notebooks/characterising.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Characterising Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": [
    "data = np.loadtxt(\"../data/dataset.txt\")\n",
    "sns.histplot(data, kde=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mean(xs):\n",
    "    summ = 0\n",
    "    for x in xs:\n",
    "        summ += x\n",
    "    return summ / len(xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n"
     ]
    }
   ],
   "source": [
    "print(get_mean([3, 5, 2, 6]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.68805056 7.68805056 7.68805056\n"
     ]
    }
   ],
   "source": [
    "μ = np.mean(data)\n",
    "print(μ, data.mean(), np.average(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_median(xs):\n",
    "    mid = len(xs) // 2\n",
    "    if len(xs) % 2 == 1:\n",
    "        return sorted(xs)[mid]\n",
    "    else:\n",
    "        return 0.5 * np.sum(sorted(xs)[mid - 1 : mid + 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.5\n"
     ]
    }
   ],
   "source": [
    "print(get_median([7, 7, 3, 1, 4, 5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.7325\n"
     ]
    }
   ],
   "source": [
    "median = np.median(data)\n",
    "print(median)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "outlier = np.insert(data, 0, 5000)\n",
    "bins = 30\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.hist(data, bins=bins, color=\"green\", label=\"data\", alpha=0.75)\n",
    "plt.axvline(np.mean(data), ls=\"--\", c=\"b\", lw=5, label=\"mean data\")\n",
    "plt.axvline(np.median(data), ls=\"-\", c=\"b\", lw=5, label=\"median data\")\n",
    "plt.axvline(np.mean(outlier), c=\"r\", ls=\"--\", lw=5, label=\"mean outlier\")\n",
    "plt.axvline(np.median(outlier), c=\"r\", ls=\":\", lw=5, label=\"median outlier\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mode(xs):\n",
    "    vals, counts = np.unique(xs, return_counts=True)\n",
    "    max_count_idx = np.argmax(counts)\n",
    "    return vals[max_count_idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "print(get_mode([1, 7, 2, 5, 3, 3, 8, 3, 2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ModeResult(mode=array([5.519]), count=array([9]))\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as ss\n",
    "\n",
    "print(ss.mode(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.41347135\n"
     ]
    }
   ],
   "source": [
    "hist, edges = np.histogram(data, bins=10000)\n",
    "edge_centers = 0.5 * (edges[1:] + edges[:-1])\n",
    "mode = edge_centers[hist.argmax()]\n",
    "print(mode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": [
    "kde = ss.gaussian_kde(data)\n",
    "xvals = np.linspace(data.min(), data.max(), 1000)\n",
    "yvals = kde(xvals)\n",
    "mode = xvals[yvals.argmax()]\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "ax.set_facecolor(\"k\")\n",
    "plt.hist(data, bins=1000, density=True, label=\"Data\", histtype=\"step\", color=\"b\")\n",
