{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testování hypotéz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "N = norm(loc=0, scale=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definujeme normální rozdělení\n",
    "$$\\cal{N}(\\mu=0, \\sigma^2=1)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f49780c8978>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aupyOYWKAFX0TNaqO+3rARMJI3KFKclI53T2AKyPL6SgmylnRN1Gjsr4db28nBVOTnI4yaoOnpBJzbR4eM7GCKvoislpE9otIjYjcMczrXxKRPSJSKSLPiUhRwGseEdnt/9k8dF1jQqWyvp2+pkPESeTNT78gOwVXHCTl2YybZmKNeLtEEXEBDwDvA+qB7SKyWVX3BDTbBZSqareIfA64F7jB/1qPql4Y4tzGvE3fgId9TWdwNx1wOsqYJMXHMS8rhc7c+U5HMVEumCP9VUCNqh5WVTewEVgb2EBVX1DVwa4H24CC0MY05vz2N3XQ79GIGpQ11JKcVBJzF6AaOWMMTOQJpujnA3UBz+v9y87lU8BTAc+TRaRcRLaJyHVjyGjMiAYnLIuUOXeGsyQnDVdKBrUt1nXTTJwRT+8Aw50gHfZQREQ+BpQClwcsnq2qDSIyF3heRKpU9dCQ9dYB6wBmz54dVHBjAlXVtzE9LZFjZ046HWXMBruaVtS3U5QVWWMNTOQI5ki/HigMeF4ANAxtJCJXA98A1qhq3+ByVW3w/3sYeBFYOXRdVV2vqqWqWpqdnT2qHTAGfBdxl+VnOh1jXOZlpeDt76PSZtw0EyiYor8dWCAic0QkEbgReFsvHBFZCfwcX8E/GbB8mogk+R/PAN4NBF4ANmbcetwe9ja088df/YTCwsKRVwhT8S5B2o9z/yObbQ4eM2FGLPqqOgDcBmwF9gKbVLVaRO4WkTX+ZvcB6cCjQ7pmLgHKRaQCeAH43pBeP8aM257GdiQujvXf+wZlZWVOxxmX66+6hGnzVlBbV+90FBOlgjmnj6puAbYMWXZXwOOrz7He68Cy8QQ0ZiQVdb6LuJE4/cJQS3JSeayimYQs6wBnJoaNyDURr+p4OwMdp8lOT3Q6yrgt8X9xJVp/fTNBrOibiFdR3xZRd8o6n9nTkklNiLPpGMyEsaJvIlpHbz+Hm7twR3D//ECuOGHRzFSS8uxI30wMK/omor11/Azgu+VgtFick0rizLm4B7xORzFRyIq+iWiDNxSP5OkXhirJSUXiEzlwosPpKCYKWdE3Ea3yeDv5U1Pw9pxxOkrILJ7pG407eJN3Y0LJir6JaBV1bawojOyRuEPlZybi6Tlz9q8YY0LJir6JWKc7+6hv7WFFwVSno4SUiOBuqjk7iZwxoWRF30Ssi672Tdp6+8c/HNHTLwzH3XiQAyc66O33OB3FRBkr+iZitbumIsBbr2yJ+OkXhsoYaMXjVRZdcpXTUUyUsaJvIlZi3kKKpieTluhyOkrI/emh+wFolQyHk5hoY0XfRCRVJSl3AUtyIn++neFkpyWQlRpPYp6NzDWhZUXfRKTG9l5c6dOituiLCEty0uxG6SbkrOibiDTYnbEkJ3rvMLU4J5X46fl09PY7HcVEESv6JiJV1LejngHmz0hxOsqEKclJRSTu7FQTxoSCFX0TkSrq2nA3HyUpPnp/hQfvD1B13AZpmdCJ3k+MiVper1JV3x41M2uey7TUBAbaT9ggLRNSQRV9EVktIvtFpEZE7hjm9S+JyB4RqRSR50SkKOC1m0XkoP/n5lCGN7HpyOkuOvoG6Gs84HSUCdfXeNCmYzAhNWLRFxEX8ADwfqAEuElESoY02wWUqupy4DHgXv+604FvAZcAq4Bvici00MU3sejszJoxUPTdTQepa+mhtcvtdBQTJYI50l8F1KjqYVV1AxuBtYENVPUFVe32P90GDN7g81rgGVVtUdVW4BlgdWiim1hVUddOSoKL/tN1TkeZcIOnsCqP2ykeExrBFP18IPDTVe9fdi6fAp4azboisk5EykWkvLm5OYhIJpb96o/P03q4ksKC8/0aRoc+/30CKuvsFI8JjWCKvgyzTIdtKPIxoBS4bzTrqup6VS1V1dLs7OwgIplY1e/xolPz+cSaK6Nuvp3hFORk0X+6nu8+8BBFRUUjr2DMCIIp+vVA4BSGBUDD0EYicjXwDWCNqvaNZl1jgnXgRAdxCUlROxJ3qLKyMj506TJmr7yM2tpap+OYKBBM0d8OLBCROSKSCNwIbA5sICIrgZ/jK/gnA17aClwjItP8F3Cv8S8zZkwq6nzntmOl6AMszknjVFc/rvTpTkcxUSB+pAaqOiAit+Er1i5gg6pWi8jdQLmqbsZ3OicdeFREAGpVdY2qtojId/F9cQDcraotE7InJiZU1rfh6emgIDPJ6SiTZvALLjF3vsNJTDQYsegDqOoWYMuQZXcFPL76POtuADaMNaAxgSrq23E3HUTkcqejTJpF2anECTbjpgkJG5FrIkaP28OBEx1RPxJ3qOSEOOZMTybJjvRNCFjRNxFjT2M7Hq/S1xRbRR9gSU4aibkLUB2245wxQbOibyLGrlr/SNyG/Q4nmXxLc9NwpWZy7HT3yI2NOQ8r+iZi7KptI39qCp6uVqejTLoLcn0Xc3fVxd6+m9Cyom8ixq7aVi4qis2pm+ZkpeDt62bnMRuZa8bHir6JCE3tvTS097KycKrTURzhihOktZYHn3jORuaacbGibyLCJR+4AYDP/eNqCgsLR2gdnT7x95eTmjefuoYTTkcxESyofvrGOO1MYhbZLuHgm8+T4IrNY5ULctPx6AkbpGXGJTY/PSbiJM1azMKZqTFb8AGW+i/mJs1a7HASE8li9xNkIoZ7wEti7nwuyE1zOoqjpqUmkJ+ZRNKsRU5HMRHMir4Je/uazhCXkMQFebFd9AGW5aWRmL/YBmmZMbOib8Le4KCsWD/SB98grfj06Rxv63E6iolQVvRN2NtZ28pAx2lmpic4HcVxg198g1+ExoyWFX0T9nbVttHXsA//tN0xbf6MFLz9veystZG5Zmys6Juwdqqzj9qWbtwN+5yOEhbiXYK7qcaO9M2YWdE3YW2wuPUdj71J1s6lr2E/1Q3t9PZ7nI5iIpAVfRPWyo+2kOiKi8nplM8lo/ck/R5l6twVNiWDGbWgir6IrBaR/SJSIyJ3DPP6ZSKyU0QGROSjQ17ziMhu/8/moesacz4/+/2znDlWReGsXKejhI2nH/5vAL51///YzdLNqI1Y9EXEBTwAvB8oAW4SkZIhzWqBTwCPDLOJHlW90P+zZpx5TQzpcXtg2mw+c93fUVZW5nScsJGZEs+c6clUNHQ6HcVEoGCO9FcBNap6WFXdwEZgbWADVT2qqpWAdwIymhi1q64VccWzYla601HCzvJZ6VQ1doLYGVozOsH8xuQDdQHP6/3LgpUsIuUisk1ErhuugYis87cpb25uHsWmTTQrP9qKqpfls2xQ1lAX5qfR5faSkG3n9M3oBFP0h+scPZox4LNVtRT4J+BHIjLvbzamul5VS1W1NDs7exSbNtFs+9EW+puPkZFkk8EONfjXT3LBUoeTmEgTTNGvBwInMC8AGoJ9A1Vt8P97GHgRWDmKfCZGDXi87DzWSl99tdNRwlJuRiIz0xNIKhh6ec2Y8wum6G8HFojIHBFJBG4EguqFIyLTRCTJ/3gG8G5gz1jDmtixp/EMXW4PvfX26zIcEWHFrHSSCpba5GtmVEYs+qo6ANwGbAX2AptUtVpE7haRNQAicrGI1APXAz8XkcHDsyVAuYhUAC8A31NV+xSbEW0/6ptmwI70z+3C/HTiM7Kobel2OoqJIEGdLFXVLcCWIcvuCni8Hd9pn6HrvQ4sG2dGE4O2H2mhYFoKxzpOOx0lbC33n9dfesUass7UcOzYMYcTmUhg/b1M2FFVth9tYVXxdKejhLW5WclkJLn45FfvsUFaJmhW9E3YOXKqi9Ndbn7xf++I2ZugByNOhOWz0myQlhkV6wtnws6bR1oAePrhn1I8PcXhNOHtwlnpvHbkDHGpU52OYiKEHembsPPaodMMdJymaFqy01HC3kUFGQAkFy13OImJFFb0TVhRVd44dIre2kq7aUoQFs1MJT3RRXLRCqejmAhhRd+ElQMnOjnV6ab3WKXTUSKCK064qCCdFCv6JkhW9E1Yea3mFAC9x3Y7nCRylBZmED81lzrrr2+CYEXfhJXXD52iKCsVzxmbeC9YpYW+8/qDX5jGnI8VfRM2Bjxeyg63cOm8GU5HiSjF05MZ6GzhtUM2kM2MzLpsmrBRdbydjr4BLp2X5XSUiCIi9B2r5I3cXFTVLoCb87IjfRM2XvcfqVrRH72UjlpOdbopXnGp01FMmLOib8LGvQ/9EffJI8zISLaRuKP0xM+/D0Br4kyHk5hwZ6d3TFjo7ffAjLn8y8UF3H5P0LdrMH55U5LIz0yi27pumhHYkb4JCzuPtSLxibzDP8LUjF5pYTrJsy9gwGO3qjbnZkXfhIWXDjajngFW5ttN0MeqtHAKcUlp7KprczqKCWNW9E1YeGHfSfrqq0lLcjkdJWJdUpSBej08v++k01FMGAuq6IvIahHZLyI1InLHMK9fJiI7RWRARD465LWbReSg/+fmUAU30aO+tZsDJzrpPrTd6SgRLSMpnr76PbxgRd+cx4hFX0RcwAPA+4ES4CYRGXo35lrgE8AjQ9adDnwLuARYBXxLRKaNP7aJJoNFqseK/rj1HNrOvqYOjrf1OB3FhKlgjvRXATWqelhV3cBGYG1gA1U9qqqVwNArSNcCz6hqi6q2As8Aq0OQ20SRb/70d/S3NpCXZmcbxyuzqw6AxVf+A0VFRQ6nMeEomE9ZPlAX8LzevywY41nXxIAetweduYB/vnIFZWVlTseJeNuefoK8KYmsueVOu4WiGVYwRX+4Md0a5PaDWldE1olIuYiUNzfbRFux5I3Dp4hLSOLS4kyno0QFEeHS4kzK6zqQ+ESn45gwFEzRrwcCh0cWAMGOnglqXVVdr6qlqlqanZ0d5KZNNHhu70m87h7rqhlC754zhb4BJWn2MqejmDAUTNHfDiwQkTkikgjcCGwOcvtbgWtEZJr/Au41/mXGoKq8sO8kvUd3kxhv5/NDZWVBBknxQsrci52OYsLQiJ80VR0AbsNXrPcCm1S1WkTuFpE1ACJysYjUA9cDPxeRav+6LcB38X1xbAfu9i8zhv0nOmho76XncLnTUaJKcnwcpYUZpM4rRTXYM7EmVgQ1946qbgG2DFl2V8Dj7fhO3Qy37gZgwzgymij13N7BrppW9EPt0uJMXjuSy4ETnSzKtaktzF/Z39TGMVuqGrmwcCqeTrv5R6hdNm8qql62VDU6HcWEGSv6xhFHTnVR3XCGDy3PczpKVJqRlkBfXTVPVjXaKR7zNlb0jSMGj0Bv+eAlNnf+BElseouak50Ur3iX01FMGLGibxzx58pGeuv3ULe/0gZlTZCn1v8HcQLtmfOdjmLCiBV9M+kONXeyt/EM3ftedTpKVJuelsDK/AzSFr/XTvGYs6zom0m3pdJ3aqd7/2sOJ4l+Vy2cSkJWAXsbO5yOYsKEFX0z6Z6sauTi4mnWa2cSXDFvKur18GSV3YLS+FjRN5Oq5mQH+5o6+OAy67UzGaalJtBbW8mTldaLx/hY0TeT6qpPfhVVL5++9h3Wa2eSJJ2o5ujpbopXvtfpKCYMWNE3k8brVQYKS7l4diZ1B6ut184keWbDvSS4hI4ZS52OYsKAFX0zacqOtJAwNZcPlWQ5HSWmTEmO57K5maSVXI57YOh9jkyssaJvJs1jO+rx9nVx+bypTkeJOR8sycKVmsnz+044HcU4zIq+mRQdvf1sqWqka+8rJCfYr91kWzV7CgMdp9lUXu90FOMw+/SZSfHEruP09HvorHza6SgxyRUndFU9wwv7T1Lf2u10HOMgK/pmwqkqD5fVsnTWFNyNB5yOE7MyTlbi9XhYtvazdtP0GGZF30y4Hcda2dfUwcsb7rFumg4qe+EvvHfedOZc/TFq622wVqwK6iYqxozHr984hrevi4rND5KS4HI6Tkz7yPIZvPrHdlIXXep0FOOQoI70RWS1iOwXkRoRuWOY15NE5Hf+18tEpNi/vFhEekRkt//nZ6GNb8Ld8bYenqxqpKNiqxX8MHBJ0RRmT01iysXX2QjdGDVi0RcRF/AA8H6gBLhJREqGNPsU0Kqq84EfAt8PeO2Qql7o/7klRLlNhPh/rx0BoKP8Tw4nMQBxItywciZJeQt584jdrjoWBXOkvwqoUdXDquoGNgJrh7RGqEx9AAAL/UlEQVRZCzzkf/wYcJWISOhimkjU0dvPxjfr+MCyPDwdzU7HMX4fWJKFp7udX7xyxOkoxgHBFP18oC7geb1/2bBtVHUAaAcGh13OEZFdIvKSiNjkHzHkgg/fSkffAOu/eL1dwA0jyQlxxB16hWf3nqBohZ3bjzXBFP3hjtiHngw8V5tGYLaqrgS+BDwiIlP+5g1E1olIuYiUNzfbEWE06OobwLvgCi4tnsLRXa/YPDthZuv9Xyc1MY7uYjsOizXBFP16IPAwrQAY2t/rbBsRiQcygRZV7VPV0wCqugM4BCwc+gaqul5VS1W1NDs7e/R7YcLOb7Ydw5WaySdX2RTK4SgzOZ7rV2STuvg9HDxhN1iJJcEU/e3AAhGZIyKJwI3A5iFtNgM3+x9/FHheVVVEsv0XghGRucAC4HBooptwdaa3n/9+6RA9h3dwQV6a03HMOdy4Mgd19/KfT+93OoqZRCMWff85+tuArcBeYJOqVovI3SKyxt/sl0CWiNTgO40z2K3zMqBSRCrwXeC9RVWty0CU+9mLh2jr7qf1pYdGbmwcMzUlHvY/y9bqEyTlL7FRujFCwq2vbmlpqZaXlzsdw4xRY3sP7/zuX+je/zopFb+zc/lhrtvt4fqHqimcmsTm26+0vvsRTER2qGrpSO1sGgYTUvc8uRdV5S/33WoFPwKkJrpY965ZVDR0kbrkcqfjmElgRd+EzOuHTvHnykbOlD3GrMwkp+OYIH2oJIslM1OZduX/oqO33+k4ZoJZ0Tch0dvv4ZtPvEXh9BTOlD3udBwzCq444ctXFuJKn8Z/brWLutHOir4JiR8+c4DDzV2U//RLFOTlOB3HjNLS3DTY/yIPvXGMotKrnY5jJpAVfTNu24+28ItXDtOx6ykOv/GUncuPUC/85IvkZyYxUHqTneaJYlb0zbi0drn5wm93UTg9ldYXNzgdx4xDSoKLf7umiPgp2dz5+yrryROlrOibMfN4lQtv+QENpzvY9l+foSBnhtORzDitmJWOVv6JP1c2Unz1x52OYyaAFX0zZvdu3YfkL+Or75tr8+tEkTc2fIdLi6fARdfz+qFTTscxIWZF34zJI2W1/Pylw3TsfJKPLLf5kqJJnAjfWT2H/tYGPvebnexvsrl5ookVfTNqmysauPP3FXQf2k7a/i1OxzETID3JRfxr6zl9somrvvsHipa+w+lIJkSs6JtReXxHPf+6cRd9ddWU/eAzlG17w+lIZoKUPb+F333uPUzPnonnii9Qc7LT6UgmBKzom6CoKutfPsSXH62g68huErf9kuR4+/WJdnOzUnjgHxbiik/gyn/fTNE7rnQ6khkn+9SaEXW7B/jKo5X8x5Z9dO17hbL7PkHZay87HctMkvkzUnj0s++ieNZMuPJ2Nr5Za905I5gVfXNeFXVtLLn9IR7bUUvbqw+TsvMRkuwIP+YUTkvmFzcsoreuijt+X8Xnf7uLU519TscyYxDvdAATnlq63Ny3dR8bt9fhiUvgpx9ZyMX/+l9OxzIOykyOJ2nbg7TWXsKfvB/j5QPNfPmaRfzzJbOJd9mBQKSw+fTN27R39/Pwm8dY//JhWjt76SjfTPrRlyl77SWno5kwcsn71tB3wVpSileirXX89Na1XLs0x4q/g4KdT9+O9A2qyv4THWx8s45N5XV0uz1ctjCbjV+7nmOV25yOZ8JQ2TObUVVeqGnj6787ya2P7EQ7T/FvN7yX61bmMyPdptYOV0Ed6YvIauDHgAt4UFW/N+T1JODXwDuA08ANqnrU/9qdwKcAD/AFVd16vveyI/3J0e/xUnW8nRf2neTJqkYON3eR4BLcNW/Q+MLD9DcfobCw0EbZmhF5vMqrR9r52oankZnzUa8Hmmv493Uf4T0LsinOSkVEnI4Z9YI90h+x6PtvbH4AeB9Qj+9G6Tep6p6ANv8bWK6qt4jIjcCHVfUGESkBfgusAmYBzwILVdVzrvezoh96vf0ejpzq4sCJDvY3dVBR38bOY2309HtQr5e+uiq69r1K94E3yM/KsEJvxqymuZvnatr41TO7kcxcALIzklhVPJ2SWVNYlJPBwpwMZk1NtlNBIRbK0zurgBpVPezf8EZgLbAnoM1a4Nv+x48B94vvq30tsFFV+4Aj/hunrwIidkTP4JekKujQZWef+/9F3/acEV4/1/a8XqVvwIt7wEvfgCfgse/fzr4BzvT0c6a3nzM9A7R2u2lq76WhvZem9h5au/86Ta56Bug/dYzeumr66qvJ8rSw6+XngE+O87+MMTA/O5X52amse2cex1r7uOG2b3AkfRaN9SU8mfnX+yzECczMSCZvajKzMlPIzkhiSkoCGUnxZCTHk5GcQEZyPOnJ8SS64kiMjyPBFUeCS0h0+R/HxxEf5/sLQsQ3fYQAIkKcYH9dnEMwRT8fqAt4Xg9ccq42qjogIu1Aln/5tiHr5o857Xm0dLl5z/efH7GgMsqCG2bXuUekXg/e3k48HacZ6DiFp+MUAx2nGGhrIsvVx6tPPU6CaxVwvdNRTRQTEYqnJ1P2yF97fHX2eTjS0sOnv3wXbZ54zmTM4EjGDOIzZuBKn0ZcUtqEZBn8AvB9IQx5TOi+GELxHbO8IJON6941/g2dRzBFf7hdGVoKz9UmmHURkXXAOv/TThEZzz3bZgDRMDVgyPejGygqLAjlJoMVLf9PwPYlHEXLfrAXZvzus2Pel6JgGgVT9OuBwoDnBUDDOdrUi0g8kAm0BLkuqroeWB9M4JGISHkw57XCXbTsB9i+hKto2Zdo2Q+YnH0J5krKdmCBiMwRkUTgRmDzkDabgZv9jz8KPK++8ySbgRtFJElE5gALgDdDE90YY8xojXik7z9HfxuwFV+XzQ2qWi0idwPlqroZ+CXwP/4LtS34vhjwt9uE76LvAHDr+XruGGOMmVhBDc5S1S3AliHL7gp43Ms5rgyq6j3APePIOFohOU0UBqJlP8D2JVxFy75Ey37AJOxL2E3DYIwxZuLY6AhjjIkhUVn0ReTzIrJfRKpF5F6n84yXiHxFRFREZjidZaxE5D4R2ScilSLyBxGZ6nSm0RCR1f7fqRoRucPpPGMlIoUi8oKI7PV/Pm53OtN4iYhLRHaJyJ+dzjIeIjJVRB7zf072isiEdNiPuqIvIlfiGwm8XFWXAv/pcKRxEZFCfFNg1DqdZZyeAS5Q1eX4pvW40+E8QfNPRfIA8H6gBLjJP8VIJBoAvqyqS4B3ArdG8L4Muh3Y63SIEPgx8BdVXQysYIL2KeqKPvA54Hv+qR9Q1ZMO5xmvHwJfZZhBbZFEVZ9W1QH/0234xmxEirNTkaiqGxiciiTiqGqjqu70P+7AV1gmZJT8ZBCRAuCDwINOZxkPEZkCXIavJySq6lbVtol4r2gs+guB94pImYi8JCIXOx1orERkDXBcVSuczhJi/wt4yukQozDcVCQRWygHiUgxsBKI5Bn2foTvoMjrdJBxmgs0A7/yn6p6UEQmZF6KiJxPX0SeBXKHeekb+PZpGr4/XS8GNonIXA3Tbkoj7MvXgWsmN9HYnW9fVPWP/jbfwHeK4eHJzDZOQU0nEklEJB14HPhXVT3jdJ6xEJEPASdVdYeIXOF0nnGKBy4CPq+qZSLyY+AO4N8m4o0ijqpefa7XRORzwO/9Rf5NEfHim5ujebLyjca59kVElgFzgAr/bIEFwE4RWaWqTZMYMWjn+/8CICI3Ax8CrgrXL+FzCGo6kUghIgn4Cv7Dqvp7p/OMw7uBNSLyASAZmCIiv1HVjzmcayzqgXpVHfyr6zF8RT/kovH0zhPA3wGIyEIgkQicjElVq1R1pqoWq2oxvl+Ki8K14I/EfyOerwFrVLXb6TyjFMxUJBHBP+X5L4G9qvoDp/OMh6reqaoF/s/Hjfimf4nEgo//c10nIov8i67i7dPXh0xEHumPYAOwQUTeAtzAzRF2VBmt7geSgGf8f7lsU9VbnI0UnHNNReJwrLF6N/BxoEpEdvuXfd0/6t446/PAw/4Di8NM0E0ubESuMcbEkGg8vWOMMeYcrOgbY0wMsaJvjDExxIq+McbEECv6xhgTQ6zoG2NMDLGib4wxMcSKvjHGxJD/D1wHFQ8192yRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f49780e92b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = N.rvs(size=1000000)\n",
    "counts, bins, plot = plt.hist(X, bins=100, histtype=\"stepfilled\", normed=True, color=\".9\", edgecolor=\"k\")\n",
    "x = np.linspace(-6, 6, 200)\n",
    "plt.plot(x, N.pdf(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ověříme metodou Monte Carlo nulovou hypotézu, že jde skutečně o $\\cal{N}(0,1)$. Jako kontrolní statistiku použijeme střední hodnotu z $n$ vzorků:\n",
    "$$\\hat\\mu_n = \\bar x_i = \\frac{1}{n}\\sum_{i=1}^n x_i$$\n",
    "V nulové hypotéze platí\n",
