pearson\",\n",
    "            \"Sterne\",\n",
    "            \"adjusted Wald\",\n",
    "            \"Wilson score\",\n",
    "            \"Bayesian\",\n",
    "        ],\n",
    "        var\"prob. of α-error\" = [\n",
    "            c_clopper_pearson,\n",
    "            c_sterne,\n",
    "            c_adjusted_wald,\n",
    "            c_wilson_score,\n",
    "            c_bayesian,\n",
    "        ]/L,\n",
    "        var\"nominal α\" = fill(α, 5),\n",
    "        var\"sample size\" = fill(n, 5),\n",
    "   )\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ab1ec3d4-7268-421c-890e-fbe7c72043d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1.902471 seconds (1.74 M allocations: 446.526 MiB, 4.19% gc time, 7.50% compilation time)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>5 rows × 4 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>method</th><th>prob. of α-error</th><th>nominal α</th><th>sample size</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>Clopper-Pearson</td><td>0.009634</td><td>0.05</td><td>5</td></tr><tr><th>2</th><td>Sterne</td><td>0.019642</td><td>0.05</td><td>5</td></tr><tr><th>3</th><td>adjusted Wald</td><td>0.004163</td><td>0.05</td><td>5</td></tr><tr><th>4</th><td>Wilson score</td><td>0.044968</td><td>0.05</td><td>5</td></tr><tr><th>5</th><td>Bayesian</td><td>0.050045</td><td>0.05</td><td>5</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& method & prob. of α-error & nominal α & sample size\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & Clopper-Pearson & 0.009634 & 0.05 & 5 \\\\\n",
       "\t2 & Sterne & 0.019642 & 0.05 & 5 \\\\\n",
       "\t3 & adjusted Wald & 0.004163 & 0.05 & 5 \\\\\n",
       "\t4 & Wilson score & 0.044968 & 0.05 & 5 \\\\\n",
       "\t5 & Bayesian & 0.050045 & 0.05 & 5 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m method          \u001b[0m\u001b[1m prob. of α-error \u001b[0m\u001b[1m nominal α \u001b[0m\u001b[1m sample size \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String          \u001b[0m\u001b[90m Float64          \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────\n",
       "   1 │ Clopper-Pearson          0.009634       0.05            5\n",
       "   2 │ Sterne                   0.019642       0.05            5\n",
       "   3 │ adjusted Wald            0.004163       0.05            5\n",
       "   4 │ Wilson score             0.044968       0.05            5\n",
       "   5 │ Bayesian                 0.050045       0.05            5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time probabilities_of_type_I_error(n = 5, α = 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "273dcf18-0290-472a-ab8d-4d07e84c4046",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.083287 seconds (1.87 M allocations: 543.210 MiB, 4.12% gc time)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>5 rows × 4 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>method</th><th>prob. of α-error</th><th>nominal α</th><th>sample size</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>Clopper-Pearson</td><td>0.016278</td><td>0.05</td><td>10</td></tr><tr><th>2</th><td>Sterne</td><td>0.026558</td><td>0.05</td><td>10</td></tr><tr><th>3</th><td>adjusted Wald</td><td>0.012484</td><td>0.05</td><td>10</td></tr><tr><th>4</th><td>Wilson score</td><td>0.045652</td><td>0.05</td><td>10</td></tr><tr><th>5</th><td>Bayesian</td><td>0.049899</td><td>0.05</td><td>10</td></tr></tbody></table></div>"
      ],
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       "\\begin{tabular}{r|cccc}\n",
       "\t& method & prob. of α-error & nominal α & sample size\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & Clopper-Pearson & 0.016278 & 0.05 & 10 \\\\\n",
       "\t2 & Sterne & 0.026558 & 0.05 & 10 \\\\\n",
       "\t3 & adjusted Wald & 0.012484 & 0.05 & 10 \\\\\n",
       "\t4 & Wilson score & 0.045652 & 0.05 & 10 \\\\\n",
       "\t5 & Bayesian & 0.049899 & 0.05 & 10 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m method          \u001b[0m\u001b[1m prob. of α-error \u001b[0m\u001b[1m nominal α \u001b[0m\u001b[1m sample size \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String          \u001b[0m\u001b[90m Float64          \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────\n",
       "   1 │ Clopper-Pearson          0.016278       0.05           10\n",
       "   2 │ Sterne                   0.026558       0.05           10\n",