    "plt.plot(xvals, yvals, label=\"Kde\", color=\"r\", lw=3, ls=\"--\")\n",
    "plt.axvline(mode, label=\"mode\", color=\"w\", lw=3, alpha=0.5)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_variance(xs):\n",
    "    μ = np.mean(xs)\n",
    "    summ = 0\n",
    "    for x in xs:\n",
    "        summ += (x - μ) ** 2\n",
    "    return summ / len(xs) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(get_variance([1, 2, 3, 4, 5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.137626632694301\n"
     ]
    }
   ],
   "source": [
    "var = np.var(data, ddof=1)\n",
    "print(var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6244414221454435\n",
      "3.624586408501569\n"
     ]
    }
   ],
   "source": [
    "σ = np.std(data)\n",
    "print(σ)\n",
    "print(np.sqrt(var))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": [
    "xs = np.linspace(data.min(), data.max(), 100)\n",
    "ys = ss.norm.pdf(xs, loc=np.mean(data), scale=np.std(data))\n",
    "\n",
    "plt.hist(data, bins=50, color=\"b\", density=True, histtype=\"step\", label=\"Data\")\n",
    "plt.plot(xs, ys, \"r--\", label=\"Normal approximation\")\n",
    "plt.ylabel(\"probability\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# skewness\n",
    "# first moment is 0\n",
    "# second moment is variance\n",
    "# third moment is skewness\n",
    "def get_skewness(xs):\n",
    "    mean = np.mean(xs)\n",
    "    var = np.var(xs)\n",
    "    summ = 0\n",
    "    for x in xs:\n",
    "        summ += (x - mean) ** 3\n",
    "    return (summ / len(xs)) / (var**1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "print(get_skewness([1, 2, 3, 4, 5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7408773663373577 0.7408773663373582\n"
     ]
    }
   ],
   "source": [
    "skew = ss.skew(data)\n",
    "print(skew, get_skewness(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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": [
    "xs = np.linspace(data.min(), data.max(), 100)\n",
    "ys1 = ss.norm.pdf(xs, loc=np.mean(data), scale=np.std(data))\n",
    "ps = ss.skewnorm.fit(data)\n",
    "ys2 = ss.skewnorm.pdf(xs, *ps)\n",
    "\n",
    "plt.hist(data, bins=50, color=\"b\", density=True, histtype=\"step\", label=\"Data\")\n",
    "plt.plot(xs, ys1, \"r--\", label=\"Normal approximation\")\n",
    "plt.plot(xs, ys2, \"g--\", label=\"Skew Normal approximation\")\n",
    "plt.ylabel(\"probability\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# kurtosis\n",
    "# fourth moment\n",
    "def get_kurtosis(xs):\n",
    "    mean = np.mean(xs)\n",
    "    var = np.var(xs)\n",
    "    summ = 0\n",
    "    for x in xs:\n",
    "        summ += (x - mean) ** 4\n",
    "    return (summ / len(xs)) / (var**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7\n"
     ]
    }
   ],
   "source": [
    "print(get_kurtosis([1, 2, 3, 4, 5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.5517538497309498 3.551753849730955\n"
     ]
    }
   ],
   "source": [
