QQ-Plot.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "41c784a0",
   "metadata": {},
   "source": [
    "## QQ Plot : "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bad1edbc",
   "metadata": {},
   "source": [
    "> a Q–Q plot (quantile-quantile plot) is a probability plot, which is a `graphical method for comparing two probability distributions by plotting their quantiles against each other`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9c22e83d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import statsmodels.api as sm\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import t\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from matplotlib import figure\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c645152",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3d3d5cb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets say this given data : \n",
    "data =[ 0.04177737,  0.97977259,  1.19684675,  0.75969411,  0.2772351 ,        1.20400739,  1.19512711, -1.33315966,  0.47241401,  0.58453053,      0.21167461,  0.87106215, -0.56663286,  0.3702523 ,  0.72724427,        0.41126015,  0.33358864,  0.72878097,  0.69929305,  0.72581333,        1.67334826, -1.54572083, -1.22840893,  0.47103287,  0.895276  ,        0.16538052, -0.43575904,  1.62784202,  0.98340417,  0.90482144,      -0.47914975,  0.71812022,  1.14243   , -0.04393411,  1.24946471,       -0.8699551 ,  1.60196517,  1.00140898,  1.48233878, -0.37088602,       -0.0954339 ,  1.2969551 ,  0.0457524 , -0.06486335,  0.43257115,       -0.18945797,  0.46525944,  0.12974487, -0.10501035,  0.94060547,      -1.57714093,  0.24292938,  0.68759359,  0.24113398,  0.74353881,        0.0129037 ,  0.47936105, -0.0596165 ,  0.3300311 , -0.19409805,       -2.15213968, -0.9169724 ,  1.40476752,  0.74067023,  0.36119747,        1.04507563, -0.54692221,  0.65000261,  0.5359208 ,  0.40091749,       0.16959609,  0.43828974,  1.69191812, -0.40588725,  0.52772481,        0.2410331 ,  1.8226663 , -1.36677194,  0.41745297,  0.94050797,\n",
    "        1.15797033,  0.13883716,  0.9648131 ,  0.71495948,  1.73284151,        0.9571359 ,  0.38785662,  0.41390929, -1.10391874, -0.41368798,      -0.90497721,  1.37201217,  0.52934518,  0.45456489, -0.23302007,        0.1206425 ,  1.43043074,  0.0599792 ,  0.39871742, -0.03524401,       -1.59860382, -1.94105256,  1.22334603, -1.76544176, -0.80324714,        1.16037195,  0.38303564, -0.44427508,  1.13694237,  0.58281873,        1.01938666,  0.85409657,  0.32051415,  0.08834169,  0.15365941,        1.68716621, -0.24197654,  1.2676363 ,  1.48518839, -0.47335603,        1.15654111,  0.76654086, -0.11389136,  1.30586524,  0.32307392,        0.54523295,  0.38590127,  0.50793605, -0.34701396,  0.74541391,        0.79535705,  1.01896308, -0.22023158, -0.48871769,  0.05838767,       -0.25024374,  0.69928181,  2.21454052,  0.20445216,  1.32931331,        0.08653597,  0.07823139,  1.14485681,  0.91738973,  0.0543534 ,       -1.45447157,  1.08313814, -0.27451755,  1.15577356,  1.15404113,       -1.82969195,  0.17610396,  1.08855269,  0.67994842,  0.0750844 ,       -0.30914221,  0.68824746, -2.02655603, -0.65056827,  0.03919982,\n",
    "        0.06828509,  1.17926148,  0.86701368,  1.45238655,  1.63738079,        0.63609739, -1.31232421,  0.98509236,  1.15594405,  0.20902709,        0.96664264,  0.11769247,  0.48530914,  1.12505311,  0.60806881,       -1.54771281,  0.92716597,  1.16839655, -0.06376581,  0.75839488,        1.05027756,  1.41329557,  0.85657177, -0.2160035 ,  1.12248554,        0.20020919,  1.1861288 ,  0.76429072, -1.83554409, -0.04585441,        1.06873376,  0.10936729,  1.48407643,  0.52580339,  1.19815856,        0.53797982, -0.42615522, -0.38198519,  0.53974062,  0.06254645,        0.11724433,  0.67580552,  0.63406064,  1.03362043, -1.88639841,        0.62474754,  0.89065659,  0.5328413 ,  0.92901562,  0.82901618,       -1.40196713,  0.25330113, -0.11682618,  0.79230788, -1.37307874,        0.37353503,  0.65753252,  0.61958929,  0.95358877, -0.63137426,        0.73935171, -0.3392893 ,  0.90018122,  1.13697138,  1.07777798,       -0.67428172,  1.20112044,  0.13277637,  0.88485663, -0.73037033,        0.73817138,  0.1309939 ,  0.77936817,  1.16422402,  1.22697646,        0.31219482,  0.6517649 ,  1.35374234, -0.11302125,  1.38551431,\n",
    "        1.4890138 ,  0.75586738,  1.76803848,  0.56651688, -0.67678907,        0.19554616,  0.46406559, -0.06019572,  1.53990381, -1.13432049,       -0.80700753, -2.31246741,  1.33986194,  1.38730476,  0.82881232,        0.70062208, -0.12381894, -0.46690349, -1.57527874,  1.72209985,        0.18183212,  0.8400035 ,  0.418469  ,  1.36179378, -0.92426075,        0.22270703, -0.13774932,  0.93111539, -0.88921133,  1.0997085 ,       -0.9937949 ,  0.38843634,  1.01148004, -0.43816108, -0.95414947,        1.32330751,  0.30404196,  0.88512404,  0.91372546,  0.32134319,        0.14559158, -0.19978188,  0.88329649,  0.30335937,  0.76175674,        0.57364537,  1.02631156,  1.66794999, -1.03792174, -0.31515864,        1.07180383,  0.59720417, -0.32040037, -0.7674771 ,  0.25057312,        0.27762623,  0.54672121, -1.34336276,  0.53814872,  1.24214509,       -1.12005068,  1.37171113,  0.0616415 , -0.74262483,  1.01415696,        0.3901361 ,  0.70918134,  0.20065952,  0.94970448,  0.73886174,        1.06909761,  0.86064287,  1.15752969,  0.82554495,  1.36024967,        0.59598245,  0.89922565,  0.7362065 ,  1.00841732,  0.55340554,\n",
    "        0.41274327,  0.50711349,  0.45157236, -0.2457261 ,  1.07731295,       -0.50619092,  0.77516586, -2.71031075,  0.69192707,  0.84959366,        1.45540949, -0.44551638,  1.28008884,  0.61377305, -0.54839374,        1.16915428,  1.1075064 ,  1.0229388 ,  1.22989514,  1.24266425,        0.17096114,  1.00952836, -0.28128762, -0.31360414,  0.50315717,        0.23675518, -0.15479312,  0.28744327,  0.66566966, -0.14055415,        0.60945716, -1.45725682, -1.76229852,  0.10049782,  0.59945138,        0.60902798,  0.92513724,  1.3161839 , -0.02831568,  0.53837944,       -3.63123097,  2.24728714,  0.14248232,  1.15824823,  0.1331667 ,        1.30352524,  0.31862759,  1.48258693,  0.82365142,  1.22927344,        0.65581787,  1.49120079,  1.26751206,  0.6596013 , -0.30466474,        0.92502302,  1.05893148,  1.25006908,  1.51266005, -0.36946192,        0.20367163,  1.54883376, -0.07722085,  0.29042734, -0.07913684,        1.0009701 ,  0.66712984,  1.72579542,  1.81505526,  1.02742471,        1.31574026, -1.10915715, -0.54120723,  0.51054351, -0.88139742,       -1.72785233,  1.9585019 ,  1.09644834, -1.27615429, -2.11919702,\n",
    "        0.10586263,  0.70464499,  0.61638469,  0.30262653, -0.40630085,       -0.2274666 ,  1.20697563,  0.36656195,  0.57455917, -0.95850539,        0.57487625,  0.09909038, -2.02132122,  0.79842403,  0.29482801,       -0.56063591,  1.22430722, -0.26074589, -0.61835677,  0.91307203,        0.98181937,  1.60472708,  0.80975178,  0.57399004,  0.20730555,        1.03604696,  1.99239206,  1.35579176, -1.06755095,  0.79769852,       -0.11886134,  0.92591275,  0.31100381,  1.45719763, -0.18650384,        0.98158411,  0.38823413,  0.03501161,  1.3873394 ,  1.06988861,       -0.61101705,  0.64726664,  0.71829533,  0.37560761,  0.32028192,        0.46012344,  0.92880202,  0.67717555,  0.04629136,  0.47546512,        1.4513086 ,  1.45343272,  1.54991229,  0.62037232,  0.01407354,        0.46979478,  0.05595689, -1.73249288,  0.23003225,  1.29352827,        0.80189453,  1.61966331,  0.69681106,  1.03215339, -1.21549361,        0.93475221,  1.30143537,  0.7254352 ,  0.22841529,  1.50249735,       -0.02415314, -0.18205881,  0.95388083,  0.66182587,  0.08282857,        1.53432986,  1.07818559,  1.04804152,  0.62920033,  0.2221568 ,\n",
    "        1.11689153,  0.70328342,  1.48907562, -0.85967934,  0.37330663,        0.10042743,  0.43601618, -0.84872277, -0.18902961,  1.16872747,        0.49445364,  0.97912906,  0.16970087,  1.43121388,  0.67825154,        0.8233865 ,  1.20263091,  0.49206124,  0.34548617,  1.58287164]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "56645dd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "51830db0",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9c1da877",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500,)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "73e91c83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# checking distribution of data  :\n",
    "plt.figure(figsize=(8,5))\n",
