2-5. 가설 검정 - 모분산, 정규성.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dca8ccfd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pandas 0.25.1\n",
      "numpy 1.18.5\n",
      "scipy 1.5.2\n",
      "matplotlib 3.5.3\n",
      "seaborn 0.12.2\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as  sns\n",
    "\n",
    "for i in [pd, np, scipy, mpl, sns]:\n",
    "    print(i.__name__, i.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f52bdfd5",
   "metadata": {},
   "source": [
    "# 2-5-1 가설 검정 - 모분산"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0edb8506",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import chi2, f, expon, norm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0bf487b",
   "metadata": {},
   "source": [
    "## 1. 단일 모집단 분산 검정\n",
    "\n",
    "모분산($\\sigma^2$)에 대한 검정입니다.\n",
    "\n",
    "$H_0: \\sigma^2 = \\sigma^2_0$\n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\sigma^2 < \\sigma^2_0$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\sigma^2 > \\sigma^2_0$$|우측 꼬리(right)|\n",
    "|$$H_1: \\sigma^2 \\ne \\sigma^2_0$$|양쪽 꼬리(two-sided)|\n",
    "\n",
    "\n",
    "모분산과 표본분산이 아래와 같은 성질이 있음을 이용합니다.\n",
    "\n",
    "$(n-1)\\frac{S^2}{\\sigma^2} \\sim \\chi^2_{n-1}$, $n$은 표본수입니다.\n",
    "\n",
    "**가정**\n",
    "\n",
    "모집단은 정규 분포를 따릅니다.\n",
    "\n",
    "표본은 서로 독립입니다.\n",
    "\n",
    "$H_0: \\frac{\\sigma^2}{\\sigma^2_0} = 1$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\frac{\\sigma^2}{\\sigma^2_0} < 1$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\frac{\\sigma^2}{\\sigma^2_0} > 1$$|우측 꼬리(right)|\n",
    "|$$H_1: \\frac{\\sigma^2}{\\sigma^2_0} \\ne 1$$|양쪽 꼬리(two-sided)|\n",
    "\n",
    "    ※ 카이제곱분포는 비대칭 분포입니다.\n",
    "       따라서 양측 검정할 때에 pvalue는 어림수(좌측과 우측 확률 중 작은(0.5 이하)×2)가 됩니다.\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$H_0$ 가 맞다면, \n",
    "\n",
    "> $\\frac{\\sigma^2}{\\sigma^2_0} = 1$\n",
    "\n",
    "확률 분포와 검정 통계량\n",
    "\n",
    "> $X^2=(n-1)\\frac{S^2}{\\sigma_0^2} \\sim \\chi^2(n-1)$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e424551",
   "metadata": {},
   "source": [
    "**[Ex.1]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "레이저를 이용한 거리 측정기를 개발 중에 있습니다. \n",
    "\n",
    "기존에 거리 측정기의 품질 합격 기준은 100m 거리를 재었을 때, \n",
    "\n",
    "유의 수준 5%로 거리의 표준편차가 0.25m 이내여야 통과가 됩니다. \n",
    "  \n",
    "모의로 100m에서 거리를 측정 했을 때의 실험 결과가 아래와 같습니다. \n",
    "\n",
    "100m 지점에서 측정된 거리는 정규 분포를 따른 다고 가정합니다. 이 때, 통과 여부를 판단해 봅니다.\n",
    "\n",
    "```\n",
    "99.674, 100.299, 100.085, 99.548, 99.826, 100.495, 99.272, 99.871, 100.380, 99.740, \n",
    "99.796, 99.972, 100.447, 99.808, 99.867, 99.870, 100.662, 100.656, 100.301, 100.116, \n",
    "100.221, 100.447, 99.719, 100.353, 99.624, 99.809, 100.272, 99.571, 99.958, 99.741\n",
    "```\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d68bf5a4",
   "metadata": {},
   "source": [
    "$H_0: \\sigma = 0.25$\n",
    "\n",
    "$H_1: \\sigma < 0.25$\n",
    "    \n",
    "$X^2=(n-1)\\frac{S^2}{0.25^2} \\sim \\chi^2(n-1)$\n",
    "\n",
    "**좌측 검정** 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0f61ee4b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(Chi2): 58.864714666667, pvalue: 0.9991467927097515\n"
     ]
    }
   ],
   "source": [
    "X = [\n",
    "    99.674, 100.299, 100.085, 99.548, 99.826, 100.495, 99.272, 99.871, 100.380, 99.740, \n",
    "    99.796, 99.972, 100.447, 99.808, 99.867, 99.870, 100.662, 100.656, 100.301, 100.116, \n",
    "    100.221, 100.447, 99.719, 100.353, 99.624, 99.809, 100.272, 99.571, 99.958, 99.741\n",
    "]\n",
    "S_sq = np.var(X, ddof=1)\n",
    "n = len(X)\n",
    "Chi2 = (n - 1) * S_sq / (0.25 ** 2)\n",
    "print(\"검정통계량(Chi2): {}, pvalue: {}\".format(Chi2, chi2.cdf(Chi2, df= n -1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6340309d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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WcCUEAGhuBt5+29Kam0VXQ+T2GBqoT5xtnQQZri6Fp8JxDx6yzms4XqEVXAkRkeNhaKA+cb7CAAAYpikRXMmN3da6guK0IQyNhsuCqyEicixdCg1r1qxBREQEtFot4uLicOjQoRv237p1K6KioqDVahEdHY2dO3det+9vfvMbSJKEVatWdaU0clDW0BChuSS4khu7xaMMgcpqtECFU3mZosshInIodoeGLVu2ICkpCcuXL8eRI0cQExODxMRElJWVddh///79mDVrFubPn4+jR49ixowZmDFjBrKzs6/p++WXX+LAgQMICwuz/5uQQ7PdaVA77nwGAJAkYKyXZRLkyXMFYoshInIwdoeGd955B08//TTmzZuH0aNHY926dfDy8sKHH37YYf/33nsP06ZNw+LFizFq1Ci8+uqruP3227F69ep2/UpKSvD888/j448/hoeHR9e+DTmstjsNFwVXcnPRrSsoTlwyCK6EiMix2BUajEYjMjMzkZCQ0PYBCgUSEhKQnp7e4XvS09Pb9QeAxMTEdv3NZjNmz56NxYsXY8yYMTeto6mpCXq9vl0jx2UyyyistPwCHurgcxoAYKznWQDAiUqN4EqIiByLXaGhoqICJpMJISEh7Z4PCQmBTqfr8D06ne6m/d944w2oVCr87ne/61QdycnJ8Pf3t7Xw8HB7vgb1sYvVDTCaZKglI8I8KkSXc1PWOw159QPRaOA5FEJ5egLZ2ZbGbaSJhBO+eiIzMxPvvfceNmzYAEmSOvWepUuXoqamxtaKi4t7uUrqDuvQxBD1JSgls+Bqbi7Moxz9lTVogQpn8o6ILse9KRTAmDGWphD+xxWR27Prv8KgoCAolUqUlpa2e760tBShoaEdvic0NPSG/ffu3YuysjIMHjwYKpUKKpUKhYWF+K//+i9EXGfPeY1GAz8/v3aNHJc1NAx18JUTVpIE286QJ84XiC2GiMiB2BUa1Go1xo8fj7S0NNtzZrMZaWlpiI+P7/A98fHx7foDQGpqqq3/7Nmzcfz4cWRlZdlaWFgYFi9ejG+++cbe70MOqC00OP4kSCvrvIaTF7kzpFBGI7BihaVxG2ki4ew+5TIpKQlz587FhAkTMGnSJKxatQoGgwHz5s0DAMyZMweDBg1CcnIyAGDhwoWYOnUqVq5cienTp2Pz5s3IyMjA+vXrAQCBgYEIDAxs9zM8PDwQGhqKW2+9tbvfjxyALTQ4+HLLK0W3Lrs8UclxdKGam4H//m/L48WLAbVabD1Ebs7u0DBz5kyUl5fjlVdegU6nQ2xsLFJSUmyTHYuKiqC4YuxxypQp2LRpE15++WW8+OKLiIyMxLZt2zB27Nie+xbk0AoqnGflhJV1eCK3YSCaDBXQeAcJroiISDxJlmVZdBHdpdfr4e/vj5qaGs5vcDDGFjOiln0NswwcGjUbwR7OsTWzLAPjTm1CtckP22epcVvMf4ouyT0ZDICPj+VxXR3g7S22HiIXZM/vUE5Hpl5VVFUPswx4K+oxQOUcgQGwTIaM5mRIIqJ2GBqoV1mHJiLUl9DJFbUOwzoZMvtineBKiIgcA0MD9SrbJEit86ycsLLeacjmzpBERAAYGqiXnXOSg6o6Yl1BkVMfBmO98wytEBH1FoYG6lUFTnRQ1dVu8SiFv7IWRtkDufncGVIIrRY4dMjStFrR1RC5PYYG6lXnKyzzAZxpuaWVZWfI1sOrzp8XXI2bUiqBiRMtTakUXQ2R22NooF5Tb2yBTt8EABiqdr47DcAV20lzMiQRkf2bOxF1VkFFPQCgn7IGASrn/KVrmwxZwZ0IhTAagffeszxeuJA7QhIJxjsN1Guc8cyJq1lDw5n6MDQ3Vostxh01NwN/+IOlNTeLrobI7TE0UK8pqLROgtQJrqTrBqt18FPWtU6GzBJdDhGRUAwN1GvOlVuXWxYLrqTrrpwMmX3unOBqiIjEYmigXmNdOeGMyy2vZJvXcFEvuBIiIrEYGqjXOOPplh0ZY112ycmQROTmGBqoV9TUN6Oq3jJxLUJ9SXA13WNddnnaEIqWJudcBUJE1BMYGqhXnG+dBBmiqoS3slFwNd0Tob4EH0U9mmQNzp7LEl0OEZEwDA3UK5x5J8irKSQZo61DFOfyBVfjZrRa4PvvLY3bSBMJx9BAveJ868ZOEZpSwZX0DNsKipIawZW4GaUSuPtuS+M20kTCMTRQryhqHZ4Y4oSnW3bEGhpOVvAXFxG5L24jTb2isMpyp2GI2nk3drqSddnlybpQmJobofTgrfI+0dwMrF9vefzrXwMeHmLrIXJzvNNAvcJ6p2GwxrlXTlgN05RAKzWi3uyJ8wXHRJfjPoxGYMECSzMaRVdD5PYYGqjH1TW1oNJgWW45xMmXW1opJTNGe1qOxz55NldwNUREYjA0UI8rbL3L0F9ZA19lg+Bqeo51XsOJC5cFV0JEJAZDA/W4wkrLfAZXGZqwsm7ylF0uCa6EiEgMhgbqcdbQMETtGsstrWwrKGpDYG7h+DoRuR+GBupxRVXW5ZbOfVDV1SK1RVBLRtSavVFUdEJ0OUREfY6hgXqc7U6Diw1PeEgmjNIWAACy88+ILYaISACGBupxbcMTrhUagLYTL7MvVAquxE1oNMCOHZam0YiuhsjtcXMn6lFNLSZcqrGsmBjsgqGhbTKk4ELchUoFTJ8uugoiasU7DdSjLlxugFkGvBQNGKCqFl1Oj7OdQaEPhmxqFlwNEVHfYmigHlVkXW6p1kFywZWJt2oLoEILqk2+KLlwSnQ5rq+5GdiwwdKaGdKIRGNooB5l3dhpiIucbnk1jaIFI7WFAIDs/NOCq3EDRiMwb56lcRtpIuEYGqhHtR1U5VrLLa9kG6K4wIkNROReGBqoR7UNT7jeJEgr64mXJ0plwZUQEfUthgbqUW13Glw3NIz1al1BoQ+CbGoRXA0RUd9haKAeYzbLV+wG6bqhYZS2AEqYUNnij4slnNdARO6DoYF6jE7fCGOLDBVaEKZ23fF+rcJomwx5Ip8rKIjIfTA0UI+x7gQ5SF0GlWQWXE3vss1rKHLdcEREdDWGBuoxtqEJjU5wJb0v2isPAHCizLXDkXAaDfDpp5bGbaSJhOM20tRj2s6ccIPQYNsZcgBkswmSQim4IhelUgGPPiq6CiJqxTsN1GPcYY8GqyjteajQgqoWP5RwMiQRuQmGBuox1t0gXXmPBiutorltZ8g8TobsNS0twNatltbC5a1EonUpNKxZswYRERHQarWIi4vDoUOHbth/69atiIqKglarRXR0NHbu3Nnu9RUrViAqKgre3t7o168fEhIScPDgwa6URoLIstw2POEGcxoA4LbW/RqOczJk72lqAh57zNKamkRXQ+T27A4NW7ZsQVJSEpYvX44jR44gJiYGiYmJKCsr67D//v37MWvWLMyfPx9Hjx7FjBkzMGPGDGRnZ9v6jBw5EqtXr8aJEyewb98+RERE4N5770V5Of8wdhbV9c2obbT8TXCwG8xpANqOyeZkSCJyF5Isy3bthRsXF4eJEydi9erVAACz2Yzw8HA8//zzWLJkyTX9Z86cCYPBgB07dtiemzx5MmJjY7Fu3boOf4Zer4e/vz++++473HPPPTetydq/pqYGfn5+9nwd6iFZxdWYseZHBKsqcWj0XNHl9Inj9SPwQP4q9FPqceTVxzgZsjcYDICPj+VxXR3g7S22HiIXZM/vULvuNBiNRmRmZiIhIaHtAxQKJCQkID09vcP3pKent+sPAImJidftbzQasX79evj7+yMmJqbDPk1NTdDr9e0aiWWdzxDhJkMTgOWYbA+pGZdNfrhwgZMhicj12RUaKioqYDKZEBIS0u75kJAQ6HQd/7LQ6XSd6r9jxw74+PhAq9Xi3XffRWpqKoKCgjr8zOTkZPj7+9taeHi4PV+DekHbQVXuExo0ihbcysmQRORGHGb1xE9/+lNkZWVh//79mDZtGh577LHrzpNYunQpampqbK24uLiPq6WrFVS6z3LLK1l3hjxe3PH/V4mIXIldoSEoKAhKpRKlpaXtni8tLUVoaGiH7wkNDe1Uf29vb4wYMQKTJ0/G3//+d6hUKvz973/v8DM1Gg38/PzaNRLLuhukOyy3vFK0p2VnyGwek01EbsCu0KBWqzF+/HikpaXZnjObzUhLS0N8fHyH74mPj2/XHwBSU1Ov2//Kz23iEiun4W7LLa1sdxr0A3hMdm9Qq4GPPrI0tVp0NURuz+5tpJOSkjB37lxMmDABkyZNwqpVq2AwGDBv3jwAwJw5czBo0CAkJycDABYuXIipU6di5cqVmD59OjZv3oyMjAysX78eAGAwGPDaa6/hgQcewMCBA1FRUYE1a9agpKQEj3L7WKfQYDShrNYS8Fz5SOyOjNQWQi01o8bkiwvF2QiPiBVdkmvx8ACefFJ0FUTUyu7QMHPmTJSXl+OVV16BTqdDbGwsUlJSbJMdi4qKoFC03cCYMmUKNm3ahJdffhkvvvgiIiMjsW3bNowdOxYAoFQqcebMGWzcuBEVFRUIDAzExIkTsXfvXowZM6aHvib1pqLW7aN9FXUIUNYKrqZvWSZDFuBEQyRO5J9maCAil2b3Pg2OiPs0iPXtSR1+/X+ZGOuZjx2Ri0SX0+devPAcNlXdh9/ceg5L5j0vuhzX0tICfPON5XFiouUAKyLqUfb8DuV/gdRtRbaDqkpv0tM1Wec1ZJc5ff52PE1NwM9+ZnlcV8fQQCSYwyy5JOdVaNujwb3mM1hFe1lWUBzXh0A2GQVXQ0TUexgaqNvc6UjsjtyqLYRGaoLe5IPzBcdEl0NE1GsYGqjbiqxHYmvc806Dh2TCWM+zAIBjuTmCqyEi6j0MDdQtLSYzLlxuAAAMcaMtpK8W45ULADhWfFlwJUREvYehgbrlUk0jWswy1FIzQj0qRZcjTIynJTRklfOkSyJyXQwN1C3WSZC3qHVQSmbB1YgT23qn4VRdGIyNdYKrISLqHVy/RN1S2HrmhLsut7QarNahn7IGl03+OJOXiduip4ouyTWo1cDq1W2PiUgo3mmgbily0zMnriZJQEzr0sus/HOCq3EhHh7Ac89ZmoeH6GqI3B5DA3WL7aAqdYngSsSzzWso4fAEEbkmDk9Qt7Tt0eCeyy2vZJ3XcKzSS3AlLsRkAvbutTz+yU8AJSeaEonE0EBdJsty2x4Nbrzc0uq21tBwtiEU+poy+PkHC67IBTQ2Aj/9qeVxXR3g7S22HiI3x+EJ6rJKgxEGowkSzAhnaECgSm+7DifOHBFcDRFRz2NooC6zzmcY6FEBjaJFcDWOwTav4Xyx4EqIiHoeQwN1WVEVhyauZp3XkHWxUXAlREQ9j6GBusy2ckLj3ns0XCnWy3L2RNbl/pDN7rvZFRG5JoYG6rIi25HY7nm6ZUfGeJ6DEiaUNwdAp8sTXQ4RUY9iaKAu43LLa3kqmnCrtgAAcOzMcbHFEBH1MC65pC4rrLRuIc3QcKUYr1ycahyOrMJSTBNdjLPz8ADefLPtMREJxdBAXWJoakFFnREAMNjNt5C+WqxXLj6pug9ZnOrRfWo1sHix6CqIqBWHJ6hLilqHJgKUevgrDYKrcSzWZZcn9KEwNXMVBRG5DoYG6pK2Myd4l+FqkdpieCkaYDB7Ii8/U3Q5zs1kAg4ftjSTSXQ1RG6PoYG6xLZHA5dbXkMpmW37NWTmcgVFtzQ2ApMmWVoj79oQicbQQF3SdqeByy07MsHrFAAgs7hWcCVERD2HoYG6xDqnYTBXTnTodu/TAIDMch/BlRAR9RyGBuqStjsNDA0dGeeVAwlmFDYFo7y8SHQ5REQ9gqGB7GZsMePCZUtoiNAwNHTEX2nASK0lLBw5xRMvicg1MDSQ3Yov18MsA16KBgSrqkSX47Bu92odojjHYEVEroGhgexWUNG2E6QkCS7GgY23hoZLvEhE5Bq4IyTZ7XxraBjKoYkbmtA6GfJEbSiamhqg0XgKrsgJeXgAy5e3PSYioRgayG4FldbQwOWWNzJEfQmBympUmgKQffowxsfeJbok56NWAytWiK6CiFpxeILsVlDROglSfUFwJY5Nkq5Yepl3VnA1RETdx9BAdmsbnuCdhpuZYJ3XcKFecCVOymwGTp60NLNZdDVEbo/DE2SXxmYTLtY0AAAiGBpuarz1TkNlP8hmMyQFc7pdGhqAsWMtj+vqAG9vsfUQuTn+CUZ2Ka6qhywDvgoDApU1ostxeGM986GWmlHR4o+iC7miyyEi6haGBrKLdWgiQnORyy07QatoxljPfABA5qksscUQEXUTQwPZpS00cLllZ1n3a8goqBBcCRFR9zA0kF3allsyNHSWdV7DkTKN4EqIiLqHoYHsYrvTwOWWnWbdTjqnPhT6aoYtInJeDA1kl7Y9GrhyorOCPaoxWH0JMhQ4kn1IdDlERF3GJZfUaQ1GE3T6RgDco8FeE71Posg4EIfyL+DuO0VX40Q8PIDf/77tMREJ1aU7DWvWrEFERAS0Wi3i4uJw6NCN//a0detWREVFQavVIjo6Gjt37rS91tzcjD/+8Y+Ijo6Gt7c3wsLCMGfOHFy8yF9KjsY6n8FfWYt+qlrB1TiXyd4nAAAHLvLmnl3UauCttyxNrRZdDZHbs/tPsC1btiApKQnLly/HkSNHEBMTg8TERJSVlXXYf//+/Zg1axbmz5+Po0ePYsaMGZgxYways7MBAPX19Thy5AiWLVuGI0eO4IsvvkBOTg4eeOCB7n0z6nEFtvkMDHT2muxjCQ3H9WEwGLi/BRE5J0mWZdmeN8TFxWHixIlYvXo1AMBsNiM8PBzPP/88lixZck3/mTNnwmAwYMeOHbbnJk+ejNjYWKxbt67Dn3H48GFMmjQJhYWFGDx48DWvNzU1oampyfbver0e4eHhqKmpgZ+fnz1fh+zw1935eDMlBzMC9mDV4LdEl+N07jj9d5Q0h+AfD3ngrrh7RZfjHMxmoKjI8njwYIA7ahL1OL1eD39//079DrXrv0Cj0YjMzEwkJCS0fYBCgYSEBKSnp3f4nvT09Hb9ASAxMfG6/QGgpqYGkiQhICCgw9eTk5Ph7+9va+Hh4fZ8Deoi250GTYngSpyT9W5Dek6h4EqcSEMDMHSopTU0iK6GyO3ZFRoqKipgMpkQEhLS7vmQkBDodLoO36PT6ezq39jYiD/+8Y+YNWvWdRPP0qVLUVNTY2vFxcX2fA3qIuvKiaFqhoauiPc+DgA4cIEHLxGRc3Ko1RPNzc147LHHIMsy1q5de91+Go0GGg03yulr5yvbtpAm+8X5WObxHNcPhMGgh7c3h9KIyLnYdachKCgISqUSpaWl7Z4vLS1FaGhoh+8JDQ3tVH9rYCgsLERqairnJjiYuqYWlNda5pEwNHRNuLoMt3joYIISGScOii6HiMhudoUGtVqN8ePHIy0tzfac2WxGWloa4uPjO3xPfHx8u/4AkJqa2q6/NTDk5eXhu+++Q2BgoD1lUR+wzmcIVFbDX2kQXI3zss5rOJBbILYQIqIusHsqclJSEj744ANs3LgRp0+fxrPPPguDwYB58+YBAObMmYOlS5fa+i9cuBApKSlYuXIlzpw5gxUrViAjIwMLFiwAYAkMv/jFL5CRkYGPP/4YJpMJOp0OOp0ORqOxh74mdVcBhyZ6RLx1MuQFuxYtERE5BLvnNMycORPl5eV45ZVXoNPpEBsbi5SUFNtkx6KiIiiuWBY1ZcoUbNq0CS+//DJefPFFREZGYtu2bRg7diwAoKSkBNu3bwcAxMbGtvtZ33//Pe6+++4ufjXqSW0rJzqewEqdE9e6ydMJfSjqDLXw8fYVXBERUed1aSLkggULbHcKrrZ79+5rnnv00Ufx6KOPdtg/IiICdm4VQQKc58qJHnGLuhzhah2KjaHIyD6Iu+MSbv4md6ZSAb/9bdtjIhKK/xVSp7QNTzA0dNdk7xMoNobiQM553B0nuhoHp9EAa9aIroKIWnF7NeqUgoo6AJzT0BPifbhfAxE5J4YGuqmahmZUGpoBABHqS4KrcX5x3pb9Gk7oB6KurkpwNQ5OloHyckvjMCaRcAwNdFPnyi13GYJVlfBRcivf7hqkLsdg9SWYoMThY/tFl+PY6uuB4GBLq68XXQ2R22NooJvKK7OEhkjtBcGVuA7rUdk8h4KInAlDA91Uvi008IyPnnKHTxYA4IcLarGFEBHZgaGBbsoaGkZo+LfinvIT3yxIMONMfRhKy3hdicg5MDTQTeWV1QIAIjVFgitxHf1VetzmmQcA2JPJcyiIyDkwNNAN1RtbcOGyZfLjCA5P9KipvpkAgD15XEFBRM6BoYFu6Fy5AbIM9FfWIFClF12OS5nqewQAsK+0H1paTIKrISK6Oe4ISTdkm8+g5dBET4vxyoW/shY1Jl8cy8nC+DHjRZfkeFQqYO7ctsdEJBTvNNAN2eYzaLl9dE9TSWbc6XMUALDn2AnB1TgojQbYsMHSNBrR1RC5PYYGuqG8UuvKCd5p6A3WIYo9Bc2CKyEiujmGBroh2x4NXG7ZK6yh4bg+FFXVnBB5DVkGDAZL4zbSRMIxNNB1NbWYUFhl2bqXGzv1jhCPKkRpz0OGAnuP/Ci6HMdTXw/4+Fgat5EmEo6hga6roKIeJrMMX0UdglX8W3BvsS29PMMTRInIsTE00HVZJ0GO0F6AJAkuxoVZQ8MPl3xhNvG4bCJyXAwNdF3WSZA8qKp3TfA6DS9FAyqa/XEqn6soiMhxMTTQdbVNguTKid6kVrRgis8xAMCerEzB1RARXR9DA10XD6rqO9Yhit3njIIrISK6PoYG6lCLyYxzFdbdILlyorf9h28GACCzJgwVlTrB1RARdYyhgTpUWFWPZpMMT6kRgzzKRZfj8gapy3GbZy7MUOK7gz+ILsdxKJXAL35haUql6GqI3B5DA3XIthOkthgKiZvq9IVE/3QAwNenLwuuxIFotcDWrZam1YquhsjtMTRQh86Wc+VEX5vmtx8AsL8iFDV1dYKrISK6FkMDdSiv1LJHw3AN5zP0leHaEkRqCtEsq/D94X2iyyEiugZDA3Uoj2dOCDGtdYgi5QTv8ACwnDkhSZZmMIiuhsjtMTTQNcxm+YrhCd5p6EuJ/pYhit26/mho5PJLInIsDA10jZLqBjQ2m6GWjAhXc/lfXxqjPYdbPHRoNGuwJ5NDFETkWBga6BrWMyeGaUqgkngWQl+SpLYhim+OnRVcDRFRewwNdI1TF/UAgJEcmhBiWusQxXclATA2twiuhoioDUMDXSO7xBIaoj3zBFfinm73OoMBqirUmryQnrVfdDlERDYMDXSN7Is1AICxnvmCK3FPCknGvX4HAAApR3MEV0NE1IahgdqprjfiwuUGAMBoz3OCq3Ff1iGK1CIftLS48RCFUgncf7+lcRtpIuEYGqidk63zGYaoL8JfyXXxokz2OYF+yhpUtPhhX+Ze0eWIo9UCX31ladxGmkg4hgZq50SJdWiCdxlE8pBMeCDAcnDV54c5t4SIHANDA7WT3RoaxjA0CPdIvzQAwLclA6CvrxdcjXgrVqyAJEntWlRUlO11nU6H2bNnIzQ0FN7e3rj99tvx+eef3/AzTSYTli1bhqFDh8LT0xPDhw/Hq6++Clluf0jb6dOn8cADD8Df3x/e3t6YOHEiioqKrvk8WZZx3333QZIkbNu2rUe+N5EjYWigdqzDE9GeuYIroWjPfERqCtEkq/HV3u9FlyOGwQB4e1ua0YgxY8bg0qVLtrZvX9sGWHPmzEFOTg62b9+OEydO4OGHH8Zjjz2Go0ePXvfj33jjDaxduxarV6/G6dOn8cYbb+DNN9/E+++/b+tz9uxZ3HnnnYiKisLu3btx/PhxLFu2DNoOhktWrVoFSZJ69hoQORCV6ALIcdQ2NuN8hWUeA+80iCdJwCP9duF13Tx8nlWGWYmiKxLkirssKpUKoaGhHXbbv38/1q5di0mTJgEAXn75Zbz77rvIzMzEuHHjrvueBx98ENOnTwcARERE4JNPPsGhQ4dsfV566SXcf//9ePPNN23PDR8+/JrPysrKwsqVK5GRkYGBAwfa/z2JnADvNJCNdVOnQR5l6K/SC66GAOChft9DARMyLgejQFcmuhzh8vLyEBYWhmHDhuGJJ55oN0QwZcoUbNmyBVVVVTCbzdi8eTMaGxtx9913X/fzpkyZgrS0NOTmWu6sHTt2DPv27cN9990HADCbzfjqq68wcuRIJCYmIjg4GHFxcdcMPdTX1+OXv/wl1qxZc91QQ+QKGBrIJrs1NIzx5PbFjiLEowp3+mQBAL7Y46ZDFK3iJk7Ehg0bkJKSgrVr1+L8+fP4yU9+gtpay7bnn376KZqbmxEYGAiNRoNnnnkGX375JUaMGHHdz1yyZAkef/xxREVFwcPDA+PGjcOiRYvwxBNPAADKyspQV1eH119/HdOmTcO3336Lhx56CA8//DD27Nlj+5wXXngBU6ZMwYMPPti7F4FIMA5PkI11EuRYr/OCK6ErPdIvDT/Ujcfnp1uwyCxDoXDPMfP77r3XMrcBwG233Ya4uDgMGTIEn376KebPn49ly5ahuroa3333HYKCgrBt2zY89thj2Lt3L6Kjozv8zE8//RQff/wxNm3ahDFjxiArKwuLFi1CWFgY5s6dC7PZcvbKgw8+iBdeeAEAEBsbi/3792PdunWYOnUqtm/fjl27dt1w7gSRq+jSnYY1a9YgIiICWq0WcXFx7cb/OrJ161ZERUVBq9UiOjoaO3fubPf6F198gXvvvReBgYGQJAlZWVldKYu6yRYatJwE6UgS/Q/AV2FASWMADp7MEl2OwwgICMDIkSORn5+Ps2fPYvXq1fjwww9xzz33ICYmBsuXL8eECROwZs2a637G4sWLbXcboqOjMXv2bLzwwgtITk4GAAQFBUGlUmH06NHt3jdq1Cjb0MiuXbtw9uxZBAQEQKVSQaWy/F3skUceueHQCJEzsjs0bNmyBUlJSVi+fDmOHDmCmJgYJCYmoqys4/HW/fv3Y9asWZg/fz6OHj2KGTNmYMaMGcjOzrb1MRgMuPPOO/HGG290/ZtQt9QbW3C2vA4At492NFqFEdMDLKsEPt9/RHA1jqOurg5nz57FwIEDUd86WVKhaP9HmlKptN0t6Eh9ff0N36NWqzFx4kTk5LTfzjs3NxdDhgwBYBniOH78OLKysmwNAN5991189NFH3fqORI7G7uGJd955B08//TTmzZsHAFi3bh2++uorfPjhh1iyZMk1/d977z1MmzYNixcvBgC8+uqrSE1NxerVq7Fu3ToAwOzZswEABQUFnaqhqakJTU1Ntn/X6zlpr7tOX6qFWQaCVZUI9qgWXQ5d5ZF+adhclYivC/3xP42N8HKX3REVCmDqVADA7196CT9/6CEMGTIEFy9exPLly6FUKjFr1iwEBARgxIgReOaZZ/D2228jMDAQ27ZtQ2pqKnbs2GH7uHvuuQcPPfQQFixYAAD4+c9/jtdeew2DBw/GmDFjcPToUbzzzjt46qmnbO9ZvHgxZs6cibvuugs//elPkZKSgn//+9/YvXs3ACA0NLTDyY+DBw/G0KFDe/HiEPU9u+40GI1GZGZmIiEhoe0DFAokJCQgPT29w/ekp6e36w8AiYmJ1+3fGcnJyfD397e18PDwLn8WWZy8yJ0gHdkEr1MYor4Ig9kT2/ekii6n73h6Art3A7t344JOh1mzZuHWW2/FY489hsDAQBw4cAADBgyAh4cHdu7ciQEDBuDnP/85brvtNvzjH//Axo0bcf/999s+7uzZs6ioqLD9+/vvv49f/OIX+O1vf4tRo0bh97//PZ555hm8+uqrtj4PPfQQ1q1bhzfffBPR0dH429/+hs8//xx33nlnX14JIodg152GiooKmEwmhISEtHs+JCQEZ86c6fA9Op2uw/46nc7OUtssXboUSUlJtn/X6/UMDt3ESZCOTZKAJwK/xp8vzcdHh6sw817Z7TYR2rx58w1fj4yMvOkOkFffzfT19cWqVauwatWqG77vqaeeanf34Wau3lGSyFU45ZJLjUYDPz+/do2650RJ63JLToJ0WDP7fQsvRQNy6oKQnn1cdDlE5IbsCg1BQUFQKpUoLS1t93xpael1NzQJDQ21qz/1vcZmE/JKLWvdozkJ0mH5qwy28yg+/N5NlvcZDMCAAZZm4KmrRKLZFRrUajXGjx+PtLQ023NmsxlpaWmIj4/v8D3x8fHt+gNAamrqdftT38strUWLWUZ/ZQ0GelTc/A0kzJOB/wYApF0MRGFppeBq+khFhaURkXB2D08kJSXhgw8+wMaNG3H69Gk8++yzMBgMttUUc+bMwdKlS239Fy5ciJSUFKxcuRJnzpzBihUrkJGRYZu9DABVVVXIysrCqVOnAAA5OTnIysrq1rwH6rzskradIN1smNzpDNeWYKpvBmQosCE17eZvICLqQXaHhpkzZ+Ltt9/GK6+8gtjYWGRlZSElJcU22bGoqAiXLl2y9Z8yZQo2bdqE9evXIyYmBp999hm2bduGsWPH2vps374d48aNsx0a8/jjj2PcuHG2JZnUu44VVwMAxnpx5YQzeCpoOwBg62klahuMgqshInciyS4wzVev18Pf3x81NTWcFNkFU9/8HoVV9fgwYgX+wy9DdDl0E7IMJOSuxdmmcCy/S8K8K5YUuhyDAfDxsTyuq7NtI01EPcee36FOuXqCes7F6gYUVtVDCRMmep8UXQ51giQBT7bebdhwuAoms9PnfiJyEgwNbu7AOctkurGe+fBVNgiuhjrrkX674KesQ2FDP+w63PWN0oiI7MHQ4ObSz1pCw2Qf3mVwJl6KJvyy/9cAgL/synfdzYQUCmDCBEtT8I8rItH4X6GbO3DeEhrifbLEFkJ2e3rAl/BSNOBETSC+zXDRg6w8PYHDhy3N01N0NURuj6HBjV24XI/iqgYoYcIEr9OiyyE7Bar0eCroXwCAd749w7kNRNTrGBrc2IFzVQCA27zy4MP5DE7p6aAv4auoQ05tAHYczBRdDhG5OIYGN2adzxDvc0JwJdRV/ioDnhnwBQBg1Xd5aDGZBVfUw+rrgYgIS6uvF10NkdtjaHBTsizbVk5M9mZocGZPBv0b/ZU1OG/wwxc/HhZdTs+SZaCw0NJcdbInkRNhaHBTFy43oKS6ASq0YAL3Z3BqPsoGPBv8GQDgvV3n0dRiElwREbkqhgY3ZR2aiPHKhZeiSXA11F2zA79CsKoSJY2+2JK2S3Q5ROSiGBrcVPo563yGbMGVUE/QKox4PngLAODdvZdRVdcouCIickUMDW7oyvkM8d7HBFdDPeXxwG8QpT2Pyy3e+POnO0WXQ0QuiKHBDRVW1uNSTSM8pGbc7n1GdDnUQzwkE14btAYSzPgsV4MDOUWiSyIiF8PQ4IasQxPjvHLgyfkMLmW89xnM6v8NAOClz9Kdf1KkJAGjR1uaJImuhsjtMTS4IdtSS85ncEl/DN2AINVlnK31wQff7BNdTvd4eQEnT1qal5foaojcHkODmzG2mLEnpxwA5zO4Kn+VAcsG/g0A8P6Pl1FYXiO4IiJyFQwNbmZvXjmqG5oRpLqMSdyfwWU9ELAHd/ocRZPZAy99vBNmnktBRD2AocHNbD92EQDw84B9UEoutuUw2UgS8KdBf4VGasI+nR/+11mHKerrgTFjLI3bSBMJx9DgRuqNLfj2ZCkA4MGA7wVXQ70tQnMJK8LWAwDe3nMZh8/qBFfUBbIMnDpladxGmkg4hgY3knqqFA3NJgxRX0SMZ67ocqgPPN7/G8wI+B4mKLHg/35EZR1XyxBR1zE0uJHtWZahiQf77eXqNTchScBrg9ZguKYYpY1avLAxhfMbiKjLGBrcxGWDEXtyLasmHvDn0IQ78VY24q9DXodWasIPxSr89ZsDoksiIifF0OAmdmZfQotZxhhtPkZoL4guh/rYrdpC/M+gtQCAd/ZU4JusfMEVEZEzYmhwE1cOTZB7eqz/d5jVPwVmKPD8lpPYn1cquiQicjIMDW7gYnUDDhVUAQB+5r9HcDUk0quD/op7/dJhlFV4ekM6jhdfFl3SjUkSMGSIpXEiDpFwDA1uYMfxi5BlYJL3CYSpK0SXQwKpJDP+MvhNTPE5BoPJA09+sBv5pbWiy7o+Ly+goMDSuI00kXAMDW7gXxyaoCtoFc1YP+RPuM0zF1VGNWb/byqKKg2iyyIiJ8DQ4OL251fg5EU9PKRm3O/H0EAWPsoGfDR0BYZpinGpXoOH//ItjhU5+FAFEQnH0ODCZFnGGylnAAC/7P8N+qkc+DY09blAlR6fDHsJo7VnUdGkxsz/3YvUk5dEl9VeQwMwcaKlNTSIrobI7TE0uLCUbB2OXaiBl6IBC4I3iy6HHFCIRxU+Hb4EU30z0GhS4pn/y8A/9jnQbqFmM5CRYWlmnpVCJBpDg4tqMZnx1rc5AID/N2A7BnhUiy2IHJaPsgF/i3jVthzzlR15eHHrAdQbW0SXRkQOhqHBRX2WeQHnyg3op9Tj6aDPRJdDDs5DMuHPg1ZjcehGAMCmzEpMf+cbZBVXiy2MiBwKQ4MLamw2YdV3eQCA50I+ha+SY8F0c5IEPBe8Ff8c+hJCPSpwvhp45K978d63p9Bi4tAAETE0uKSN+wug0zdikEcZftX/K9HlkJO50/cYUiIX4Gf+P8AkK/DurvN4YNW32J/PPT6I3B1Dg4upMhjx191nAQCLQjdDq2gWXBE5owBVHVYPeRPvhb8FX0UdTpWb8Mu/HcRTf9+HPEfeDIqIehVDgwtpMJowf+Nh1DQ0Y6SmEA8HfCe6JHJyD/bbg91Rv8acwB1QwoRdeTVIXLUHS7ZmIr+sj8JDUJClEZFwkizLsugiukuv18Pf3x81NTXw8/MTXY4QLSYznvm/TKSdKYO/shafDf8DIrXFossiF3K2cRDe0D2Jb/XxtuemjgjAU3eNxF2RQZB4NgSRU7LndyhDgwuQZRlLvziBzYeLoZGM+Hj4MkzwOim6LHJRGYZR+N/yh/GdPg5y683KYf1VeGj8MPwsJgxDg7wFV0hE9mBocDPvpubivbQ8KGDG2og3kOj3o+iSyA0UNoViY+XP8GnVvagztx0mNXagF34WOxj/ERWMyGAf3oEgcnAMDW6ipr4ZK1Nz8I/0QgDAnwatxa8CuVqC+latyRNf19yBHdV34ce6GJigtL02wFuJOyJDMGVEECZF9MeQQC/7QkRDA3DffZbHX38NeHr2cPVExNDg4kxmGZ9mFOOtb3JQZTACABaFfIJFIR8LrozcXWWLH1JqpiClZgoOG8agUda0e91Po0D0Lf0QfUsARof5YcQAHwwN8oanWtnxBxoMgI+P5XFdHeDNoQ+intbroWHNmjV46623oNPpEBMTg/fffx+TJk26bv+tW7di2bJlKCgoQGRkJN544w3cf//9ttdlWcby5cvxwQcfoLq6GnfccQfWrl2LyMjITtXjLqGhymDEj/kV+GDvORy/UAMAGKkpxIpBH2CKT5bY4oiu0mRW4Uj9KPxYF4P9dbHIbhgGo6zusO8gfzWGDfDDoH6eGBTgibDWFqxowfBhoZZODA1EvcKe36Eqez98y5YtSEpKwrp16xAXF4dVq1YhMTEROTk5CA4Ovqb//v37MWvWLCQnJ+NnP/sZNm3ahBkzZuDIkSMYO3YsAODNN9/EX/7yF2zcuBFDhw7FsmXLkJiYiFOnTkGr1dpbotNrNplRVtuEUn0jSmsacexCDfbll+PkRT2sEc9XYcCi0E8wJ/Df8JBMYgsm6oBG0YJ4nxOI9zkB4J9olpXIbRyME/WRONYQidzGCOQ33YIaky9Kaowoqbl28yhPYyNOtz7+6dvfQxvgD39PFfw9PRDgqYavVgVvjQo+Gss/vTVKaD2U8PRo+6dapWhrSktTKSWolBI8FAooFJxzQdRZdt9piIuLw8SJE7F69WoAgNlsRnh4OJ5//nksWbLkmv4zZ86EwWDAjh07bM9NnjwZsbGxWLduHWRZRlhYGP7rv/4Lv//97wEANTU1CAkJwYYNG/D4449f85lNTU1oamqy/bter0d4eHiv3mlY/8NZfHuy1O73XX1xZVmGWbb8U4ZlqMHYYkZTixlNLSY0Npugb2i55n1WUdrzmOp7FP8v6AseQkVOT5aBKpMfzjaFo6BpIC42D8BF4wCUNIfgUnMQ6gwaHFr5JABg1AufoUHd83+JUEiASqGAUiFBpZCgUEhQKiQoJAlKBaCUJEiSBIUCkCBBIQEKSYIkwfK8ZHneOlXDOmdDAlr7tD5/ZR+g7QVc8RzQvs9N3Gx+COOQ6/rtT4fjP6JCeuSzeu1Og9FoRGZmJpYuXWp7TqFQICEhAenp6R2+Jz09HUlJSe2eS0xMxLZt2wAA58+fh06nQ0JCgu11f39/xMXFIT09vcPQkJycjP/+7/+2p/SuKdgE7H8CAFB44bfIqLr/Jm/oOR5SM4JVlxHiUYmhmhLc4XMMd/pkIdjjMiBZ/2ez+0YRkUORJCBQUY9AjxxM8sm5tkND20mbn/56IqoUnqiuN0Lf0Izq+mbUNbWgrqkFhqYW1DWZUG9sQWOzCQ3NZjQ1m9DQbIKxxWwJ5ibLP69mlgGjyQzwhh05kYo6o5Cfa9dvnYqKCphMJoSEtE83ISEhOHPmTIfv0el0HfbX6XS2163PXa/P1ZYuXdouiFjvNPS4oMmA5yCgWY9ZwXvxE/+Ov+NNSZb7Bta/FSggQwEZkkIBCYBGaYJGCUtTq9HPE+jv4wWFZwigDQWUwQD+s7URuZF6I4AVAIDo8MBuz2mQZRktZhktJhnNZjNaTDJazGaYWp8zmS2vm2XLY1PrY1kGzK13Ca/8d/mKu4ayDMit9wgtj9tes946vPL1dv/soM5rar/pd+vCBbH7p5CjGBPmL+TnOuVfVTUaDTQazc07dpfPMOChCwCAsa2NiPqQwQB4vdljHydJEjyUEjyUgCeus2KDiK7LrrMngoKCoFQqUVrafmy/tLQUoaGhHb4nNDT0hv2t/7TnM4nITXh7W4KDwcCVE0QOwK7QoFarMX78eKSlpdmeM5vNSEtLQ3x8fIfviY+Pb9cfAFJTU239hw4ditDQ0HZ99Ho9Dh48eN3PJCIior5n9/BEUlIS5s6diwkTJmDSpElYtWoVDAYD5s2bBwCYM2cOBg0ahOTkZADAwoULMXXqVKxcuRLTp0/H5s2bkZGRgfXr1wOw3C5ctGgR/vSnPyEyMtK25DIsLAwzZszouW9KRERE3WJ3aJg5cybKy8vxyiuvQKfTITY2FikpKbaJjEVFRVAo2m5gTJkyBZs2bcLLL7+MF198EZGRkdi2bZttjwYA+MMf/gCDwYBf//rXqK6uxp133omUlBS33KOBiK7Q2Ag88ojl8eefA/wzgUgobiNNRI6L20gT9Tp7fofaNaeBiIiI3BdDAxEREXUKQwMRERF1CkMDERERdQpDAxEREXWKU24jfTXrAhC9Xi+4EiLqUQZD22O9HjDxVCminmb93dmZxZQuERpqa2sBoHcOrSIixxAWJroCIpdWW1sLf/8bH4TlEvs0