    "$${\\rm Var}[\\mu_n] = \\frac{1}{n}{\\rm Var}[x]$$\n",
    "$$\\mu_n \\sim \\cal{N}(0, \\sigma^2/n)$$\n",
    "a oboustranné kvantily pro hladinu signifikance $\\alpha$ lze určit z CDF normálního rozdělení. Požadujeme tedy:\n",
    "$${\\rm CDF}[{\\cal N}(0, \\sigma^2/n)](\\alpha/2) < \\hat\\mu_n < {\\rm CDF}[{\\cal N}(0, \\sigma^2/n)](1-\\alpha/2)$$\n",
    "nebo\n",
    "$${\\rm CDF}[{\\cal N}(0, \\sigma^2)](\\alpha/2) < \\hat\\mu_n\\sqrt{n} < {\\rm CDF}[{\\cal N}(0, \\sigma^2)](1-\\alpha/2)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k1 = -2.576\n",
      "S  = -0.147\n",
      "k2 = 2.576\n",
      "k1 < S < k2: OK\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(12)\n",
    "nsampl = 2\n",
    "X = N.rvs(size=nsampl)\n",
    "S = np.mean(X)*np.sqrt(nsampl) # mean(X)*sqrt(n)\n",
    "\n",
    "alpha = 0.01\n",
    "k1 = N.ppf(alpha/2)\n",
    "k2 = N.ppf(1-alpha/2)\n",
    "print(\"k1 = %.3f\" % k1)\n",
    "print(\"S  = %.3f\" % S)\n",
    "print(\"k2 = %.3f\" % k2)\n",
    "print(\"k1 < S < k2: %s\" % (\"OK\" if k1 < S and S < k2 else \"FAIL\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'num. samples')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f497804d048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(12)\n",
    "nmax = 100\n",
    "X = N.rvs(size=(nmax))\n",
    "n = np.arange(1,len(X)+1)\n",
    "S = np.cumsum(X)/np.sqrt(n)\n",
    "plt.plot(n, S)\n",
    "\n",
    "alpha = 0.01\n",
    "k1 = N.ppf(alpha/2)\n",
    "k2 = N.ppf(1-alpha/2)\n",
    "plt.plot(n, k1+0*n)\n",
    "plt.plot(n, k2+0*n)\n",
    "plt.grid()\n",
    "plt.ylabel(r\"$\\hat\\mu_n\\sqrt{n}$\")\n",
    "plt.xlabel(\"num. samples\")\n",
    "#plt.gca().set_xscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test má správnou hladinu signifikance pokud je proveden pouze jednou.\n",
    "Opakovaným testováním lze vždy dostat signifikantní výsledek! Případně je nutné provást korekci\n",
    "vypočtené signifikace - viz např https://en.wikipedia.org/wiki/Multiple_comparisons_problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'num. samples')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4977e9c160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(12)\n",