       "   3 │ adjusted Wald            0.012484       0.05           10\n",
       "   4 │ Wilson score             0.045652       0.05           10\n",
       "   5 │ Bayesian                 0.049899       0.05           10"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time probabilities_of_type_I_error(n = 10, α = 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b574168e-8274-48b1-815b-5a360e0f98ab",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.352967 seconds (2.37 M allocations: 688.199 MiB, 3.28% gc time)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>5 rows × 4 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>method</th><th>prob. of α-error</th><th>nominal α</th><th>sample size</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>Clopper-Pearson</td><td>0.022803</td><td>0.05</td><td>20</td></tr><tr><th>2</th><td>Sterne</td><td>0.033161</td><td>0.05</td><td>20</td></tr><tr><th>3</th><td>adjusted Wald</td><td>0.022719</td><td>0.05</td><td>20</td></tr><tr><th>4</th><td>Wilson score</td><td>0.046898</td><td>0.05</td><td>20</td></tr><tr><th>5</th><td>Bayesian</td><td>0.0499</td><td>0.05</td><td>20</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& method & prob. of α-error & nominal α & sample size\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & Clopper-Pearson & 0.022803 & 0.05 & 20 \\\\\n",
       "\t2 & Sterne & 0.033161 & 0.05 & 20 \\\\\n",
       "\t3 & adjusted Wald & 0.022719 & 0.05 & 20 \\\\\n",
       "\t4 & Wilson score & 0.046898 & 0.05 & 20 \\\\\n",
       "\t5 & Bayesian & 0.0499 & 0.05 & 20 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m method          \u001b[0m\u001b[1m prob. of α-error \u001b[0m\u001b[1m nominal α \u001b[0m\u001b[1m sample size \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String          \u001b[0m\u001b[90m Float64          \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────\n",
       "   1 │ Clopper-Pearson          0.022803       0.05           20\n",
       "   2 │ Sterne                   0.033161       0.05           20\n",
       "   3 │ adjusted Wald            0.022719       0.05           20\n",
       "   4 │ Wilson score             0.046898       0.05           20\n",
       "   5 │ Bayesian                 0.0499         0.05           20"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time probabilities_of_type_I_error(n = 20, α = 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e298cea5-b488-45e4-9cec-2761e0d4ba9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.438074 seconds (2.61 M allocations: 755.332 MiB, 3.44% gc time)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>5 rows × 4 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>method</th><th>prob. of α-error</th><th>nominal α</th><th>sample size</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>Clopper-Pearson</td><td>0.026824</td><td>0.05</td><td>30</td></tr><tr><th>2</th><td>Sterne</td><td>0.037072</td><td>0.05</td><td>30</td></tr><tr><th>3</th><td>adjusted Wald</td><td>0.028636</td><td>0.05</td><td>30</td></tr><tr><th>4</th><td>Wilson score</td><td>0.04786</td><td>0.05</td><td>30</td></tr><tr><th>5</th><td>Bayesian</td><td>0.050232</td><td>0.05</td><td>30</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& method & prob. of α-error & nominal α & sample size\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & Clopper-Pearson & 0.026824 & 0.05 & 30 \\\\\n",
       "\t2 & Sterne & 0.037072 & 0.05 & 30 \\\\\n",
       "\t3 & adjusted Wald & 0.028636 & 0.05 & 30 \\\\\n",
       "\t4 & Wilson score & 0.04786 & 0.05 & 30 \\\\\n",
       "\t5 & Bayesian & 0.050232 & 0.05 & 30 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m method          \u001b[0m\u001b[1m prob. of α-error \u001b[0m\u001b[1m nominal α \u001b[0m\u001b[1m sample size \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String          \u001b[0m\u001b[90m Float64          \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────\n",
       "   1 │ Clopper-Pearson          0.026824       0.05           30\n",
       "   2 │ Sterne                   0.037072       0.05           30\n",
       "   3 │ adjusted Wald            0.028636       0.05           30\n",
       "   4 │ Wilson score             0.04786        0.05           30\n",