mM1mXLx4Eb6+vjc9X94e1tMzi4uLuf9DJ/B62Y/XzH68ZvbjNbOfO10zWZZRW1uLsLCwdpszdsQl7jQoFArccsstvfb5fn5+Lv9/mp7E62U/XjP78ZrZj9fMfu5yzW52h8GKEyGJiIioUxgaiIiIqFMYGm5Ao9Fg+fLl0Gg0oktxCrxe9uM1sx+vmf14zezHa9Yxl5gISURERL2PdxqIiIioUxgaiIiIqFMYGoiIiKhTGBqIiIioUxgaiIiIqFMYGq5jzZo1iIiIgFarRVxcHA4dOiS6JIeRnJyMiRMnwtfXF8HBwZgxYwZycnLa9WlsbMRzzz2HwMBA+Pj44JFHHkFpaamgih3L66+/DkmSsGjRIttzvF7XKikpwa9+9SsEBgbC09MT0dHRyMjIsL0uyzJeeeUVDBw4EJ6enkhISEBeXp7AisUymUxYtmwZhg4dCk9PTwwfPhyvvvpqu0OI3P2a/fDDD/j5z3+OsLAwSJKEbdu2tXu9M9enqqoKTzzxBPz8/BAQEID58+ejrq6uD7+FYDJdY/PmzbJarZY//PBD+eTJk/LTTz8tBwQEyKWlpaJLcwiJiYnyRx99JGdnZ8tZWVny/fffLw8ePFiuq6uz9fnNb34jh4eHy2lpaXJGRoY8efJkecqUKQKrdgyHDh2SIyIi5Ntuu01euHCh7Xler/aqqqrkIUOGyE8++aR88OBB+dy5c/I333wj5+fn2/q8/vrrsr+/v7xt2zb52LFj8gMPPCAPHTpUbmhoEFi5OK+99pocGBgo79ixQz5//ry8detW2cfHR37vvfdsfdz9mu3cuVN+6aWX5C+++EIGIH/55ZftXu/M9Zk2bZocExMjHzhwQN67d688YsQIedasWX38TcRhaOjApEmT5Oeee8727yaTSQ4LC5OTk5MFVuW4ysrKZADynj17ZFmW5erqatnDw0PeunWrrc/p06dlAHJ6erqoMoWrra2VIyMj5dTUVHnq1Km20MDrda0//vGP8p133nnd181msxwaGiq/9dZbtueqq6tljUYjf/LJJ31RosOZPn26/NRTT7V77uGHH5afeOIJWZZ5za52dWjozPU5deqUDEA+fPiwrc/XX38tS5Ikl5SU9FntInF44ipGoxGZmZlISEiwPadQKJCQkID09HSBlTmumpoaAED//v0BAJmZmWhubm53DaOiojB48GC3vobPPfccpk+f3u66ALxeHdm+fTsmTJiARx99FMHBwRg3bhw++OAD2+vnz5+HTqdrd838/f0RFxfnttdsypQpSEtLQ25uLgDg2LFj2LdvH+677z4AvGY305nrk56ejoCAAEyYMMHWJyEhAQqFAgcPHuzzmkVwiVMue1JFRQVMJhNCQkLaPR8SEoIzZ84Iqspxmc1mLFq0CHfccQfGjh0LANDpdFCr1QgICGjXNyQkBDqdTkCV4m3evBlHjhzB4cOHr3mN1+ta586dw9q1a5GUlIQXX3wRhw8fxu9+9zuo1WrMnTvXdl06+u/UXa/ZkiVLoNfrERUVBaVSCZPJhNdeew1PPPEEAPCa3URnro9Op0NwcHC711UqFfr37+8215ChgbrlueeeQ3Z2Nvbt2ye6FIdVXFyMhQsXIjU1FVqtVnQ5TsFsNmPChAn485//DAAYN24csrOzsW7dOsydO1dwdY7p008/xccff4xNmzZhzJgxyMrKwqJFixAWFsZrRj2GwxNXCQoKglKpvGbmemlpKUJDQwVV5ZgWLFiAHTt24Pvvv8ctt9xiez40NBRGoxHV1dXt+rvrNczMzERZWRluv/12qFQqqFQq7NmzB3/5y1+gUqkQEhLC63WVgQMHYvTo0e2eGzVqFIqKigDAdl3432mbxYsXY8mSJXj88ccRHR2N2bNn44UXXkBycjIAXrOb6cz1CQ0NRVlZWbvXW1paUFVV5TbXkKHhKmq1GuPHj0daWprtObPZjLS0NMTHxwuszHHIsowFCxbgyy+/xK5duzB06NB2r48fPx4eHh7trmFOTg6Kiorc8hrec889OHHiBLKysmxtwoQJeOKJJ2yPeb3au+OOO65Zxpubm4shQ4YAAIYOHYrQ0NB210yv1+PgwYNue83q6+uhULT/I12pVMJsNgPgNbuZzlyf+Ph4VFdXIzMz09Zn165dMJvNiIuL6/OahRA9E9MRbd68WdZoNPKGDRvkU6dOyb/+9a/lgIAAWafTiS7NITz77LOyv7+/vHv3bvnSpUu2Vl9fb+vzm9/8Rh48eLC8a9cuOSMjQ46Pj5fj4+MFVu1Yrlw9Icu8Xlc7dOiQrFKp5Ndee03Oy8uTP/74Y9nLy0v+5z//aevz+uuvywEBAfK//vUv+fjx4/KDDz7oVssHrzZ37lx50KBBtiWXX3zxhRwUFCT/4Q9/sPVx92tWW1srHz16VD569KgMQH7nnXfko0ePyoWFhbIsd+76TJs2TR43bpx88OBBed++fXJkZCSXXJIsv//++/LgwYNltVotT5o0ST5w4IDokhwGgA7bRx99ZOvT0NAg//a3v5X79esne3l5yQ899JB86dIlcUU7mKtDA6/Xtf7973/LY8eOlTUajRwVFSWvX7++3etms1letmyZHBISIms0Gvmee+6Rc3JyBFUrnl6vlxcuXCgPHjxY1mq18rBhw+SXXnpJbmpqsvVx92v2/fffd/hn19y5c2VZ7tz1qayslGfNmiX7+PjIfn5+8rx58+Ta2loB30YMSZav2C6MiIiI6Do4p4GIiIg6haGBiIiIOoWhgYiIiDqFoYGIiIg6haGBiIiIOoWhgYiIiDqFoYGIiIg6haGBiIiIOoWhgYiIiDqFoYGIiIg6haGBiIiIOuX/AwxIMNoRw6b6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "plt.plot(np.linspace(1, 110, 100), chi2.pdf(np.linspace(1, 110, 100), df=n-1))\n",
    "plt.axvline(Chi2, color='red', linestyle='--')\n",
    "plt.text(Chi2, 0.01, str(Chi2)[:6])\n",
    "\n",
    "plt.fill_between(np.linspace(0, Chi2, 100), np.zeros(shape=100),\n",
    "                chi2.pdf(np.linspace(0, Chi2, 100), df=n-1), color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e7b4f009",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "85500b8e",
   "metadata": {},
   "source": [
    "## 두 개의 모집단의 분산 검정\n",
    "\n",
    "두 개의 모집단의 분산($\\sigma^2_1$), 분산($\\sigma^2_2$)에 대한 검정입니다.\n",
    "\n",
    "$H_0: \\sigma^2_1 = \\sigma^2_2$\n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\sigma^2_1 < \\sigma^2_2$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\sigma^2_1 > \\sigma^2_2$$|우측 꼬리(right)|\n",
    "|$$H_1: \\sigma^2_1 \\ne \\sigma^2_2$$|양쪽 꼬리(two-sided)|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cab96c44",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "f6170cf5",
   "metadata": {},
   "source": [
    "### F 검정 (F-test)\n",
    "\n",
    "**가정**\n",
    "\n",
    "두 개의 모집단은 정규 분포를 따릅니다.\n",
    "\n",
    "각 표본들은 서로 독립입니다.\n",
    "\n",
    "\n",
    "$H_0: \\frac{\\sigma^2_1}{\\sigma^2_2} = 1$\n",
    "\n",
    "$H_1:$\n",
    "\n",
    "|대립 가설|검정 종류|\n",
    "|---|---|\n",
    "|$$H_1: \\frac{\\sigma^2_1}{\\sigma^2_2} < 1$$|좌측 꼬리(left)|\n",
    "|$$H_1: \\frac{\\sigma^2_1}{\\sigma^2_2} > 1$$|우측 꼬리(right)|\n",
    "|$$H_1: \\sigma^2_1 \\ne \\sigma^2_2$$|양쪽 꼬리(two-sided)|\n",
    "\n",
    "    ※ F분포는 비대칭 분포입니다.\n",
    "       따라서 양측 검정할 때에 pvalue는 어림수(좌측과 우측 확률 중 작은(0.5 이하)×2)가 됩니다.\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$H_0$ 가 맞다면, \n",
    "\n",
    "> $\\frac{\\sigma^2_1}{\\sigma^2_2} = 1$가 됩니다.\n",
    "\n",
    "확률 분포와 검정 통계량\n",
    "\n",
    "> $F=\\frac{S_1^2}{S_2^2} \\sim F(n_1-1, n_2-1)$, n: 표본수\n",
    "\n",
    "**유도 과정**\n",
    "\n",
    "$(n_1-1)\\frac{S_1^2}{\\sigma_1^2} \\sim \\chi^2(n_1-1)$\n",
    "\n",
    "$(n_2-1)\\frac{S_2^2}{\\sigma_2^2} \\sim \\chi^2(n_2-1)$\n",
    "\n",
    "$\\frac{\\frac{S_1^2}{\\sigma_1^2}}{\\frac{S_2^2}{\\sigma_2^2}} \\sim \\frac{\\chi^2(n_1-1)/(n_1-1)}{\\chi^2(n_2-1)/(n_2-1)}$\n",
    "\n",
    "$\\frac{S_1^2}{S_2^2} \\sim F(n_1-1, n_2-1)$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6ae0f7e",
   "metadata": {},
   "source": [
    "**[Ex.2]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "신형 거리 계산기를 개발 중에 있습니다. \n",