    "#nmax = 1030000\n",
    "nmax = 300\n",
    "X = N.rvs(size=(nmax))\n",
    "n = np.arange(1,len(X)+1)\n",
    "S = np.cumsum(X)/np.sqrt(n)\n",
    "plt.plot(n, S)\n",
    "\n",
    "alpha = 0.01\n",
    "k1 = N.ppf(alpha/2)\n",
    "k2 = N.ppf(1-alpha/2)\n",
    "plt.plot(n, k1+0*n)\n",
    "plt.plot(n, k2+0*n)\n",
    "plt.grid()\n",
    "plt.ylabel(r\"$\\hat\\mu_n\\sqrt{n}$\")\n",
    "plt.xlabel(\"num. samples\")\n",
    "#plt.gca().set_xscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testování hypotéz - neznámé rozdělení testovací statistiky\n",
    "Příklad: hod kostkou"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4977c04128>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4977c04160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ziskane hodnoty:\n",
    "sample = [1, 1, 1, 1, 2, 2, 2, 3, 3, 3]\n",
    "vals = np.arange(1, 7)\n",
    "bins=np.arange(7)+0.5\n",
    "cts, _, _ = plt.hist(sample, bins=bins, normed=True, label=\"data\")\n",
    "cts0 = np.ones(6)/6\n",
    "plt.bar(vals, cts0, color=\"C1\", label=\"H0\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Je ta kostka vyvážená? Můžeme použít chi-square test, ale ten je pouze pro velké počty vzorků. Nebo Kolmogorov-Smirnov, ale ten je zase pouze pro spojité distribuce :-(. Obrázek níže ilustruje výpočet Kolmogorovovy-Smirnovovy statistiky."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4977b1cf60>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4977c04e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf = np.cumsum(cts)\n",
    "cdf0 = np.cumsum(cts0)\n",
    "plt.step(vals, cdf, where=\"post\", label=\"data CDF\")\n",
    "plt.step(vals, cdf0, where=\"post\", label=\"H0 CDF\")\n",
    "iD = np.argmax(np.abs(cdf-cdf0))\n",
    "D = np.abs(cdf-cdf0)[iD]\n",
    "\n",
    "plt.plot([vals[iD]+.5, vals[iD]+.5], [cdf[iD], cdf0[iD]], label=r\"$D=%.2f$\"%D, lw=5)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nebo můžeme provést MC simulaci vyvážené kostky, vypočíst rozdělení testovací statistiky a porovnat s měřením:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsampl = 10000\n",