    "sns.distplot(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f09b4534",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "88dcbe0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = sm.qqplot(X,line=\"45\",fit=True,)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "370c6420",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.40812679178 0.8571215209422999\n"
     ]
    }
   ],
   "source": [
    "mu = np.mean(X)\n",
    "s = np.std(X)\n",
    "print(mu,s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f39d67da",
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating normally distributed 500 data points with same above mean and std (for comparision)\n",
    "\n",
    "Y = stats.norm.rvs(loc = mu, scale = s , size = 500)   #(for theoretical cdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9d9fdb38",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.grid()\n",
    "plt.hist(X,bins = 100,cumulative=True,density=True,histtype=\"step\", label=\"Empirical CDF\")\n",
    "plt.hist(Y,bins = 100,cumulative=True,density=True,histtype=\"step\", label=\"Theoretical CDF\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a3360ba2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# plt.figure(figsize=(8,5))\n",
    "# plt.grid()\n",
    "# sns.distplot(X,label = \"Emperical pdf\")\n",
    "# sns.distplot(Y,label = \"Theoretical pdf\")\n",
    "# plt.legend()\n",
    "# plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "91c33efb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a265b623",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7e552f2d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3955446",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "39841887",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b5726914",
   "metadata": {},
   "outputs": [],
   "source": [
    "def QQPlot(data):\n",
    "    X = np.array(data)\n",
    "    \n",
    "    mu = np.mean(X)\n",
    "    s = np.std(X)\n",
    "    Y = stats.norm.rvs(loc = mu, scale = s , size = len(X))  \n",
    "    \n",
    "    def standardisation_of_data(data):\n",
    "        data= np.array(data)\n",
    "        return (data - np.mean(data))/np.std(data)\n",
    "    \n",
    "    X = standardisation_of_data(X)\n",
    "    Y = standardisation_of_data(Y)\n",
    "    \n",
    "    def get_percentils(X):\n",
    "        percentiles = []\n",
    "        for i in range(1,101):\n",
    "            percentiles.append(np.percentile(X,i))\n",
    "        return np.array(percentiles)\n",
    "\n",
    "    Ax,Ay = get_percentils(X),get_percentils(Y)\n",
    "    T  = pd.DataFrame([Ax,Ay],index=[\"Empirical Quantiles\",\"Theoretical Quantiles\"]).T\n",
    "    sns.scatterplot(T[\"Theoretical Quantiles\"],T[\"Empirical Quantiles\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d5394ace",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1fcc1052",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c05c620",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "693236f9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "990d9f74",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "QQPlot(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "061bd911",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = sm.qqplot(X,line=\"45\",fit=True,)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2bcc746",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "df837cb1",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      55\n",
       "1      79\n",
       "2      96\n",
       "3      91\n",
       "4      89\n",
       "       ..\n",
       "515    74\n",
       "516    95\n",
       "517    60\n",
       "518    93\n",
       "519    85\n",
       "Length: 520, dtype: int32"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asd = pd.Series(np.random.randint(50,100,520))\n",
    "asd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "af031ad2",
   "metadata": {},
   "outputs": [],
   "source": [
    "asd = pd.Series(np.random.randint(50,100,520))\n",
    "\n",
    "E = np.array([asd.sample(100,replace=True).mean() for _ in range(100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6ab28e2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c5d2abbc",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "QQPlot(E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7c13ac46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot(E)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "2a87ee86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "stats.probplot(E, dist='norm',  plot=plt)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "389ce465",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f77f7d20",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c8004cc4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "90ae1652",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a1d0b715",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dd954328",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc7a853a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56c9aca7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "5fa82c2b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3f553d86",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "46e95c62",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.random.randint(150,200,500000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "bdcc4e8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(174.492922, 14.42991593537246)"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(X),np.std(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "6979559b",
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = np.random.normal(np.mean(X),np.std(X),500000 )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "f1aa7618",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166.20943972, 183.97567127, 176.64607083, ..., 183.85653589,\n",
       "       168.36293488, 149.11425665])"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "d4463ac1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "def standardisation_of_data(data):\n",
    "    data= np.array(data)\n",
    "    return (data - np.mean(data))/np.std(data)\n",
    "\n",
    "    \n",
    "X = standardisation_of_data(X)\n",
    "Y = standardisation_of_data(Y)\n",
    "    \n",
    "\n",
    "def get_percentils(X):\n",
    "    percentiles = []\n",
    "    for i in range(1,101):\n",
    "        percentiles.append(np.percentile(X,i))\n",
    "    return np.array(percentiles)\n",
    "\n",
    "Ax= get_percentils(X)\n",
    "Ay= get_percentils(Y)\n",
    "T  = pd.DataFrame([Ax,Ay],index=[\"Empirical Quantiles\",\"Theoretical Quantiles\"]).T\n",
    "sns.scatterplot(T[\"Theoretical Quantiles\"],T[\"Empirical Quantiles\"])\n",
    "plt.xticks(np.array([-4,-3,-2,-1,0,1,2,3,4]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "06a026fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot(X)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "053e450a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3daf644",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "91f26b50",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a9e7c02f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "d7a5bad7",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = sns.load_dataset(\"titanic\")[\"age\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "7ad50d3f",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "7942eb50",
   "metadata": {},
   "outputs": [],
   "source": [
    "def QQplot_(data):\n",
    "    X = np.array(data)\n",
    "\n",
    "    Y = np.random.normal(np.mean(X),np.std(X),len(X))\n",
    "\n",
    "    def standardisation_of_data(data):\n",
    "        data= np.array(data)\n",
    "        return (data - np.mean(data))/np.std(data)\n",
    "\n",
    "\n",
    "    X = standardisation_of_data(X)\n",
    "    Y = standardisation_of_data(Y)\n",
    "\n",
    "\n",
    "    def get_percentils(X):\n",
    "        percentiles = []\n",
    "        for i in range(1,101):\n",
    "            percentiles.append(np.percentile(X,i))\n",
    "        return np.array(percentiles)\n",
    "\n",
    "    Ax= get_percentils(X)\n",
    "    Ay= get_percentils(Y)\n",
    "    T  = pd.DataFrame([Ax,Ay],index=[\"Empirical Quantiles\",\"Theoretical Quantiles\"]).T\n",
    "    sns.scatterplot(T[\"Theoretical Quantiles\"],T[\"Empirical Quantiles\"])\n",