       "   5 │ Bayesian                 0.050232       0.05           30"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time probabilities_of_type_I_error(n = 30, α = 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "648e1826-05d0-4ca9-ad5e-be0b76515c30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.373036 seconds (2.83 M allocations: 821.659 MiB, 3.40% gc time)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>5 rows × 4 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>method</th><th>prob. of α-error</th><th>nominal α</th><th>sample size</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>Clopper-Pearson</td><td>0.030689</td><td>0.05</td><td>50</td></tr><tr><th>2</th><td>Sterne</td><td>0.039397</td><td>0.05</td><td>50</td></tr><tr><th>3</th><td>adjusted Wald</td><td>0.034456</td><td>0.05</td><td>50</td></tr><tr><th>4</th><td>Wilson score</td><td>0.048039</td><td>0.05</td><td>50</td></tr><tr><th>5</th><td>Bayesian</td><td>0.049805</td><td>0.05</td><td>50</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& method & prob. of α-error & nominal α & sample size\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & Clopper-Pearson & 0.030689 & 0.05 & 50 \\\\\n",
       "\t2 & Sterne & 0.039397 & 0.05 & 50 \\\\\n",
       "\t3 & adjusted Wald & 0.034456 & 0.05 & 50 \\\\\n",
       "\t4 & Wilson score & 0.048039 & 0.05 & 50 \\\\\n",
       "\t5 & Bayesian & 0.049805 & 0.05 & 50 \\\\\n",
       "\\end{tabular}\n"
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      "text/plain": [
       "\u001b[1m5×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m method          \u001b[0m\u001b[1m prob. of α-error \u001b[0m\u001b[1m nominal α \u001b[0m\u001b[1m sample size \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String          \u001b[0m\u001b[90m Float64          \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────\n",
       "   1 │ Clopper-Pearson          0.030689       0.05           50\n",
       "   2 │ Sterne                   0.039397       0.05           50\n",
       "   3 │ adjusted Wald            0.034456       0.05           50\n",
       "   4 │ Wilson score             0.048039       0.05           50\n",
       "   5 │ Bayesian                 0.049805       0.05           50"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time probabilities_of_type_I_error(n = 50, α = 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f08520f9-ea0d-4250-8f8c-0ed8f167af07",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.555169 seconds (3.07 M allocations: 891.250 MiB, 4.01% gc time)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>5 rows × 4 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>method</th><th>prob. of α-error</th><th>nominal α</th><th>sample size</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>Clopper-Pearson</td><td>0.035484</td><td>0.05</td><td>100</td></tr><tr><th>2</th><td>Sterne</td><td>0.042228</td><td>0.05</td><td>100</td></tr><tr><th>3</th><td>adjusted Wald</td><td>0.040517</td><td>0.05</td><td>100</td></tr><tr><th>4</th><td>Wilson score</td><td>0.048927</td><td>0.05</td><td>100</td></tr><tr><th>5</th><td>Bayesian</td><td>0.050047</td><td>0.05</td><td>100</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& method & prob. of α-error & nominal α & sample size\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & Clopper-Pearson & 0.035484 & 0.05 & 100 \\\\\n",
       "\t2 & Sterne & 0.042228 & 0.05 & 100 \\\\\n",
       "\t3 & adjusted Wald & 0.040517 & 0.05 & 100 \\\\\n",
       "\t4 & Wilson score & 0.048927 & 0.05 & 100 \\\\\n",
       "\t5 & Bayesian & 0.050047 & 0.05 & 100 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m method          \u001b[0m\u001b[1m prob. of α-error \u001b[0m\u001b[1m nominal α \u001b[0m\u001b[1m sample size \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String          \u001b[0m\u001b[90m Float64          \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────\n",
       "   1 │ Clopper-Pearson          0.035484       0.05          100\n",
       "   2 │ Sterne                   0.042228       0.05          100\n",
       "   3 │ adjusted Wald            0.040517       0.05          100\n",
       "   4 │ Wilson score             0.048927       0.05          100\n",