    "\n",
    "기존에 거리 계산기 보다 거리를 재었을 때보다 분산이 낮게 만드는 것을 목표로 하고 있습니다.\n",
    "\n",
    "신형 거리 계산기의 개발의 성공 기준은 100m 거리를 재었을 때를 기준으로 합니다.\n",
    "\n",
    "100m에서 거리를 측정 했을 때의 실험 결과가 아래와 같습니다. \n",
    "\n",
    "유의 수준을 5%로 했을 때 기존 거리 계산기 보다 분산이 낮다고 판단할 수 있는지 확인합니다.\n",
    "\n",
    "기존 거리 계산기 기록\n",
    "```\n",
    "99.674, 100.299, 100.085, 99.548, 99.826, 100.495, 99.272, 99.871, 100.380, 99.740, \n",
    "99.796, 99.972, 100.447, 99.808, 99.867, 99.870, 100.662, 100.656, 100.301, 100.116, \n",
    "100.221, 100.447, 99.719, 100.353, 99.624, 99.809, 100.272, 99.571, 99.958, 99.741\n",
    "```\n",
    "\n",
    "신형 거리 계산기 기록\n",
    "\n",
    "```\n",
    "99.696, 100.279, 100.079, 99.578, 99.838, 100.462, 99.321, 99.880, 100.354, 99.757, \n",
    "99.810, 99.973, 100.418, 99.821, 99.876, 99.878, 100.618, 100.612, 100.281, 100.108, \n",
    "100.206, 100.417, 99.738, 100.329, 99.649, 99.821, 100.254, 99.600, 99.961, 99.759, \n",
    "99.928, 99.216, 99.504, 99.804, 100.260\n",
    "```\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca1edecb",
   "metadata": {},
   "source": [
    "$H_0: \\frac{\\sigma^2_1}{\\sigma^2_2} = 1$\n",
    "\n",
    "$H_1: \\frac{\\sigma^2_1}{\\sigma^2_2} > 1$\n",
    "    \n",
    "$F=\\frac{S_1^2}{S_2^2} \\sim F(n_1-1, n_2-1)$\n",
    "\n",
    "**우측 검정** 입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f0617a4a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(F): 1.0379777993154704, pvalue: 0.45501804967354664\n"
     ]
    }
   ],
   "source": [
    "X1 = [\n",
    "    99.674, 100.299, 100.085, 99.548, 99.826, 100.495, 99.272, 99.871, 100.380, 99.740, \n",
    "    99.796, 99.972, 100.447, 99.808, 99.867, 99.870, 100.662, 100.656, 100.301, 100.116, \n",
    "    100.221, 100.447, 99.719, 100.353, 99.624, 99.809, 100.272, 99.571, 99.958, 99.741\n",
    "]\n",
    "\n",
    "X2 = [\n",
    "    99.696, 100.279, 100.079, 99.578, 99.838, 100.462, 99.321, 99.880, 100.354, 99.757, \n",
    "    99.810, 99.973, 100.418, 99.821, 99.876, 99.878, 100.618, 100.612, 100.281, 100.108, \n",
    "    100.206, 100.417, 99.738, 100.329, 99.649, 99.821, 100.254, 99.600, 99.961, 99.759, \n",
    "    99.928, 99.216, 99.504, 99.804, 100.260\n",
    "]\n",
    "\n",
    "S1_sq = np.var(X1, ddof=1)\n",
    "S2_sq = np.var(X2, ddof=1)\n",
    "\n",
    "n1 = len(X1)\n",
    "n2 = len(X2)\n",
    "\n",
    "F = S1_sq / S2_sq\n",
    "print(\"검정통계량(F): {}, pvalue: {}\".format(F, f.sf(F, n1 - 1, n2 - 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "12f70786",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.linspace(0, 3, 100), f.pdf(np.linspace(0, 3, 100), n1 - 1, n2 - 1))\n",
    "plt.axvline(F, color='red', linestyle='--')\n",
    "plt.text(F, 0.01, str(F)[:6])\n",
    "\n",
    "plt.fill_between(np.linspace(F, 3, 100), np.zeros(shape=100),\n",
    "                f.pdf(np.linspace(F, 3, 100), n1-1, n2-1), color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d8c4372",
   "metadata": {},
   "source": [
    "## 2. 다수의 모집단의 등분산 검정\n",
    "\n",
    "$H_0: \\sigma^2_0 = \\sigma^2_1 = ... = \\sigma^2_{k}$\n",
    "\n",
    "$H_1$: 모집단 간 분산에 차이가 존재합니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd209b95",
   "metadata": {},
   "source": [
    "### Bartlett 검정\n",
    "\n",
    "**가정**\n",
    "\n",
    "모집단들은 정규분포를 따릅니다.\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$H_0$가 맞다면,\n",
    "\n",
    "아래 B는 근사적으로 카이제곱분포를 따릅니다. \n",
    "\n",
    "우측 검정입니다.\n",
    "\n",
    "$B = \\frac{(N - k) \\ln(S_p^2) - \\sum_{i=1}^k(n_i - 1)ln(S_i^2)}{1 + \\frac{1}{3(k-1)} \\left(\\sum_{i=1}^{k}\\left(\\frac{1}{n_i-1}\\right) - \\frac{1}{N-k}\\right)} \\sim \\chi^2(k - 1)$ \n",
    "\n",
    "- k: 모집단의 수 \n",
    "- N: 전체표본의 수\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3f8de03",
   "metadata": {},
   "source": [
    "**[Ex.3]**\n",
    "\n",
    "<div style=\"border: 1px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "다음 거리 계산기 모집단이 등분산인지 조사해보세요. 세 모집단은 모두 정규 분포를 따릅니다.\n",
    "\n",
    "기존 거리 계산기 기록\n",
    "```\n",
    "99.674, 100.299, 100.085, 99.548, 99.826, 100.495, 99.272, 99.871, 100.380, 99.740, \n",
    "99.796, 99.972, 100.447, 99.808, 99.867, 99.870, 100.662, 100.656, 100.301, 100.116, \n",
    "100.221, 100.447, 99.719, 100.353, 99.624, 99.809, 100.272, 99.571, 99.958, 99.741\n",
    "```\n",
    "\n",
    "신형 거리 계산기 기록\n",
    "```\n",
    "99.696, 100.279, 100.079, 99.578, 99.838, 100.462, 99.321, 99.880, 100.354, 99.757, \n",
    "99.810, 99.973, 100.418, 99.821, 99.876, 99.878, 100.618, 100.612, 100.281, 100.108, \n",
    "100.206, 100.417, 99.738, 100.329, 99.649, 99.821, 100.254, 99.600, 99.961, 99.759, \n",
    "99.928, 99.216, 99.504, 99.804, 100.260\n",
    "```\n",
    "\n",
    "경쟁사 거리 계산기 기록\n",
    "```\n",
    "99.653, 100.319, 100.091, 99.518, 99.815, 100.528, 99.223, 99.863, 100.405, 99.723, \n",
    "99.783, 99.970, 100.477, 99.796, 99.858, 99.861, 100.706, 100.700, 100.321, 100.124, \n",
    "100.236, 100.477, 99.701, 100.376, 99.599\n",
    "```\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9a2793e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m</th>\n",
       "      <th>model</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>99.674</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>100.299</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>100.085</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>99.548</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>99.826</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>20</td>\n",