    "    plt.xticks(np.array([-4,-3,-2,-1,0,1,2,3,4]))\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "b4123fe5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "QQplot_(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "9ead5306",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(data, dist='norm',  plot=plt)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69ce1653",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab2065f8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4b78c40",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce61931c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1c8a78e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "35999aa2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "0282212f",
   "metadata": {},
   "source": [
    "# QQ_plot implementation "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e6f6e94",
   "metadata": {},
   "source": [
    "## Gaussian vs Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "af150eea",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([11.57784747, 11.2491053 , 13.61389724, 10.43431545, 19.07394786,\n",
    "        9.82403715, 13.4244426 ,  9.44118008, 14.38563498, 20.18550907,\n",
    "       19.4045435 , 12.68474753,  8.71613424, 15.37961119, 11.5821208 ,\n",
    "       13.87797766,  9.49664077, 10.85808951, 14.63660789,  8.03715599,\n",
    "       13.9350733 ,  9.73475394, 15.88874849, 13.93616509, 13.37910841,\n",
    "       13.54297006, 12.49945327,  6.52392492,  6.31793451, 14.52702842,\n",
    "        7.59369013, 11.77629841, 10.45925437, 13.06359334, 13.81378955,\n",
    "       11.82158292, 16.93834671, 10.48777936, 14.17230283,  6.63886888,\n",
    "        7.2857522 , 14.62914074, 11.41255324, 14.38723848, 14.80092607,\n",
    "       10.45656004, 15.31127067, 14.33445367,  9.40400727,  6.36676962,\n",
    "       14.1418542 , 15.25370069, 12.48852017, 18.07942359, 12.1269647 ,\n",
    "       12.74866696, 16.74745308, 15.42834694, 12.10071153,  9.87623163,\n",
    "       12.50152178,  7.62084636, 10.40931342, 10.83547897, 10.2147319 ,\n",
    "       11.88774592, 15.56120705, 11.4014432 , 12.67275508, 11.25627126,\n",
    "       14.4804238 , 14.94150826,  8.1418573 ,  9.16408019,  7.71009653,\n",
    "        9.84448243, 13.7946926 ,  4.65222642, 11.48392034, 11.36194669,\n",
    "       11.2585006 , 13.59213915, 12.70468726, 16.27678778, 15.30801449,\n",
    "       19.80718169, 13.96550335,  4.51583695, 12.43701101, 11.50437664,\n",
    "        4.74791649, 12.16490674, 14.6385116 , 15.85842418, 15.76061832,\n",
    "       14.14511039, 13.37113669, 11.85226093, 15.79962348,  9.12222972,\n",
    "       11.60917497,  9.56242753, 13.01923881, 14.36331826,  7.40176422,\n",
    "       11.81959174, 13.72300771, 15.83969842, 11.57059114,  9.91605704,\n",
    "       19.34938723,  8.162288  , 10.74142509, 15.63186143, 11.58238432,\n",
    "        9.89346539,  9.38142614, 12.89340615, 12.96678986,  9.66350771,\n",
    "       16.99826563,  2.58284943, 12.70393319,  8.06963446,  9.73111822,\n",
    "       13.38506972, 15.10831298, 15.08498269,  6.92483515,  8.80525993,\n",
    "       10.390112  , 13.5461753 ,  8.75106316, 11.36924482,  9.69871704,\n",
    "        9.23275979, 12.43550329, 15.23176802,  9.91491463, 10.95943307,\n",
    "       11.77935338, 12.02364726, 13.3787093 , 10.75947082, 16.19614796,\n",
    "       10.92101502,  9.47236272, 13.91946103, 10.62493488, 12.2627494 ,\n",
    "       16.91801027, 12.71757097, 12.13055668, 16.36272878,  3.03983226,\n",
    "       14.19186518,  8.08063056,  9.8224435 ,  7.52489477, 11.28703284,\n",
    "       13.65644155, 14.0003042 , 14.13200882, 17.11634758, 14.96438543,\n",
    "       15.60263135,  9.27161065, 10.95739162, 11.63160764, 13.23908988,\n",
    "       10.0719898 ,  9.8796056 , 13.05554173, 14.7211202 , 14.83531548,\n",
    "       12.41639441, 17.26388048,  7.19055017, 10.74548465, 14.71763177,\n",
    "        7.48907317, 10.47710346,  9.97995926,  7.6495366 , 16.09693928,\n",
    "       13.26458585,  9.79034016, 18.74994343, 13.39659268, 14.24175426,\n",
    "       14.23621363,  6.78345096,  9.15719056, 11.61440847, 16.91722468,\n",
    "       13.90746381, 12.44531802, 12.62615478, 10.59495711, 10.13040348,\n",
    "        3.76657486, 15.81098028,  8.93455288, 11.95859969, 15.16344815,\n",
    "       11.80785278, 11.60122961, 11.99121613, 11.30130027,  9.99075238,\n",
    "       14.59353462,  9.08941503, 13.52158757, 15.40176301, 13.46787943,\n",
    "       11.74853818,  5.83513502, 12.15539973, 16.7891168 ,  8.09875172,\n",
    "       10.6310082 , 10.25618539,  6.21767497, 11.39837608,  9.59825852,\n",
    "       11.49465916, 14.29015963, 11.48315165, 15.66291869, 15.77957956,\n",
    "        4.88255399,  9.04458048, 15.62509581, 16.95018948, 13.3775874 ,\n",
    "       12.88460329, 13.24887651, 13.02214038, 13.8878541 , 15.66745438,\n",
    "       17.20639472, 11.9222186 ,  8.85100222,  9.95637784, 13.45446542,\n",
    "       13.54589738, 10.19396684, 10.31850862, 13.65769365, 10.26450834,\n",
    "       13.03164463, 16.4101971 , 11.89410484, 13.30320091,  9.38985916,\n",
    "        9.36131454, 14.93142961,  8.37673077, 11.5666218 , 15.51856477,\n",
    "       16.93052606, 11.46392373, 10.7071838 , 11.03657804,  9.18587141,\n",
    "       12.66000884,  9.10254542,  9.01776288, 13.90184705, 10.85414438,\n",
    "       15.81496996, 13.09905247, 10.07405055, 13.55861097, 14.82254442,\n",
    "       13.25174647,  8.17114623, 11.4953884 ,  8.02098619, 16.40002953,\n",
    "        9.4421317 , 11.88583757, 13.31227571, 14.95553065, 12.98428806,\n",
    "       11.1544708 , 13.40493049, 14.68919196, 12.440527  , 14.80701851,\n",
    "        6.57335148, 13.12571847, 13.82276238, 11.27165485,  9.65698752,\n",
    "       10.44903102, 10.95038812, 12.44366971,  9.86378511,  8.19112957,\n",
    "       10.2571676 ,  9.78105677, 11.21610962, 12.20475101, 10.45296661,\n",
    "       11.36748801, 14.9713108 ,  9.35001919, 15.99673101, 10.01563558,\n",
    "        9.59455089, 12.56848901,  8.17248203, 13.1895009 , 12.4293327 ,\n",
    "       13.14075275, 10.86593221, 13.32774828, 11.81153178, 13.90469108,\n",
    "       11.92063022, 13.71915611, 12.43453495, 15.70137597, 18.45901754,\n",
    "       14.6197433 ,  9.08884872,  5.15850014, 13.62333839, 11.04689724,\n",
    "       10.32119393, 17.91836777, 16.12399235, 12.41544643, 10.61299773,\n",
    "       19.2215383 , 15.18056861, 13.67688575, 11.33347782, 17.25661304,\n",
    "       15.16867507,  9.40715939, 14.03765542, 15.1503099 , 10.622078  ,\n",
    "       14.46106249, 11.04414728,  9.4665142 , 11.8714194 , 10.75685762,\n",
    "       10.77930357, 18.27803743, 13.44076954,  9.09071156, 12.99549238,\n",
    "       21.08760397,  9.02794452, 10.58456245, 13.02807663, 13.99149013,\n",
    "       13.69021892, 13.34233145, 18.46203371, 12.09409091, 13.89071504,\n",
    "        8.04164928, 10.33845976, 15.75377701,  9.89822645, 13.44711474,\n",
    "       14.3879143 , 17.20070526, 14.29210793, 18.27220542, 13.06642842,\n",
    "       13.00203395, 12.67410587,  7.12242434, 12.44652844, 10.13101132,\n",
    "        8.46635559, 11.9721057 , 15.47008364, 10.96698706,  6.05834163,\n",
    "        9.7531667 , 11.07756905,  9.59407186, 12.87481635, 11.694318  ,\n",
    "       14.78554439, 22.33221432,  6.84246646, 15.54975901, 11.11097571,\n",
    "       12.10674748,  9.49406724, 17.01665082, 10.99313794, 10.04778473,\n",
    "       14.40618557, 11.66664777, 11.98496279,  7.9726323 ,  8.56541709,\n",
    "       14.52105503, 14.68946799, 12.9448191 , 12.42843901, 16.15789865,\n",
    "        8.8113074 , 14.6655148 , 11.88793674, 14.76393398, 10.65796408,\n",
    "       10.66200286, 15.73645844, 12.20152003, 10.00266264, 12.9524175 ,\n",
    "       10.98355626, 20.35114473, 17.47530313,  9.14644249, 12.39268866,\n",
    "        9.40639098, 11.04232065, 12.24852286, 12.26360038, 10.87001996,\n",
    "       11.3733785 , 14.72465634, 13.50317832, 11.93362816,  7.52379566,\n",
    "       10.4680425 ,  7.8258331 , 11.19155117, 13.65729264,  7.01196691,\n",
    "       12.93385747, 13.31150831, 12.64664186, 14.78618476,  4.44415109,\n",
    "       12.81294031, 13.34684482, 12.1277528 ,  8.99405593, 13.46200704,\n",
    "        6.91128576,  9.35019668,  8.97055521, 11.28466444, 10.64399464,\n",
    "       12.05216807, 14.59059316, 12.31426901,  9.24310909, 14.54720685,\n",
    "        6.76053488,  8.09768217, 12.32363793,  9.02387847, 17.0286219 ,\n",
    "       19.0669372 , 15.84366113,  5.42203737,  9.41875147, 14.37555289,\n",
    "       11.15951297, 10.28333559, 14.49172936, 17.77046609,  9.16512068,\n",
    "       16.9575815 , 10.56507815, 13.64254405, 13.08350843, 13.81232518,\n",
    "       11.11322292,  9.4135368 , 10.26330365,  9.7081287 , 11.41922434,\n",
    "       13.66072764, 14.0416686 ,  9.661806  , 13.28447577,  9.80461106,\n",