       "   5 │ Bayesian                 0.050047       0.05          100"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time probabilities_of_type_I_error(n = 100, α = 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "254b0b71-4bc8-4901-90f8-90c19dd07e02",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.695926 seconds (2.62 M allocations: 759.867 MiB, 3.07% gc time)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>5 rows × 4 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>method</th><th>prob. of α-error</th><th>nominal α</th><th>sample size</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>Clopper-Pearson</td><td>0.039386</td><td>0.05</td><td>200</td></tr><tr><th>2</th><td>Sterne</td><td>0.044321</td><td>0.05</td><td>200</td></tr><tr><th>3</th><td>adjusted Wald</td><td>0.04453</td><td>0.05</td><td>200</td></tr><tr><th>4</th><td>Wilson score</td><td>0.049435</td><td>0.05</td><td>200</td></tr><tr><th>5</th><td>Bayesian</td><td>0.050195</td><td>0.05</td><td>200</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& method & prob. of α-error & nominal α & sample size\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & Clopper-Pearson & 0.039386 & 0.05 & 200 \\\\\n",
       "\t2 & Sterne & 0.044321 & 0.05 & 200 \\\\\n",
       "\t3 & adjusted Wald & 0.04453 & 0.05 & 200 \\\\\n",
       "\t4 & Wilson score & 0.049435 & 0.05 & 200 \\\\\n",
       "\t5 & Bayesian & 0.050195 & 0.05 & 200 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m method          \u001b[0m\u001b[1m prob. of α-error \u001b[0m\u001b[1m nominal α \u001b[0m\u001b[1m sample size \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String          \u001b[0m\u001b[90m Float64          \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Int64       \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────\n",
       "   1 │ Clopper-Pearson          0.039386       0.05          200\n",
       "   2 │ Sterne                   0.044321       0.05          200\n",
       "   3 │ adjusted Wald            0.04453        0.05          200\n",
       "   4 │ Wilson score             0.049435       0.05          200\n",
       "   5 │ Bayesian                 0.050195       0.05          200"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "@time probabilities_of_type_I_error(n = 200, α = 0.05)"
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   "execution_count": 18,
   "id": "d8d3b69d-236b-4a94-a021-36671f38a74d",
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  3.502945 seconds (4.43 M allocations: 1.095 GiB, 3.25% gc time)\n"
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    },
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       "<div class=\"data-frame\"><p>5 rows × 4 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>method</th><th>prob. of α-error</th><th>nominal α</th><th>sample size</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>Clopper-Pearson</td><td>0.040976</td><td>0.05</td><td>300</td></tr><tr><th>2</th><td>Sterne</td><td>0.045371</td><td>0.05</td><td>300</td></tr><tr><th>3</th><td>adjusted Wald</td><td>0.045898</td><td>0.05</td><td>300</td></tr><tr><th>4</th><td>Wilson score</td><td>0.049489</td><td>0.05</td><td>300</td></tr><tr><th>5</th><td>Bayesian</td><td>0.050043</td><td>0.05</td><td>300</td></tr></tbody></table></div>"
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       "\t1 & Clopper-Pearson & 0.040976 & 0.05 & 300 \\\\\n",
       "\t2 & Sterne & 0.045371 & 0.05 & 300 \\\\\n",
       "\t3 & adjusted Wald & 0.045898 & 0.05 & 300 \\\\\n",
       "\t4 & Wilson score & 0.049489 & 0.05 & 300 \\\\\n",
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       "─────┼───────────────────────────────────────────────────────────\n",
       "   1 │ Clopper-Pearson          0.040976       0.05          300\n",
       "   2 │ Sterne                   0.045371       0.05          300\n",
       "   3 │ adjusted Wald            0.045898       0.05          300\n",
       "   4 │ Wilson score             0.049489       0.05          300\n",
       "   5 │ Bayesian                 0.050043       0.05          300"
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   "source": [
    "@time probabilities_of_type_I_error(n = 300, α = 0.05)"
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   "execution_count": 19,
   "id": "f8722461-64a3-45f3-b95f-f5cc12a0db78",
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   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  4.688539 seconds (9.30 M allocations: 2.111 GiB, 4.71% gc time)\n"
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    "@time probabilities_of_type_I_error(n = 1000, α = 0.05)"
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