    "MCsamples = np.random.randint(1, 7, (len(sample), nsampl))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "MC_cts = np.apply_along_axis(lambda a: np.histogram(a, bins=bins, normed=True)[0], 0, MCsamples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "MC_cdf = np.cumsum(MC_cts, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ds = np.max(np.abs(MC_cdf - cdf0[:,np.newaxis]), axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3fEoZcM8PA5cneRZ4C/i1qvrW+Fa9MgPu+TPAl5L8Cr1DIZ+c5B/oktxP7xDeuu68xq3AuwGq6ov0znNsAeaAN4Abh/r4E/zfTpK0ApN+CEiStEwGQJIaZQAkqVEGQJIaZQAkqVEGQJIaZQAkqVEGQJIa9b/+2NXnoIxKnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4977b4e550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, _, _ = plt.hist(Ds, bins=np.linspace(0, 1, 200))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A dostaneme pravděpodobnost, že testovací statistika bude "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0031"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(Ds[Ds>=D])/len(Ds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrap - odhad intervalů spolehlivosti"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4e9KmYyR74NKmasstu1/8av58qIKXXupWnwyWkTaE/4SkEXjDGwYHRxcs6FY/bx4sXQp7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\nMsAlqVH/H2WQxjd6uekqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa0b46b7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(12)\n",
    "x = np.concatenate([np.random.exponential(size=200), np.random.normal(size=100)])\n",
    "plt.hist(x, 25, histtype='step');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7ffa0b314f28>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa0b679cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = len(x)\n",
    "reps = 10000\n",
    "xb = np.random.choice(x, (n, reps), replace=True)\n",
    "mb = xb.mean(axis=0)\n",
    "mb.sort()\n",
    "\n",
    "plt.hist(x, 25, histtype='step');\n",
    "plt.axvline(np.mean(x), c=\"r\", lw=2)\n",
    "alpha = 0.01\n",
    "perc = np.percentile(mb, [100*alpha/2, 100*(1-alpha/2)])\n",
    "plt.axvline(perc[0], c=\"r\", lw=2, ls=\"--\")\n",
    "plt.axvline(perc[1], c=\"r\", lw=2, ls=\"--\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xb = np.random.choice?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xb = np.random.choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}