    "        7.13412165, 10.26586752, 14.90528691, 13.65151123, 11.46129682,\n",
    "       14.28189362,  9.25854953, 10.40331241, 14.82192117,  9.85303781])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "b5754d44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "d8e221a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ivXpGPa9ubSHh8PNnN3LVuSdSafDdy6fyzv4ORp9wPOecqMldKS89rQT+Hhk2ggm5+zV5iUikAMLtGJ8PVvGaJSd7w7LOO59ax+wpY2jdvofptUN08pey1NMngMaCRSFSYOt27E1txxhW+KTX9Idlnarpl3LWbQJw958WMhCRQggXeK16a3fqij+s8Ol68ldNv5S7bDaEqSG58OtUkltCAuDu5+cxLpGcSyScR1Zt5dWtLRiHX/H3qYD/e+kUzFThI/GQzSTwPcC9wIeBzwGfBpryGZRIrqQ3caswY96iFXx2Zn3GVbwTR1VzVt1QXfFLbGTzL32Yu98BHHD3P7n7VcDZeY5L5JiFV/yf+cmzvLK5hXU79qYWd4XlnbOnjMGCi/wTh/XXyV9iJZt/7QeC71vM7MNmdjowNo8xiRyzRMJ5afMu5i1awewpY2hu28+f3247rJXDbY+/wY+WrmXSqGpqhw6IOmyRgspmCOgbZjYY+BLwPaAa+KdcvLiZzQJuASqBH7n7t3JxXImnTJuxp5d4Ztqg5aSagUx+12C1cpBYymZP4N8EN3eTbAaXE2ZWCdwGfBDYBDxnZr9291dy9RoSH+Fwz7xFKzptxh6WeFbaoWGfq2fUp4Z9powdTN3wgRFGLhKdXoeAzOynZnZC2v0hZnZnDl77LOANd1/r7vuBXwCX5OC4EkNrm1qZt2hFp7bN4RX/Qy9uZmj/Q60dNOwjkpTNENAUd98V3nH3ncE8wLEaA/w57f4m4L1df8jM5gJzAWpra3PwslIu0pu4bdm977B9ebfsbufuZRu4bPpY9nUc5Jz6YUyvHULb/g5qhw7QsI/EXjaTwBVmNiS8Y2ZDyU0PoUx/eYe1nnD3he7e4O4NNTU1OXhZKQddm7gl3FPDPeGVf5gE7nhyLWOHDmDK2BN4b/0wPjBpJBNGqJGbSDYn8n8DnjKz/wruXwH8aw5eexMwLu3+WOCtHBxXylymJm79+1Vy7QUTuWXxoX15/33ONKr6VjB+2AAt6hLJIJtJ4LvMrJHkzmAGXJajidrngIlmdiKwGfg48MkcHFfKWHjy79rELezgOfe8ehIOFQZm8P6TR+jEL9KNboeAzKw6+D4U2Ar8jOSq4K3BY8fE3TuAzwO/B1YDi9x91bEeV8pX+sk/UxO3O59ax8FE8uQ/vXYIF04aqZO/SA96+gTwM2A2hzaED1lwv/5YX9zdfwv89liPI+UrbN7W3LqflvYOXvjzTjVxE8mRnrqBzjYzA97v7hsLGJNIWtfOFja+3cY7Bw4mH3c1cRPJld42hXczewA4o0DxiNDRkeDhl7fwZlMrAAufSC7qgsw9+09WEzeRo5LNX8wyMzsz75FIrCUSztqmVp5b35yq8El48oo/rO/Xhi0iuZVNGegHgL83sw3AXoI5AHefktfIJDbCK/6wrLOy4tBJv9JINXDr2r5ZY/0ixyabBPBXeY9CYiu9pj+9rDM86X/uvPpUff/dyzZwRcNYTh45iFNGVWslr8gx6mlT+Gp3bwH2FDAeiYlwknddcxsvBDX9obDCZ8GSNdz+xFo+c+54fnDlGSQSrhYOIjl0JGWg6X9xOSkDlfgJT/zPb9zF+ua9yceCK/6wgVs41BMOB00aPVhDPSJ50GMZaPD9xMKFI+Usvbqna2VPeMUftnG46eLTOK5Phco6RfIoq6ZuZnYZMIPklf9Sd38wn0FJeQi7dW5raeddJ1Sxbkcb19+3ks/OrM9Y2RNe8auyR6Qwek0AZvZ94CTg58FDnzOzD7r7P+Y1Milp6Ru0DOnfj6/OPpXVW1tSJ35V9ohEL5tPAO8HTnN3h+QGMcBLeY1KSlL6loyGpTZouWz6WFZvbelU3ZO+NaMqe0SikU0CeA2oBTYE98cBK/MWkZSk8Ir/24+s5mMNtbR3HExd7Yelnelj/eGevBNHDOTU0dqTVyQK2SSAYcBqM3s2uH8m8LSZ/RrA3S/OV3BS3MKKnm0t++hIJFL78S5Ysia1H6/G+kWKVzYJ4Kt5j0JKTiLhLHltG2u2tXLL4jWpid2u+/EuWLKG+5Zv4lPnjOcXz2msX6SYZLMhzJ8gtT9An7TH385jXFLEEgnnpc27WLlpNwufWNtpYjf8Hu7HG17tz5w4nA+dOoqm1nZGDFJpp0gx6PXyy8zmmtk2kuP+jSQXhjXmOzApPomEs35HKw+u2MziV7d3atQWXvGH4/zp+/FOGlXNqaMHM2HEQM6uH059jfbjFSkG2QwBXQdMdvcd+Q5GilemRVxho7b2A4nUFf8VDWOZMraae+eeTdv+g1rIJVLEshmAfRNoy3cgUnzCK/7l699m6RuHWjSHY/xD+/fj2gsmpoZ+drbtZ9Koas6dUMPUcUM4Z4Ku9kWKWTafAP4FeMrMngH2hQ+6+zV5i0oi1d1uXOlj/Vt2t3P7E2v51DnjufnyqRzXt4L64QNVzilSQrL5BPADYAmwjOT4f/glZSZ9jP/+Fzbz2rY93LJ4TWpjlvRFXGESuGXxGioqjAsmjWTCCF3ti5SSbD4BdLj7vLxHIpHp2qEzvVFbeh2/FnGJlJdsEsDjZjYXeIjOQ0AqAy1h6W0b3trV3mlyt6fduMKyTtXxi5S+bP56P0kwD8Ch4R+VgZaoRMLZ0Jwc5rlowVL++FrnyV04dNIPJ3l3tu3n7mUbuGTaGE4ZPYhLpo5hxklawStS6rJZCKb9AMpEuHr3QIdzwwMvdVq5C4c3agt341p45Rkc1G5cImWnpy0h/6e7fye4fYW7/zLtuW+6+w2FCFByI331LtBpC8ZMHTrnnlevDp0iZc6CLs+HP2H2vLtP73o70/0jflGzK4CvA6cAZ7l7VkNKDQ0N3tio0aeepG/CMnpwFQcT8HbboXH+RPC/+0dLky0cRg+u4sqzx7NgyRqG9O+n1swiZcjMlrt7Q9fHexoCsm5uZ7p/pF4GLiNZYio5kF7Jc8MDLzGkfz8+dc54blm8hqtn1HPHk4dW7z644vAtGG//mzO0BaNIzPSUALyb25nuHxF3Xw1gppNMLoS9+F/d2pJqznbZ9LHcsnjNYR06P3dePR8/s5ZfPKeKHpG46+kvfqqZtZjZHmBKcDu8/54CxRc2o2s0s8ampqZCvWxJWd+8l3mLVnSq5Emf3IXOq3cBrvvQJKaNG6yKHpEY6/av3t0r3b3a3Qe5e5/gdni/b28HNrPHzOzlDF+XHEmA7r7Q3RvcvaGmpuZIfrXsJRLO2qZWXt+257CWzOm3tXpXRDLJZiHYUXH3C/N1bOm86Xq4+1bXTViuvWAityw+NM6/8MoG+laaxvlFBMhjApD8Cod9uu6+lV7COXl0tTZhEZFuRZIAzOxS4HtADfCwma1w97+MIpZSta2lPTXsk7771pQx1UwcOajTyX7CiIFRhioiRSqSmT93f8Ddx7r7ce4+Uif/7oXj/E+/uYO1Ta0kgkL+kdVVncb7w923Jo4cpB78IpIVlX4UsXCc/6IFS/nED5/hogVLeWTVVhIJp27YAObPmdZpH975c6ZRN2xAxFGLSKnodiVwMYrbSuC1Ta1ctGDpYeWcv71mJvU1A1Orfrfv0Ri/iHTvaFYCS4TCk3v6yR+Stf3b97SnhnnqawZSX6MxfhE5ckoARSa9pcOG5r2pTddDVX0rGDGoKsIIRaRcKAEUka4tHYb075cq72w/kNA4v4jklBJAEQlr+8NdudLLO81g5knDObNuqMb5RSQnlACKSHptfzj0s2V3O7c9/gZVfSu47PQxOvmLSM6oDDRCXWv8Rwyq6tTSQSWeIpJP+gQQkfRePuH4/q2fPJ35c6Yxb9EK7colInmndQAFFpZ3Nu3Zx6d//OxhFT6PXDuThKPafhHJme7WAWgIqIDSV/YufWNHxhr/rS3JGv+z64erpYOI5JUSQAGld/CEzr37w/uq8ReRQlECKKD0Kh9N9IpI1DQJXADhuH+FWafyznCi9/RxJzB+2ACN94tIQSkB5Fl6tc+Q/v1Su3S1H0iws20/k0ZV8/6TR+jELyIFpwSQZ+nj/lt2t3PX07rqF5HioDmAHMq0eUv6uD8kN25ZsPgNju9XqSofEYmUPgHkSKaFXfPnTOPdIwepo6eIFCV9AsiRriWe7QcSzFu0gsoKtHOXiBQlfQLIka5DPXBoYdesyaOYdM1Mre4VkaKiBHCUwtLObS3tjKyuSjVyyzTUo527RKQYKQEchd4auWnzFhEpBWoGdxS626xdjdxEpBhpU/gc6mm8P2ziJiJS7FQFdBRGVlepkZuIlLxIEoCZfdfMXjWzlWb2gJmdEEUcR6tu2ACVdopIyYtkDsDMPgQscfcOM/s2gLtf39vvFcscAByqAtJ4v4gUu6KaA3D3P6TdXQZcHkUcx0KlnSJS6ophDuAq4HfdPWlmc82s0cwam5qaChZUpr4+IiLlJG+fAMzsMWBUhqe+4u6/Cn7mK0AHcE93x3H3hcBCSA4B5SHUw3TX12fW5FEa5hGRspG3BODuF/b0vJl9GpgNXOBFthihu74+k66ZqSEfESkbUVUBzQKuBy5297YoYuhJd3X+2/e0RxSRiEjuRTUHcCswCHjUzFaY2e0RxZGR6vxFJA4iSQDufpK7j3P3acHX56KIozuq8xeROFAriAwqKkwtnEWk7CkBdEN1/iJS7ophHYCIiERACUBEJKaUAEREYkoJQEQkppQARERiquyrgLpu3q5yThGRpLJOAGrqJiLSvbIeAuquqdv65r0RRyYiEr2yTgBq6iYi0r2yTgBq6iYi0r2yTgBq6iYi0r2yngRWUzcRke6VdQIANXUTEelOWQ8BiYhI95QARERiSglARCSmlABERGJKCUBEJKbM3aOOIWtm1gRsKNDLDQd2FOi1Cq2c3xuU9/sr5/cG5f3+onxv4929puuDJZUACsnMGt29Ieo48qGc3xuU9/sr5/cG5f3+ivG9aQhIRCSmlABERGJKCaB7C6MOII/K+b1Beb+/cn5vUN7vr+jem+YARERiSp8ARERiSglARCSmlAB6YGbfNbNXzWylmT1gZidEHVOumNkVZrbKzBJmVlSlaUfLzGaZ2Wtm9oaZ/XPU8eSSmd1pZtvN7OWoY8k1MxtnZo+b2erg3+S1UceUS2ZWZWbPmtmLwfu7KeqYQkoAPXsUOM3dpwCvA/8ScTy59DJwGfBE1IHkgplVArcBfwWcCnzCzE6NNqqc+gkwK+og8qQD+JK7nwKcDfxjmf2/2wec7+5TgWnALDM7O9qQkpQAeuDuf3D3juDuMmBslPHkkruvdvfXoo4jh84C3nD3te6+H/gFcEnEMeWMuz8BvB11HPng7lvc/fng9h5gNTAm2qhyx5Nag7t9g6+iqL5RAsjeVcDvog5CujUG+HPa/U2U0UkkLsysDjgdeCbiUHLKzCrNbAWwHXjU3Yvi/ZX9jmC9MbPHgFEZnvqKu/8q+JmvkPyYek8hYztW2by3MpJpn8+iuMqS7JjZQOA+4Ivu3hJ1PLnk7geBacE84gNmdpq7Rz6fE/sE4O4X9vS8mX0amA1c4CW2aKK391ZmNgHj0u6PBd6KKBY5QmbWl+TJ/x53vz/qePLF3XeZ2R9JzudEngA0BNQDM5sFXA9c7O5tUccjPXoOmGhmJ5pZP+DjwK8jjkmyYGYG3AGsdvf5UceTa2ZWE1YQmtnxwIXAq5EGFVAC6NmtwCDgUTNbYWa3Rx1QrpjZpWa2CTgHeNjMfh91TMcimKz/PPB7kpOIi9x9VbRR5Y6Z/Rx4Gni3mW0ys6ujjimH3gdcCZwf/J2tMLOLog4qh0YDj5vZSpIXKo+6+28ijglQKwgRkdjSJwARkZhSAhARiSklABGRmFICEBGJKSUAEZGYUgKQgjOzYWnlflvNbHNwe5eZvVLgWD6S3njMzP63mR3xAjozq+uuU6eZTTazJWb2upm9aWY3mVnO//Z6ei9m9sdy6foquaMEIAXn7s3uPs3dpwG3A/8e3J4GJHL9embW04r3j5DsHhrG9lV3fyyHr308yQVp33L3k4H3kGxcl4+Wxx8hj+9Fyo8SgBSbSjP7YdA3/Q/BCRQzm2Bmj5jZcjNbamaTgsfHm9niYM+GxWZWGzz+EzObb2aPA9/O9Ptmdi5wMfDd4BPIhOD3Lg+OcaaZPRX0cX/WzAYFV/pLzez54OvcXt7PJ4H/dvc/AAQryj8PXBe8xtfN7MvhD5vZy0FDNMzswSDeVWY2N+1nWs3sX4O4lpnZyN7eSzoz+5CZPR3E/8ugBw9m9i0zeyX4b3nzkf+vk1KjBCDFZiJwm7tPBnYBHw0eXwh8wd3PAL4MfD94/FbgrmDPhnuABWnHOhm40N2/lOn33f0pklfn1wWfSN4MfzFoJ3EvcG3Qx/1C4B2S3Rw/6O7TgY91eb1MJgPL0x8IXud4632DoauCeBuAa8xsWPD4AGBZENcTwN/19F7Smdlw4Mbgv8t0oBGYZ2ZDgUuBycF/y2/0EpuUgdg3g5Ois87dVwS3lwN1wRXqucAvk21jADgu+H4OyY1tAO4GvpN2rF+6+8Fefr877wa2uPtzAGF3SjMbANxqZtOAgySTTE+MzF1JM3Uv7eoaM7s0uD2OZHJsBvYDYSuB5cAHszhW6GySw0T/Hfy36EeyxUQL0A78yMweTju+lDElACk2+9JuHwSOJ/lJdVcwT9Cb9JPt3uD7kfx+qLsT9z8B24CpwXHbeznOKuC8Tgc2qwd2BJ0hO+j8Sbwq+Jm/IPmp4xx3b7NkB8mq4GcOpHWmPciR/R0byV40nzjsCbOzgAtINtL7PHD+ERxXSpCGgKToBVff68zsCkh2jzSzqcHTT5E8YQH8NfDkEf7+HpIN/7p6FXiXmZ0Z/M6gYDJ5MMlPBgmSDcwqewn/HmBGWjXO8SSHjb4WPL8emB48Nx04MXh8MLAzOPlPInnl3pvu3ku6ZcD7zOyk4DX7m9nJwaekwe7+W+CLJCfkpcwpAUip+GvgajN7keRVdbjd4zXAZyzZafFKuq+u6e73fwFcZ2YvmNmE8IeDbSU/Bnwv+J1HSV6Bfx/4tJktIzn8s5ceuPs7JCdnv2JmrwM7SE4Kh5sL3QcMteRuUf9Acu9pgEeAPsH7+j8kT9y9yfheusTTBPwt8PPg2MuASSQTx2+Cx/5E8pOOlDl1AxUpIDP7CDAf+IC7b4g4HIk5JQARkZjSEJCISEwpAYiIxJQSgIhITCkBiIjElBKAiEhMKQGIiMTU/weyIZ2Ko28xhwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "QQPlot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "8d13863a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot(x,line= \"45\", fit = True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d22cd16",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5723d538",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f388283e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c7d80688",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17a14fd7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a48c8b2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "a9b3f041",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.special import ndtri # Used to calculate theoretical z values.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data_points = np.random.normal(0, 1, 1000)\n",
    "df = pd.DataFrame(data_points, columns=[\"Points\"])\n",
    "df = df.sort_values(by=[\"Points\"], ascending=True).reset_index(drop=True)\n",
    "df[\"count\"] = df.index + 1\n",
    "n_rows = df.shape[0]\n",
    "df[\"percentile_area\"] = (df[\"count\"]) / n_rows\n",