       "      <td>100.236</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>21</td>\n",
       "      <td>100.477</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>99.701</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>23</td>\n",
       "      <td>100.376</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>24</td>\n",
       "      <td>99.599</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>90 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          m model\n",
       "0    99.674     A\n",
       "1   100.299     A\n",
       "2   100.085     A\n",
       "3    99.548     A\n",
       "4    99.826     A\n",
       "..      ...   ...\n",
       "20  100.236     C\n",
       "21  100.477     C\n",
       "22   99.701     C\n",
       "23  100.376     C\n",
       "24   99.599     C\n",
       "\n",
       "[90 rows x 2 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_A = pd.Series(\n",
    "    [99.674, 100.299, 100.085, 99.548, 99.826, 100.495, 99.272, 99.871, 100.380, 99.740, \n",
    "    99.796, 99.972, 100.447, 99.808, 99.867, 99.870, 100.662, 100.656, 100.301, 100.116, \n",
    "    100.221, 100.447, 99.719, 100.353, 99.624, 99.809, 100.272, 99.571, 99.958, 99.741], name='m'\n",
    ")\n",
    "s_B = pd.Series(\n",
    "    [99.696, 100.279, 100.079, 99.578, 99.838, 100.462, 99.321, 99.880, 100.354, 99.757, \n",
    "    99.810, 99.973, 100.418, 99.821, 99.876, 99.878, 100.618, 100.612, 100.281, 100.108, \n",
    "    100.206, 100.417, 99.738, 100.329, 99.649, 99.821, 100.254, 99.600, 99.961, 99.759, \n",
    "    99.928, 99.216, 99.504, 99.804, 100.260], name='m'\n",
    ")\n",
    "s_C = pd.Series(\n",
    "    [99.653, 100.319, 100.091, 99.518, 99.815, 100.528, 99.223, 99.863, 100.405, 99.723, \n",
    "    99.783, 99.970, 100.477, 99.796, 99.858, 99.861, 100.706, 100.700, 100.321, 100.124, \n",
    "    100.236, 100.477, 99.701, 100.376, 99.599], name='m'\n",
    ")\n",
    "\n",
    "df_m = pd.concat(\n",
    "    [a.to_frame().assign(model=b) for a, b in zip([s_A, s_B, s_C], ['A', 'B', 'C'])]\n",
    ")\n",
    "df_m"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cd89899",
   "metadata": {},
   "source": [
    "$B = \\frac{(N - k) \\ln(S_p^2) - \\sum_{i=1}^k(n_i - 1)ln(S_i^2)}{1 + \\frac{1}{3(k-1)} \\left(\\sum_{i=1}^{k}\\left(\\frac{1}{n_i-1}\\right) - \\frac{1}{N-k}\\right)} \\sim \\chi^2(k - 1)$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ea4b60cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>var</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>A</td>\n",
       "      <td>0.126864</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>B</td>\n",
       "      <td>0.122222</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>C</td>\n",
       "      <td>0.155286</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            var  count\n",
       "model                 \n",
       "A      0.126864     30\n",
       "B      0.122222     35\n",
       "C      0.155286     25"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sp = df_m.groupby('model')['m'].agg(['var', 'count'])\n",
    "df_sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "04d936d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "검정통계량(B): 0.4463582365057818, pvalue: 0.7999715469550519\n"
     ]
    }
   ],
   "source": [
    "# Pooled Variance를 구합니다.\n",
    "Sp_sq = (df_sp['var'] * (df_sp['count'] - 1)).sum() / (df_sp['count'] - 1).sum()\n",
    "k = 3\n",
    "n = len(df_m)\n",
    "# B의 분모를 구합니다.\n",
    "B_num = (n - k) * np.log(Sp_sq) - (np.log(df_sp['var']) * (df_sp['count']- 1)).sum()\n",
    "# B의 분자를 구합니다.\n",
    "B_denom = 1 + 1 / (3 * (k - 1)) * ((1 / (df_sp['count'] - 1)).sum() - 1 / (n - k))\n",
    "B = B_num / B_denom\n",
    "print(\"검정통계량(B): {}, pvalue: {}\".format(B, chi2.sf(B, k - 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "79dc44c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BartlettResult(statistic=0.4463582365057818, pvalue=0.7999715469550519)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy.stats.bartlett 으로도 구할 수 있습니다.\n",
    "from scipy.stats import bartlett\n",
    "bartlett(s_A, s_B, s_C)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11cf873e",
   "metadata": {},
   "source": [
    "# 2-5-2 정규성 검정\n",
    "\n",
    "정규성 검정은 모집단이 정규 분포를 따르는 지를 표본을 통해 확인하는 방법입니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "826f8c47",
   "metadata": {},
   "source": [
    "정규 분포를 따르는 정도를 비교하기 위해,\n",
    "\n",
    "표본의 수가 클수록 표본의 평균은 정규 분포에 가까워지는 성질을 이용하여 데이터셋을 만듭니다.\n",
    "\n",
    "$\\lambda=3$인 포아송 분포를 따르는 표본수를 3개로 할 때와 30개로 할 때의 표본의 평균을 각각 100개씩 만듭니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9d63e62f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import poisson\n",
    "# lambda=3인 포아송 분포의 표본을 3개씩 뽑아 평균을 100개 만듭니다.\n",
    "s_mean_3 = [poisson.rvs(mu=3, size=3).mean() for _ in range(100)]\n",
    "# lambda=3인 포아송 분포의 표본을 30개씩 뽑아 평균을 100개 만듭니다.\n",
    "s_mean_30 = [poisson.rvs(mu=3, size=30).mean() for _ in range(100)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79952a61",
   "metadata": {},
   "source": [
    "### Q-Q Plot\n",
    "\n",