    "df[\"z_theortical\"] = ndtri(df[\"percentile_area\"])\n",
    "df[\"z_actual\"] = (df[\"Points\"] - df[\"Points\"].mean()) / df[\"Points\"].std()\n",
    "plt.scatter(df[\"z_actual\"], df[\"z_theortical\"])\n",
    "plt.plot([-4,-3,-2,-1,0,1,2,3,4],[-4,-3,-2,-1,0,1,2,3,4],\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "46ab2f04",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "95ab28f9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "e6ab4854",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "18815cb3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d28da7b4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e0dd74bc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e155734",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aa34ba7c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "1e75f1e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "age_data_titanic=  sns.load_dataset(\"titanic\")[\"age\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "d938f599",
   "metadata": {},
   "outputs": [],
   "source": [
    "def QQplot__(data):\n",
    "\n",
    "    data = data.sort_values(ascending=True).reset_index(drop=True)\n",
    "    data = data.dropna()\n",
    "    df = pd.DataFrame(data)\n",
    "    df[\"Count\"] = df.index+1\n",
    "    nrow = df.shape[0]\n",
    "    df[\"percentile_area\"] = df[\"Count\"]/nrow\n",
    "    df[\"Z_theoretical\"] = norm.ppf(df[\"percentile_area\"])\n",
    "    df[\"Z_Emperical\"] = (data-data.mean())/data.std()\n",
    "    \n",
    "    plt.scatter(df[\"Z_theoretical\"],df[\"Z_Emperical\"],c=\"c\")\n",
    "    plt.plot([-2,-1,0,1,2],[-2,-1,0,1,2],\"b-\")\n",
    "    \n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "38054971",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "QQplot__(age_data_titanic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "33c766fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='age', ylabel='Density'>"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(age_data_titanic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "155d4c9e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "29c3d78e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d3a0b78",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9e5ef683",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a970440",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee761237",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "005719b3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2456ac33",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4c6a115",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "90b075d5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da67f1ac",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "a9602362",
   "metadata": {},
   "source": [
    "# steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "fbf29457",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = sns.load_dataset(\"titanic\")[\"age\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "a55301de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      22.0\n",
       "1      38.0\n",
       "2      26.0\n",
       "3      35.0\n",
       "4      35.0\n",
       "       ... \n",
       "886    27.0\n",
       "887    19.0\n",
       "888     NaN\n",
       "889    26.0\n",
       "890    32.0\n",
       "Name: age, Length: 891, dtype: float64"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "e878f7d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.sort_values(ascending=True).reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "338d7b79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      0.42\n",
       "1      0.67\n",
       "2      0.75\n",
       "3      0.75\n",
       "4      0.83\n",
       "       ... \n",
       "886     NaN\n",
       "887     NaN\n",
       "888     NaN\n",
       "889     NaN\n",
       "890     NaN\n",
       "Name: age, Length: 891, dtype: float64"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "2545b288",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.dropna()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "acca8e1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "8e70a97f",
   "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>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    age\n",
       "0  0.42\n",
       "1  0.67\n",
       "2  0.75\n",
       "3  0.75\n",
       "4  0.83"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "f7a2ae9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"Count\"] = df.index+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "ab316aad",
   "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",
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       "    age  Count\n",
       "0  0.42      1\n",
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       "2  0.75      3\n",
       "3  0.75      4\n",
       "4  0.83      5"
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     "execution_count": 76,
     "metadata": {},
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    }
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    "df.head()"
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  {
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   "execution_count": 77,
   "id": "6ff53b94",
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
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    "nrow = df.shape[0]\n",
    "nrow"
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   "cell_type": "code",
   "execution_count": 78,
   "id": "bc18952f",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"percentile_area\"] = df[\"Count\"]/nrow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "6af3c43d",
   "metadata": {},
   "outputs": [
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       "    age  Count  percentile_area\n",
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    "df[\"Z_theoretical\"] = norm.ppf(df[\"percentile_area\"])"
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  {
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   "execution_count": 81,
   "id": "6b9483bf",
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   "outputs": [
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       "    age  Count  percentile_area  Z_theoretical\n",
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   "cell_type": "code",
   "execution_count": 82,
   "id": "3a113b2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"Z_Emperical\"] = (df[\"age\"]-df[\"age\"].mean())/df[\"age\"].std()"
   ]
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   "cell_type": "code",
   "execution_count": 83,
   "id": "4d4b98cf",
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       "    age  Count  percentile_area  Z_theoretical  Z_Emperical\n",
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     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df[\"Z_theoretical\"],df[\"age\"],c=\"c\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "ed95871c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df[\"Z_theoretical\"],df[\"Z_Emperical\"],c=\"c\")\n",
    "plt.plot([-2,-1,0,1,2],[-2,-1,0,1,2],\"b-\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1f7c687",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "71235362",
   "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>Points</th>\n",
       "      <th>count</th>\n",
       "      <th>percentile_area</th>\n",
       "      <th>z_theortical</th>\n",
       "      <th>z_actual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>2.725759</td>\n",
       "      <td>996</td>\n",
       "      <td>0.996</td>\n",
       "      <td>2.652070</td>\n",
       "      <td>2.685608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>2.821955</td>\n",
       "      <td>997</td>\n",
       "      <td>0.997</td>\n",
       "      <td>2.747781</td>\n",
       "      <td>2.780807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>2.925424</td>\n",
       "      <td>998</td>\n",
       "      <td>0.998</td>\n",
       "      <td>2.878162</td>\n",
       "      <td>2.883204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>3.028240</td>\n",
       "      <td>999</td>\n",
       "      <td>0.999</td>\n",
       "      <td>3.090232</td>\n",
       "      <td>2.984954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>3.523451</td>\n",
       "      <td>1000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>inf</td>\n",
       "      <td>3.475031</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Points  count  percentile_area  z_theortical  z_actual\n",
       "995  2.725759    996            0.996      2.652070  2.685608\n",
       "996  2.821955    997            0.997      2.747781  2.780807\n",
       "997  2.925424    998            0.998      2.878162  2.883204\n",
       "998  3.028240    999            0.999      3.090232  2.984954\n",
       "999  3.523451   1000            1.000           inf  3.475031"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "f13c42a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='z_theortical', ylabel='count'>"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(x = df[\"z_theortical\"],\n",
    "            y = (df[\"count\"])/1000)\n",
    "sns.lineplot(x = df[\"z_actual\"],\n",
    "            y = (df[\"count\"])/1000)\n",
    "sns.distplot(x = df[\"Points\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "510f563d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f768e3cc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69fc7530",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4183f4a8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47763c3f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fc05a683",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b25e5b5e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "82cf0cdb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a43be60",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "9c9c5025",
   "metadata": {},
   "source": [
    "## QQ plot between Non Gaussian and Non Gaussian dist : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "d7e53d10",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import poisson\n",
    "x = np.array([ 3,  4,  2,  6,  5,  2,  5,  8,  5,  2,  4,  2,  4,  5,  1,  3,  4,\n",
    "        3,  4,  4,  2,  3,  4,  3,  5,  5,  2,  5,  6,  3,  6,  3,  1,  3,\n",
    "        4,  3,  5,  6,  6,  7,  4,  4,  3,  4,  5,  3,  6,  2,  4,  6,  9,\n",
    "        4,  4,  0,  2,  0,  1,  8,  2,  4,  0,  1,  4,  6,  0,  3,  5,  2,\n",
    "        3,  4,  6,  8,  7,  6,  3,  2,  4,  1,  3,  5,  3,  4,  4,  7,  4,\n",
    "        2,  3,  5,  5,  6,  3,  3,  7,  3,  3,  3,  3,  4,  4,  6,  4,  5,\n",
    "        5,  4,  3,  3,  4,  5,  2,  2,  6,  5,  3,  6,  4,  8,  8,  2,  5,\n",
    "        3,  5,  3,  5,  0,  6,  3,  5,  4,  7,  7,  2,  2,  4,  4,  3,  4,\n",
    "        4,  4,  3,  7,  4,  4,  2,  6,  3,  2,  1,  5,  4,  2,  3,  2,  5,\n",
    "        1,  5,  5,  5,  6,  2,  4,  3,  5,  5,  4,  5,  3,  1,  4,  6,  6,\n",
    "        4,  1,  5,  3,  0,  3,  2,  5,  1,  4,  6,  4,  3,  6,  5,  1,  4,\n",
    "        4,  5,  5,  2,  6,  1,  3,  4,  6,  6,  4,  3,  5,  6,  3,  6,  4,\n",
    "        3,  4,  4,  6,  4,  1,  6,  2,  2,  4,  4,  2,  5,  4,  1,  2,  2,\n",
    "        4,  3,  4,  7,  8,  2,  2,  1,  6,  2,  8,  4,  5,  4,  6,  3,  4,\n",
    "        3,  3,  7,  6,  5,  5,  6,  3,  3,  4,  4,  7,  7,  1,  2,  4,  8,\n",
    "        6,  4,  4,  1,  1,  4,  2,  5,  4,  5,  9,  8,  3,  3,  5,  3,  6,\n",
    "        5,  6,  1,  5,  2,  9,  5,  2,  5,  7,  3,  6,  8,  5,  5,  5,  6,\n",
    "        1,  2,  1,  8,  8,  3,  6,  3,  4,  3,  7,  9,  2,  6,  7,  2,  0,\n",
    "        4,  2,  3,  3,  2,  7,  2,  4,  4,  4,  1,  5,  3,  5,  5,  5,  8,\n",
    "        0,  4,  2,  4,  1,  2,  3,  3,  5,  3,  2,  3,  2,  6,  2,  4,  3,\n",
    "        3,  4,  3,  5,  2,  2,  1,  1,  4,  5,  7,  5,  4,  6,  6,  1,  2,\n",
    "        2,  1,  3,  1,  6,  5,  5,  0,  3,  3,  2,  7,  7,  2,  4,  5,  3,\n",
    "        3,  6,  6,  6,  1,  3,  7,  1,  5,  4,  5,  6,  4,  3,  4,  4,  5,\n",
    "        4,  5,  4,  6,  3,  2,  3,  4,  3,  4,  5,  6,  6,  4,  4,  2,  7,\n",
    "        7,  6,  5,  4,  4,  5,  3,  4,  3,  4,  7,  3,  8,  4,  6,  3,  4,\n",
    "        3,  3,  6,  5,  5,  2,  6,  4,  3,  7,  4,  4,  2,  4,  8,  3,  3,\n",
    "        4,  1,  4,  3,  7,  5,  3,  1, 12,  4,  3,  3,  3,  4,  6,  5,  4,\n",
    "        8,  1,  5,  5,  7,  6,  5,  8,  4,  4,  4,  6,  5,  3,  7,  1,  2,\n",
    "       10,  1,  5,  2,  2,  3,  2,  3,  8,  5,  4,  4,  4,  7,  5,  6,  4,\n",
    "        4,  6,  8,  3,  3,  2,  2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "28526821",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "261a45a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(x,dist=\"poisson\",sparams = (4,), plot = plt)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "32f288f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# stats.probplot(x,dist=\"norm\",sparams = (0,1), plot = plt)\n",
    "# plt.grid()\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a35bc7a6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "6473f657",
   "metadata": {},
   "outputs": [],
   "source": [
    "def QQplot_poisson(data):\n",
    "\n",
    "    data = data.sort_values(ascending=True).reset_index(drop=True)\n",
    "    data = data.dropna()\n",
    "    df = pd.DataFrame(data)\n",
    "    df[\"Count\"] = df.index+1\n",
    "    nrow = df.shape[0]\n",
    "    df[\"percentile_area\"] = df[\"Count\"]/nrow\n",
    "    df[\"Z_theoretical\"] = poisson.ppf(df[\"percentile_area\"],data.mean())\n",
    "    df[\"Z_Emperical\"] = (data-data.mean())/data.std()\n",
    "    \n",
    "    plt.scatter(df[\"Z_theoretical\"],df[\"Z_Emperical\"],c=\"c\")\n",
    "    \n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "30bfe1fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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O0o2rjncr+Y95q9nerpUQn4qIJ8qup0B3SPqI7f/Qyu2wu2z/bbklFeqcpHMRcfknqMe1Euz94KCkf4+IxYh4U9ITkn6p5Jo6YcH2+yWp/vsbJdfTskxB/oKkm23fZPtarbzo8nTJNRXCtrVyj/VURHyx7HqKFBGfj4jdETGile/ZtyOib1Z1EfFfkl6zPVYfOiDp5RJLKtJZSbfb3lH/M3pAffJCboOnJd1b//heSU+VWMumpGm+HBGXbH9a0jNaefX84Yg4WXJZRblD0icl/avt2frYH0fE35VXElrwGUlT9QXGvKTfLrmeQkTE87Yfl/SiVnZWfVfJ385u+1FJ+yXttH1O0hck/amkx2z/rlb+8fpYeRVuDm/RB4DkMt1aAQA0QZADQHIEOQAkR5ADQHIEOQAkR5ADQHIEOQAk93+OwUThb24c5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "QQplot_poisson(pd.Series(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "d3c8d8ee",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "dc69764f",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = pd.Series(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "faa8e447",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = X.sort_values(ascending=True).reset_index(drop=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "c0a6c146",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.dropna()\n",
    "df = pd.DataFrame(data)\n",
    "df[\"Count\"] = df.index+1\n",
    "nrow = df.shape[0]\n",
    "df[\"percentile_area\"] = df[\"Count\"]/nrow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "8c489d86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>0</th>\n",
       "      <th>Count</th>\n",
       "      <th>percentile_area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <td>0.002</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>9</td>\n",
       "      <td>496</td>\n",
       "      <td>0.992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>9</td>\n",
       "      <td>497</td>\n",
       "      <td>0.994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>9</td>\n",
       "      <td>498</td>\n",
       "      <td>0.996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>10</td>\n",
       "      <td>499</td>\n",
       "      <td>0.998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>12</td>\n",
       "      <td>500</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      0  Count  percentile_area\n",
       "0     0      1            0.002\n",
       "1     0      2            0.004\n",
       "2     0      3            0.006\n",
       "3     0      4            0.008\n",
       "4     0      5            0.010\n",
       "..   ..    ...              ...\n",
       "495   9    496            0.992\n",
       "496   9    497            0.994\n",
       "497   9    498            0.996\n",
       "498  10    499            0.998\n",
       "499  12    500            1.000\n",
       "\n",
       "[500 rows x 3 columns]"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "d646bc4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"Z_theoretical\"] = poisson.ppf(df[\"percentile_area\"],data.mean())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "a2df8617",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>Count</th>\n",
       "      <th>percentile_area</th>\n",
       "      <th>Z_theoretical</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
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       "    <tr>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