    "비교할 대상 확률 분포를 정규 분포로하여 Q-Q Plot을 출력하여 판단합니다. \n",
    "\n",
    "Q-Q Plot의 모양이 직선에 가까울 수록 두 확률 변수의 분포가 비슷합니다.\n",
    "  \n",
    "**Q-Q Plot 그리기**\n",
    "\n",
    "<div style=\"border: 0px solid #ddd; padding: 12px; margin-top: 10px\">\n",
    "\n",
    "수열을 정렬합니다.\n",
    "\n",
    "Y좌표: 수열\n",
    "\n",
    "X좌표: \n",
    "\n",
    "> 1. 수열의 값을 분위수(0~1사이)로 변환하고 (순위 / 표본수)\n",
    ">\n",
    "> 2. 백분위수로 변환된 값을 정규 분포의 확률 변수로 변환합니다.(norm.ppf)\n",
    "  \n",
    "산포도 그래프로 출력합니다.\n",
    "    \n",
    "- X와 Y의 분포가 비슷할 수록 산포도 그래프의 출력 형태는 직선에 가깝게 됩니다.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e425da6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.sort(s_mean_3) # 분위를 구하기 위해 정렬합니다\n",
    "X_ppf = np.arange(0, 100) / 100 # 표본의 등분위(0~1사이)를 구합니다.\n",
    "X_norm_ppf = norm.ppf(X_ppf, loc=np.mean(X), scale=np.std(X))\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "sns.kdeplot(X, ax=axes[0])\n",
    "# 0분위와 1분위의 정규 분포의 확률 변수는 -∞과 ∞ 이므로 생략합니다.\n",
    "sns.scatterplot(x=X_norm_ppf[1:-1], y=X[1:-1])\n",
    "plt.gca().set_xlabel('Normal theoretical quantiles')\n",
    "plt.gca().set_ylabel('s_mea3')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4cc5c575",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.sort(s_mean_30) # 분위를 구하기 위해 정렬합니다\n",
    "X_ppf = np.arange(0, 100) / 100 # 표본의 등분위(0~1사이)를 구합니다.\n",
    "X_norm_ppf = norm.ppf(X_ppf, loc=np.mean(X), scale=np.std(X))\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "sns.kdeplot(X, ax=axes[0])\n",
    "# 0분위와 1분위의 정규 분포의 확률 변수는 -∞과 ∞ 이므로 생략합니다.\n",
    "sns.scatterplot(x=X_norm_ppf[1:-1], y=X[1:-1])\n",
    "plt.gca().set_xlabel('Normal theoretical quantiles')\n",
    "plt.gca().set_ylabel('s_mea3')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0432dda",
   "metadata": {},
   "source": [
    "$H_0$: 모집단은 정규 분포를 따릅니다.\n",
    "\n",
    "$H_1$: 모집단은 정규 분포를 따르지 않습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "978799ba",
   "metadata": {},
   "source": [
    "### Shapiro-Wilks\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$W = \\frac{\\left(\\sum_{i=1}^{n} a_i x_{(i)}\\right)^2}{\\sum_{i=1}^{n} (x_i - \\bar{x})^2}$\n",
    "\n",
    "$x_{(i)}$: i번째로 큰수\n",
    "\n",
    "$(a_1, ..., a_n) = \\frac{m^TV^{-1}}{C}$\n",
    "\n",
    "$C=||V^{-1}m||=\\left(m^TV^{-1}V^{-1}m\\right)$\n",
    "\n",
    "n: 표본수\n",
    "\n",
    "**m과 V의 정체**\n",
    "\n",
    "표본의 통계량(평균, 분산)으로 정규 분포에서 n개씩 표본 수집을 여러 번 수행합니다. \n",
    "\n",
    "각 수행에서 순위가 1, ... , n까지 수들의 평균이 **m** 입니다.\n",
    "\n",
    "그리고 순위가 1, ..., n까지의 수들 간에 공분산 행렬이 **V**입니다.\n",
    "\n",
    "\n",
    "**W**가 따르는 분포는 정의할 수 없습니다. 단지 **W**가 클수록 정규 분포에 가깝습니다.\n",
    "\n",
    "pvalue와 임계치는 Monte Carlo Simulation을 통해 구해집니다.\n",
    "\n",
    "중소 규모(보통 2000개 이하)의 표본에 적합합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0e53c6fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(ShapiroResult(statistic=0.977840006351471, pvalue=0.09010078758001328),\n",
       " ShapiroResult(statistic=0.9881731271743774, pvalue=0.5210586786270142))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import shapiro\n",
    "shapiro(s_mean_3), shapiro(s_mean_30)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33430d13",
   "metadata": {},
   "source": [
    "### Kolmogorov-Smirnof\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "이론적 누적분포함수와 표본의 누적분포를 비교합니다.\n",
    "\n",
    "$D_n = sup_x|F_n(x) - F(x)|$\n",
    "\n",
    "$F_n(x) = \\frac{1}{n}\\sum_{i=1}^{n}{1_{(-\\inf, x]}(X_i)}$, $1_{(-\\inf, x]}(X_i)$:는 $X_i$보다 x가 작거나 같으면 1 아니면 0\n",
    "\n",
    "즉, $F_n(x)$는 표본에서 x보다 작거나 같은 수의 수를 의미합니다.\n",
    "\n",
    "$D_n$가 클수록 정규 분포와 거리가 먼 것을 의미합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "80d11da8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(KstestResult(statistic=0.12148267865059054, pvalue=0.09604161663865285),\n",
       " KstestResult(statistic=0.061131904039490204, pvalue=0.8266301444594338))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import kstest\n",
    "(\n",
    "    kstest(s_mean_3, norm.cdf, args=[np.mean(s_mean_3), np.std(s_mean_3, ddof=1)]), \n",
    "    kstest(s_mean_30, norm.cdf, args=[np.mean(s_mean_30), np.std(s_mean_30, ddof=1)])\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8eef155",
   "metadata": {},
   "source": [
    "### Jaque-Bera\n",
    "\n",
    "왜도(skewness)와 첨도(kurtosis)를  이용하여 정규성 검정을 합니다. \n",
    "\n",
    "검정 통계량은 카이제곱분포에 표본수가 커짐에 따라 점진적으로 수렴합니다.\n",
    "\n",
    "따라서, 표본수가 적으면(2000개 미만) 정확도가 떨어 집니다.\n",
    "\n",
    "**증거의 확률 분포 및 통계량**\n",
    "\n",
    "$JB = \\frac{n}{6} \\left(\\frac{S^2}{6} + \\frac{(K-3)^2}{24}\\right)$\n",
    "\n",
    "S: 첨도, K: 왜도\n",
    "\n",
    "$S = \\frac{\\sum_{i=1}^{n} (x_i - \\bar{x})^3}{n \\cdot s^3}$\n",
    "\n",
    "$K = \\frac{\\sum_{i=1}^{n} (x_i - \\bar{x})^4}{n \\cdot s^4}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "987beda8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Jarque_beraResult(statistic=1.4532685703487411, pvalue=0.483533690928881),\n",
       " Jarque_beraResult(statistic=1.697293156117136, pvalue=0.4279937963312388))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import jarque_bera\n",
    "jarque_bera(s_mean_3), jarque_bera(s_mean_30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cec1de87",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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