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       "      <td>0.008</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <td>496</td>\n",
       "      <td>0.992</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>9</td>\n",
       "      <td>497</td>\n",
       "      <td>0.994</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>9</td>\n",
       "      <td>498</td>\n",
       "      <td>0.996</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>10</td>\n",
       "      <td>499</td>\n",
       "      <td>0.998</td>\n",
       "      <td>11.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>12</td>\n",
       "      <td>500</td>\n",
       "      <td>1.000</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      0  Count  percentile_area  Z_theoretical\n",
       "0     0      1            0.002            0.0\n",
       "1     0      2            0.004            0.0\n",
       "2     0      3            0.006            0.0\n",
       "3     0      4            0.008            0.0\n",
       "4     0      5            0.010            0.0\n",
       "..   ..    ...              ...            ...\n",
       "495   9    496            0.992           10.0\n",
       "496   9    497            0.994           10.0\n",
       "497   9    498            0.996           10.0\n",
       "498  10    499            0.998           11.0\n",
       "499  12    500            1.000            inf\n",
       "\n",
       "[500 rows x 4 columns]"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "b258f6a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"Z_Emperical\"] = (data-data.mean())/data.std()\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "08d1f7b6",
   "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>0</th>\n",
       "      <th>Count</th>\n",
       "      <th>percentile_area</th>\n",
       "      <th>Z_theoretical</th>\n",
       "      <th>Z_Emperical</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.096145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.096145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.096145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.096145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.096145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>9</td>\n",
       "      <td>496</td>\n",
       "      <td>0.992</td>\n",
       "      <td>10.0</td>\n",
       "      <td>2.559656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>9</td>\n",
       "      <td>497</td>\n",
       "      <td>0.994</td>\n",
       "      <td>10.0</td>\n",
       "      <td>2.559656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>9</td>\n",
       "      <td>498</td>\n",
       "      <td>0.996</td>\n",
       "      <td>10.0</td>\n",
       "      <td>2.559656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>10</td>\n",
       "      <td>499</td>\n",
       "      <td>0.998</td>\n",
       "      <td>11.0</td>\n",
       "      <td>3.076967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>12</td>\n",
       "      <td>500</td>\n",
       "      <td>1.000</td>\n",
       "      <td>inf</td>\n",
       "      <td>4.111589</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      0  Count  percentile_area  Z_theoretical  Z_Emperical\n",
       "0     0      1            0.002            0.0    -2.096145\n",
       "1     0      2            0.004            0.0    -2.096145\n",
       "2     0      3            0.006            0.0    -2.096145\n",
       "3     0      4            0.008            0.0    -2.096145\n",
       "4     0      5            0.010            0.0    -2.096145\n",
       "..   ..    ...              ...            ...          ...\n",
       "495   9    496            0.992           10.0     2.559656\n",
       "496   9    497            0.994           10.0     2.559656\n",
       "497   9    498            0.996           10.0     2.559656\n",
       "498  10    499            0.998           11.0     3.076967\n",
       "499  12    500            1.000            inf     4.111589\n",
       "\n",
       "[500 rows x 5 columns]"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "70edee92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df[\"Z_Emperical\"],df[\"Z_theoretical\"],c=\"c\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "b005e520",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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e5wfQtD7rReuuA4wF1gOaAc8CJ1a3TkFBgddXUVFRvdfNBNm8f9q3zBIu03HP5zsfzMleivlcWnsh97kvW5aSvip7pFom/e6ACV5JTq3Nyd18MxtiZi9Hyx2BXg34rtkX+Mrd57n7MuBpYLcGbE9EGoHV+Z2LuZEZtKcnD3Mr59GeGQzi9HqN41enTZu6tcvKanNydxjwKlD+I/0MOKcBfX4DdDGz5mZmwD7Apw3YnojEyR2efJLf23XgRi7hDfalIx9zIf1ZQCu8oWcEKzFnzqpJvk2b0C41q03ib+3uTwBlAO6+HKj3TJPu/j4wCpgEfBTFkKFTFovkuIkTYa+94O9/h7XXhjFjONKfYXDRnD8GX1JlzpyVB3mU9GuvNol/oZn9GXAAM+sCLGhIp+5+pbtv5e6d3L2nuy9pyPZEJM2+/RZOOgl22gk++wweeCDU19l777gjk1qozcDbv4Hngc3N7G3CSdkeKY1KRBqnxYtDeeSbboJly+DCC+GSS8LRvmSMGhO/u08ys67AloTrp6ZHJ2VFJFe4w+OPw0UXwTffwNFHhxuyNtss7sikHmpM/Gb2fxWadjQz3P2hFMUkIo3Jf/8b7rR9551QMvmhh6Br17ijkgaozVDPTgmv1yBchTMJUOIXyWZz5kC/fvDww5CfD0OGQK9eYXIUyWi1Geo5M3HZzP4EPJyyiEQkXosWhfLIN98MpaUh+ffrBy1bxh2ZJEl97qpYBLRPdiAiEjN3eOyxMI4/ezYcc0xI/ptuGndkkmS1GeN/gehSTsLlnx2BJ1IZlIik2XvvhXH8996DggJ49FHYc8+4o5IUqc0R/4CE18uBme4+O0XxiEg6zZoFF18cEv0GG8CwYdCzJzTRdNzZrMbfrruPS3i8raQvkjkSJypZaWKUhQvhyithyy3h6afhssvCjVi9ejUo6ZeX1+/evStNm4ZlaXyqPOI3s99YMcSz0luEEni6Y0OkEVtl9ivAKKOnjeDhNheHu2+POy7cjNW2bYP769MH7r13RU+lpSuWBw5s8OYliar8anf3lu6+diWPlkr6IplnV97hPbrwMP8Xpqp6661wMjcJSR9gUBUVt6pql/jU+m86M1vfzDYpf6QyKBFJnk2YyaP8g3fYnQ2ZQ08eCidxd989qf2UVlG6sap2iU9t6vEfZmYzgK+AcYTZuF5OcVwi0kBrUcI1XM40tuJwnuNqrmALPuMRUnPytqr7unS/V+NTm9/+tUAX4DN335Rw5+7bKY1KROqvrAyGDeMztuByruMpjmZLpnMVV7OItVLWbWFh3dolPrVJ/Mvc/SegiZk1cfciYPvUhiUi9fLmm7DzznDSSbTZZRO68C49eYTZbPzHR1JVI3/gQDjjjPIjfCcvLyzrxG7jU5vEP9/MWgDjgRFmdifhen4RaSy++ipMhrLXXvDDDzBiBLzzDu95l1VmpU2lgQNh+XIoKhrH8uVK+o1VlYnfzHqY2RrA4YQyDecCrwBfAIemJzwRqdZvv4V6+B06wIsvwtVXw/TpcPzxuglLqlTdnbsnAAMJyf4x4DV3H56WqESkeqWlMHx4SPo//BDutr3hBthoo7gjkwxQ3XX8RwJ/BcYAZwGzzOxeM9srXcGJSCXGjQtTHp5ySpgI5f33Q418JX2ppWr/FnT3X919uLsfCGwDTAHuNrNZ6QhORBJ8+SX06AHdusFPP4Wbr95+O5zMFamDWg0Cmtk6wFHAscC6wFOpDEpEEvz6ayiV3KEDvPIKXHcdTJsWyi1UVpdBpAbV1eppCRwB/APYkTDh+nVAkXuqrw0QEUpL4cEHQwG1uXOhd2+4/npo0ybuyCTDVXdy9yvgVeBe4BVNsC6SRkVFcM458OGHsMce4Yqdzp3jjkqyRHWJfxN3X5S2SEQEPv8cLrgAnn02FE974okwrq8hHUmi6q7qSVnSN7NWZjbKzKaZ2admtmuq+hJpTMpr4nfv3nXl+vgLFoSE37EjvPFGuDRz2rQw/WEDkv4666xci3+ddZKzH5LZ6jPnbjLcSRg+6mFmqwHNY4pDJG1Wzt9hIY/lnG5DuH+9y+HHH+Gkk8LJ2w02aHB/66wD8+ev3DZ/fmj/5ZcGb14yWNoTv5mtDewF9AZw96XA0nTHIRK3fXiD2/g32/IRdNgLbr8ddtwxaduvmPRrapfcYVVdoFNhkvVVuPth9erQbHtgEPAJsB0wETjb3RdW+FwhUAiQn59fMHLkyPp0R0lJCS1atKjXupkgm/cv2/ate/eugNGezxjA+RzGC3zJppxPf84au27Sx/HL+1uVU1Q0Lql9VZRtv7tEmbRv3bt3n+juq14V4O6VPoCu0eNO4HFCfZ5DgUeBG6par6YH0JlQ5G2XaPlO4Nrq1ikoKPD6Kioqqve6mSCb9y/b9q0VP/utnOtLaeoLaOkXcLOvzmIPM5km38ql2VZ+pFq2/e4SZdK+ARO8kpxa5VCPu48DMLNr3T2xTMMLZja+AV9Cs4HZ7v5+tDwKuLgB2xNp3JYvh0GDmMEVrMvPDOZULuda5pKf0m5btap8WKdVq5R2KxmgNnfurmdmm5UvmNmmwHr17dDdvyfU/dkyatqHMOwjkn1eew222w769qV1t23YkUmcziDmsv4fH0nV7ZC//LJqkm/VSid2pXaJ/1yg2MyKzawYKALOaWC/ZxJq+39ImNTlhgZuT6RxmTYNDjkE9t8fliyBZ56BsWOZ4tvjHurVp6M+/i+/rDzIo6QvUIuretz9FTNrD2wVNU1z9yUN6dTdpxDG+kWyy88/h5r4AwdC8+bQvz+ceSasvnrckYn8ocbEb2bNgX8Dbd39NDNrb2Zbuvvo1IcnkiGWLYP77oMrrww3Y512GlxzDay/fs3riqRZbYZ6hhKusy+/u3Y2oVibiAC8/DJsuy2cdVa4Dn/KlPAloKQvjVRtEv/m7n4LsAzA3RdT+cXBIrnlk0/gwAPhoINCJc3nn4fXX4dttok7MpFq1SbxLzWzNYlu5jKzzYEGjfGLZLSffgrj9ttuC+++C7fdBlOnwqGHqpiaZITalGy4kjDv7sZmNgLYnajcgkhOWbYsnLS96qowOco//xlO5LZuHXdkInVSbeI3syZA+exbXQhDPGe7+49piE2kcXCHl16C886D6dPhb38LR/mdOsUdmUi91DTnbhnwL3f/yd1fdPfRSvqSU6ZODdfiH3JI+AIYPRpefVVJXzJabcb4Xzez881sYzNbt/yR8shE4jRvHvTpE+66nTAB7rgjfAkcfLDG8SXj1WaM/+TouW9CmwObVfJZkYyTmMebsZR/8R9u+9M1UFICffuGa/P//Of4AhRJstrcubtpOgIRicOKpO8cygvcynm053NeWnAgB31yK3ToEGd4IilR41CPmTU3s8vMbFC03N7MDkl9aCLpsQ0f8jp/43kOZxnNOJCXOJiXlPQla9Xlzt3domXduSvZYe5c7uWfTGYHdmAy/+JutuMDXuHAuCMTSSnduSu5Z8mSUDytfXtOYQh3cybtmcE9/IvlNIs7OpGUq83JXd25K9nBHZ59Fs4/H778Eg4+mG1eHMD0PwrPiuSG2hzxV7xzdwxwYUqjEkm2KVNg773hqKNgzTXDtfijRzPNK0/6qa6TLxKn2lzV87qZTUJ37kom+uEHuOwyGDIE1l03lFw47TRouuKfvpK85JoqE7+Z7Vih6bvoeRMz28TdJ6UuLJEG+v13uPNOuP56WLwYzj0XLr9cE86KUP0R/63R8xqE2bI+IBzxbwu8D+yR2tBE6sEdnn4aLrgAvvoKDjssnMjdYou4IxNpNKoc43f37u7eHZgJ7Ojund29ANgB+DxdAYrU2qRJ0K0b9OgBa60VauM/95ySvkgFtTm5u5W7f1S+4O5TCROkizQO330HJ58MnTuHyVHuuw8mT4Z99407MpFGqTaXc04zs8HAI4RLOk8EPk1pVCK1sXgx3H473HADLF0ayiZfdhn86U9xRybSqNUm8fcGzgDOjpbHA/emKiCRGrnDk0/ChRfCzJlw5JFwyy3w17/GHZlIRqhpIpY8YLS77wvcnp6QRKoxYQKccw68/XYomTx0KHTvHndUIhmlpolYSoFFZqa/nSVe334LvXvDTjvBjBnwwAMwcaKSvkg91Obk7u/AR2Y2xMzuKn80tGMzyzOzyWY2uqHbktQyW/WRjv66d+/KmraYy+w6aN8eHnsMLrooJP5TT4W8vKT016dPuJ/LLDz36ZOUzYo0WrUZ438xeiTb2YSTxGunYNuSJFUlebPU3PGaWB//OEZyMxexCbMYtehoenxxC2yW3Pl/+vSBexPOWJWWrlgeODCpXYk0GrU54n8cmAhMAB539+HuPrwhnZrZRsDBwOCGbEey0868z9vszmMcz4+0pivFHMOopCd9gEGD6tYukg2qK9nQFLiBMPXiTMKXxEZmNhS41N2XNaDfOwiF3lpW038hUAiQn59PcXFxvToqKSmp97qZIPX715XKq3A7xcXjktrT6vPm8RDP05NH+J58TmYIw+lFGXkp6Q+gtLTy/SstTU1/5fTvMnNlxb65e6UPwlU8g4GWCW1rA4OAO6tar6YHcAgwMHrdjXDVULXrFBQUeH0VFRXVe91MkOr9CwM6lT+SZuFC96uucl9zTV/M6n4dl3gLfk1dfwny8irft7y81PRXTv8uM1cm7RswwSvJqdUN9RwCnObuvyV8SfxKuKb/oAZ81+wOHGZmXwMjgb3N7JEGbE8yVVkZjBgBW24JV10Fhx7KVkzjMq6npOo/BpOqsLBu7SLZoLrEX/6NUbGxlGhSlvpw937uvpG7twOOA8a6+4n13Z6kVlUncBt8Yve992C33eDEEyE/H958Ex5/nK+9XWIvyeuvCgMHwhlnrLhAKC8vLOvErmSz6hL/J2b2fxUbzexEYFrqQpLGprLBkHqbNQtOOAF23RW++QaGDYP//hf2WFHstbyPoqJxDe+vFgYOhOXLQz/LlyvpS/ar7nLOvsDTZnYy4aoeB3YC1gSOTEbn7l4MFCdjW9LIlZSEsgoDBoQMe9ll4Zr8Fi3ijkwk51SZ+N19DrCLme0NbE249OFldx+TruAkC5SVwSOPQL9+4e7b446Dm26Ctm3jjkwkZ9Vm6sWxwNg0xCLZ5u23Q12dCRNCqYUnnwzj+iISq9rcwCVSNzNnhiP7PfYItfIffnjFyVwRiV1tSjaI1E5JSRjGGTAAmjSBK68MUyCutVbckYlIAiV+abiyMnjooTCO//334aqdG2+EjTeOOzIRqYQSvzTM+PFw7rlhvttddoFnnoEuXeKOSkSqoTF+qZ+vvoJjjoGuXWHu3HAH7rvvKumLZAAd8Weo1VaDZcsgFFGDZs3CtLOpkFiauSW/0o8b6bfabaF4/dVXw/nnQ/PmqelcRJJOiT8DrUj6UF5Zctmy0J7s5F+e9JtQSm+GcT2X8hd+YPjS/6PXlzfAhhsmt0MRSTkN9WSgZVUUxK6qvaG6UswEOjOEU/mCzdmZ9+nNcCV9kQylxC9V++ILRnE0xXRnXX7mWEayB2/xP3aOOzIRaQAlflnVr7+GOjodO7I/r3Ip17EV03iCY6l8UhYRySQa489AzZpVPqzTrFkDN1xaCkOGhAJq8+ZB795sMex6vqNNAzcsIo2Jjvgz0NKliUk+1Cxu8FU9Y8fCjjvC6aeHiVEmTIChQ/nWK0/6qS6VLCKpo8SfoZYuXblmfb2T/owZcMQRsM8+YYjnySfDTVkFBX98JKn1+EUkdkr8uWr+/HD9/dZbw5gxocTCp59Cjx4rX7gvIllHY/y5ZvlyGDwYLr8cfvoJTj4ZrrsO/vKXuCMTkTTREX8uef112GGHMKns1lvDxInhS0BJXySnKPHngunT4dBDYb/9YOFCeOopKCoKXwIiknOU+LPZL7+EypmdOsG4cXDzzWEc/6ijNI4vksM0xp+Nli+H+++HK64Iyf+00+CaayA/P+7IRKQR0BF/tnn1VdhuO/jXv8Lz5MnhS0BJX0QiSvzZYto0OPhgOOAAWLIEnn02XKa53XZxRyYijYwSf4Zr+uuvcPbZYRz/rbfCfLcffwyHH65xfBGpVNrH+M1sY+Ah4C9AGTDI3e9MdxyZrpkt45/cx9VcSSkLGEQhZ3x+Day3XtyhiUgjF8cR/3LgPHfvAHQB+ppZxxjiyEzuHGQv8SHbcjdnMZECtmcKfbgXW19JX0RqlvbE7+7fufuk6PVvwKeAZvSojY8/hgMP5CUOJo9SDuEF9uM1prJN3JGJSAYxj7Hilpm1A8YDndz91wrvFQKFAPn5+QUjR46sVx8lJSW0aNGigZHGq9mCBbQbNow2zz/P8ubNuaDkGgbSl2WsVuGTTlHRuFhiTIVs+N1VJZv3DbJ7/zJp37p37z7R3Tuv8oa7x/IAWgATgaNq+mxBQYHXV1FRUb3Xjd2SJe633+7eqpV7Xp57377u8+ZVUitzxSObZPTvrgbZvG/u2b1/mbRvwASvJKfGcgOXmTUDngJGuPvTccTQqLnDiy/CeefBZ5+FUgu33Rbq64iINFDax/jNzIAhwKfuflu6+2/0pk6F/fcPtXXMwhfAK6+slPRXHp3zKtpFRCoXx1U9uwM9gb3NbEr0OCiGOBqXefNC1czttguzX915J3z0ERx0UKXX45cP7pRPxKKkLyK1lfahHnd/C83YvcLSpXD33aGWzsKFodTClVfCuuvGHZmIZCkVaYuLOzz/fJgF6/PPw5H9gAHQoUPckYlIllPJhjh8+CHsu2+Y67ZZM3j55TCWr6QvImmgxJ9Oc+fC6aeHCVCmTIH//Ac++CAUVhMRSRMN9aTDkiVw111w7bWweDGcdVaolb/OOnFHJiI5SIk/ldxDeeTzz4cvv4RDDgnj+FtuGXdkIpLDNNSTKpMnQ/fuYZrDNdeE116DF15Q0heR2CnxJ9v338Opp0JBQSiqdu+9YTz/b3+LOzIREUBDPUmzhv3OOdzBpVzP6izhLv7N+TMug1at4g5NRGQlOuJvKHd62Cg+pQM30Y8x7MPWfMwFDMDWaRV3dCIiq1Dib4iJE6FrV0ZxDL/Rkn14gyN5ls9pH3dkIiJVUuKvj+++g5NPhp12gmnTKOR+dmAyY9kn7shERGqkxF8XixfD9ddD+/bwyCPhMs0ZM3iAQsrIizs6EZFa0cnd2nCHJ56ACy+Eb74Jl2jecgtsvnnckYmI1JmO+Gvyv//BHnvAcceFO22LiuCpp1ZK+lWVRFapZBFpjJT4qzJnDvTqBTvvHKpnDh4cTuZ261bpxyubCFFEpDHSUE9FixbBrbfCTTfB8uVw8cXQrx+svXbckYmIJIUSfzl3GDkSLroIZs2CHj3g5pths83ijkxEJKk01APw/vuw225w/PHQujWMGwdPPqmkLyJZKbcT/6xZcOKJ0KULfP01PPhgOJm7115xRyYikjK5OdSzcCH07x8uySwrg0svDUM8LVvGHZmISMrlVuIvK4NHHw0nbOfMgWOPDSdx27WLOzIRkbTJnaGed9+FXXeFnj1hgw3gzTfDyVwlfRHJMVmf+Ff/4Ydw0na33cKY/vDh4WTuHnvEHZqISCyye6jnttvYuV8/aNIELr88lFxo0SLuqEREYhXLEb+ZHWBm083sczO7OBV95OVB4XkteHzp0Wzy+3Tyrr9GSV9EhBiO+M0sD7gH+BswG/ifmT3v7p8kq4+8vHAe9wEKeYDC0FgW2ktLk9WLiEhmiuOIf2fgc3f/0t2XAiOBw5PZQVlZ3dpFRHJJHGP8GwKzEpZnA7tU/JCZFUI4XM/Pz6e4uLgOXXQFrJJ2p7h4XB220/iVlJTU8WeTObRvmSub9y8b9i2OxF95Rq7Y4D4IGATQuXNn71ZFVcy6dp2c7TQexcXFWbdP5bRvmSub9y8b9i2OoZ7ZwMYJyxsB3yazgyZV7FVV7SIiuSSOVPg/oL2ZbWpmqwHHAc8ns4PS0sQkH/6YaNJEJ3ZFRCCGxO/uy4F/Aa8CnwJPuPvHye6ntDRUWi4qGoe7kr6ISLlYbuBy95eAl+LoW0Qk12nUW0Qkxyjxi4jkGCV+EZEco8QvIpJjzH2Ve6caHTObB8ys5+qtgR+TGE5jk837p33LXNm8f5m0b23dfb2KjRmR+BvCzCa4e+e440iVbN4/7Vvmyub9y4Z901CPiEiOUeIXEckxuZD4B8UdQIpl8/5p3zJXNu9fxu9b1o/xi4jIynLhiF9ERBIo8YuI5JisTvzpmNQ9Dma2sZkVmdmnZvaxmZ0dd0zJZmZ5ZjbZzEbHHUuymVkrMxtlZtOi3+GucceULGZ2bvRvcqqZPWZma8QdU0OY2YNmNtfMpia0rWtmr5vZjOh5nThjrI+sTfwJk7ofCHQE/mFmHeONKmmWA+e5ewegC9A3i/at3NmEst3Z6E7gFXffCtiOLNlPM9sQOAvo7O6dgDzCfBuZbBhwQIW2i4Ex7t4eGBMtZ5SsTfykYVL3uLj7d+4+KXr9GyFxbBhvVMljZhsBBwOD444l2cxsbWAvYAiAuy919/mxBpVcTYE1zawp0Jwkz66Xbu4+Hvi5QvPhwPDo9XDgiHTGlAzZnPgrm9Q9a5JjOTNrB+wAvB9zKMl0B3AhUBZzHKmwGTAPGBoNZQ02s7XiDioZ3H0OMAD4BvgOWODur8UbVUrku/t3EA7CgPVjjqfOsjnx12pS90xmZi2Ap4Bz3P3XuONJBjM7BJjr7hPjjiVFmgI7Ave6+w7AQjJwqKAy0Vj34cCmQBtgLTM7Md6opDLZnPhTPql7nMysGSHpj3D3p+OOJ4l2Bw4zs68Jw3N7m9kj8YaUVLOB2e5e/hfaKMIXQTbYF/jK3ee5+zLgaWC3mGNKhR/MbAOA6HluzPHUWTYn/pRP6h4XMzPCGPGn7n5b3PEkk7v3c/eN3L0d4Xc21t2z5qjR3b8HZpnZllHTPsAnMYaUTN8AXcysefRvdB+y5MR1Bc8DvaLXvYDnYoylXmKZczcd3H25mZVP6p4HPJiKSd1jsjvQE/jIzKZEbZdEcxlL43cmMCI6IPkSOCnmeJLC3d83s1HAJMKVZ5PJ8PIGZvYY0A1obWazgSuBm4AnzOwUwpfdMfFFWD8q2SAikmOyeahHREQqocQvIpJjlPhFRHKMEr+ISI5R4hcRyTFK/JJWZvZnM5sSPb43sznR6/lmltbr2c3siMTidmZ2jZntW4/ttEus3phuZnZJheV3oudY45LGS4lf0srdf3L37d19e+A+4Pbo9fakoDZPVCysKkcQKreWx3aFu7+R7BjSYKXE7+7ZeLesJJESvzQmeWb2QFTP/TUzWxPAzDY3s1fMbKKZvWlmW0Xtbc1sjJl9GD1vErUPM7PbzKwIuLmy9c1sN+AwoH/0F8fm0Xo9om3sZGbvmNkHZvZfM2sZHUG/aWaToke1CdaC/5jZJ2b2opm9lLD9r82sdfS6s5kVR693jvqdHD1vGbX3NrOno/2YYWa3RO03EaphTjGzEVFbSSWx5JlZfzP7X/TzOj1q38DMxkfrTzWzPRv4O5RM4O566BHLA7gKOD963Y5wt+f20fITwInR6zFA++j1LoQyDgAvAL2i1ycDz0avhwGjgbwa1h8G9EiIZxjQAyi/o3anqH1twl3uzYE1orb2wISE2KdWsn9HAa8T7hxvA8wv7w/4Gmgdve4MFCf2Fb3eF3gqet07iulPwBrATGDj6L2SCv2WVIwLKAQui16vDkwgFFM7D7g0as8DWsb970KP1D+ytmSDZKSv3H1K9Hoi0C6qQLob8GQo/wKExAWwKyG5AjwM3JKwrSfdvbSG9auyJfCdu/8PwKPKp1H55P+Y2fZAKbBFDdvZC3jM3UuBb81sbA2fh5DYh5tZe0I12WYJ741x9wVRLJ8AbVm59Hh19gO2Lf+LI+qnPaGm1YNR0b9nE37+ksWU+KUxWZLwuhRYkzAcOd/DeYCaJNYfWRg912X9ckblJbzPBX4gzJrVBPi9jjElWs6KodbE6QmvBYrc/UgLcy0UJ7xX8edTl/+/Bpzp7q+u8obZXoSJbx42s/7u/lAdtisZSGP80qhFR9tfmdkx8Me4+XbR2++wYmq/E4C36rj+b0DLSrqdBrQxs52idVpGJ4n/RPhLoIxQJC+vhvDHA8dF4+sbAN0T3vsaKIheH53Q/idgTvS6dw3bL7csOmKvzqvAGeWfM7MtzGwtM2tLmP/gAULF12wpES3VUOKXTHACcIqZfQB8zIopNM8CTjKzDwmJuKpJ56tafyRwQXQidfPyD3uYqvNY4O5ondcJR+UDgV5m9h5hmGch1XsGmAF8BNwLjEt472rgTjN7k3D0Xu4W4EYze5uav1jKDQI+LD+5W4XBhPLPk6JLPO8n/MXQDZhiZpMJX0B31rJPyWCqzimSJmY2DBjt7qPijkVym474RURyjI74RURyjI74RURyjBK/iEiOUeIXEckxSvwiIjlGiV9EJMf8P3w91fCdlGJOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(x,dist=\"poisson\",sparams = (np.mean(x)), plot = plt)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "57da2e37",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b0b96307",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "565c8aaa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92846554",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cec3b635",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "0ebb61a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# if data has outliers : \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "bed3bab0",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = list(np.random.normal(0,1,100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "f6482246",
   "metadata": {},
   "outputs": [],
   "source": [
    "X.append(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "09762c7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "X.insert(0,-7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "4d491bff",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "616eed41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(X,dist=\"norm\", plot = plt,fit=True)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "f4f0c4db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "QQplot__(pd.Series(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "a19f3471",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot(X)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc2a779b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4880d850",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "65f40085",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b15b8a8e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "46537578",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88ca6434",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea071ede",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4eeaec7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8915fc69",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c7d233f7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76328b21",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "397a6128",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "34c4723f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cb790fed",
   "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",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}