    "kurt = ss.kurtosis(data, fisher=False)\n",
    "print(kurt, get_kurtosis(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "ps = np.linspace(0, 100, 30)\n",
    "x_p = np.percentile(data, ps)\n",
    "\n",
    "xs = np.sort(data)\n",
    "ys = np.linspace(0, 1, len(data))\n",
    "\n",
    "plt.plot(xs, ys * 100, label=\"ECDF\", color=\"b\", lw=3)\n",
    "plt.plot(x_p, ps, label=\"Percentiles\", color=\"r\", lw=3, ls=\"--\")\n",
    "plt.ylabel(\"Percentile\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5n+PnNnfSaddnwbYl971C/bsu9DCVSPiIugvP69Spw7p169iyZYvXUaJaYmIiderU8TrGcfvyvKH0WPlacP7XHg9z5ohC7mQXKaOirijExcVRr149r2NIGJr88CS6f/twcH5qoxs4a+JfPUwkEn6i7vCRSGFW/ryJZk9fH+ztdHbVc2kz/XV1bCdyGBUFiXo5+/LZduH1nEQGAFtiU6j3yzvEV9BACCKHU1GQqDfxghGk7/4GAB/G9uf/Q+WGKR6nEglPKgoS1b77Dm79oS8T8V9d9Mv5g2l0p/ozEjkSFQWJWlu3wg03wFZq0pNPebblv2g/8VGvY4mEtai7+kgE/B3a3n47rF3rn69UOYbrPuuD6Tde5Ki0pyBR6fUnNxEYyRSAN9+E2rW9yyMSKTwpCmZ2v5nNN7N5Zva2mSWaWT0zm2pmy8zsXTPTpSFSLPPemcd1j9bnbwwijhz694dLL/U6lUhkKPWiYGa1gXuBdOdccyAWuAZ4BhjhnDsd2AH0K+1sEvl2btxHuRuvJZksBvEM79cYwHPPeZ1KJHJ4dfioHJBkZuWA8sBGoBswLvD8WKCXN9Ekkk3v9ica584DIIskWrz5IElJHocSiSClXhScc+uBYcAa/MVgFzAD2OmcOzDA8Dqg0CPAZtbfzKab2XT1byQFzXjiU85f9GJwftFtwzn1oqYeJhKJPF4cPqoKXAbUA04BkoEid1HpnBvtnEt3zqXXVOf3ErB5bganPn5zcP7X2pfR9tUBHiYSiUxeHD46H1jpnNvinMsF3gc6AlUCh5MA6gDrPcgmESg/H+acfz81fP49xw12CvUmqV8jkeLwoiisAc42s/JmZsB5wAJgMnBlYJm+wEceZJMI9PnAiXTPeCs4v+GJN6jRuIaHiUQilxfnFKbiP6E8E5gbyDAaeAh4wMyWAdWBN0o7m0SejBV7afHyHcH535pfT/ojGjBHpLg8ub/TOfcY8NhhzSuAdh7EkQg2vedjXOxWA7A9pjqNPhvhcSKRyKY7miViffMNPLLoembSBoD1Dwwnsa4uPhApCRUFiUj798Odd8Is2tKOaYw8+21a/P0Gr2OJRDx1DyYR6e9/h8WL/dPlK5bjqvHXgC42Eikx7SlIxJk3LYsnnjg4/8QTcMop3uURiSYqChJRctduokanxgzMGwY42reHu+/2OpVI9NDhI4kcubls6Hw1p+auZRgP0ihmGZ3eGEU5/RaLnDDaU5CIse2WBzl19RQA8omh8i1X0KSJx6FEooyKgkSEzNfeovq/RwbnX63zJFeM6u5hIpHopKIgYW/3D3OIvf3W4PyHMZfTZeIgYmM9DCUSpVQUJKxlrd/B7u69SfTtA2ARjch5dQzNmuv6U5FQUFGQsLV/Tw7z2/ahTvZyAPZQge/ufZ+rb63kcTKR6KWiIGFp3ZztLEjtwZkZnwXbJl33TwaM1KA5IqGkoiBhZ+JEOK99Fik7Fwfbvj5zEJf/58qjrCUiJ4KKgoQN52DECPjDH2BJVh3+wCfsoQLfnP803X552ut4ImWCbvuRsJCT4+/g7o0Co2hsrduWWcOW0u3qk70LJlLGqCiI57ZkOD5q9xSrV58F+O89OPts+OADOPlkFQSR0qSiIJ6aN2M/i7v059bMN7mSynTgJ868sSmvvgqJiV6nEyl7dE5BPDN53DZ2truAKzLfBKAKu3g3/VnGjFFBEPGK9hTEE4s+Xkrdq3tyulsabFvTvR8tPn1F4yKIeEh7ClLq1vywhhqXdTikIGy+fyipX7wGcXEeJhMR7SlIqcrance2C68n1W0FYB+JbH72X6T9r+5BEAkH2lOQUuMcTDznadpk/gBAHrEse+FzFQSRMKKiIKXmnXt+pNdvjwfnZ14yhBZ3d/EwkYgcTkVBSsW0abD9lXeIxQfAopqdOfP9P3ucSkQOp6IgIbd/P9x8M9zte57beYWMuFOo9+O/sXIaEEEk3KgoSMj95S+wYAGA8e/k28n8bTkJDVK9jiUihVBRkJD69Vd/J3cHDB0K9ZrozjSRcKWiICGTvy+HH3r/H/EuG4ALLvB3eici4UtFQUJm5hVPcf+6/+UXzqZV3AJefhli9BsnEtb0JyohkTEvg6YThwHQmt94puvn1K/vcSgROSZPioKZVTGzcWa2yMwWmll7M6tmZl+Z2dLAz6peZJMTY8b/PEMyWQAsiG9Flw/u8zaQiBSJV3sKI4HPnXONgVbAQmAQ8LVzrgHwdWBeItAvH2zk3AUvB+ezBz1OYnntlIpEgiL9pZpZipm9YWYTA/NNzaxfcd7QzCoD5wBvADjncpxzO4HLgLGBxcYCvYrz+uItnw+W3zaUJPwnl5dXOYO2Qy71OJWIFFVRv76NAb4ATgnMLwHuK+Z71gO2AP80s1lm9rqZJQMpzrmNgWU2ASmFrWxm/c1suplN37JlSzEjSKh8PXYdV2x7NThf6bknwNQXtkikKGpRqOGcew/8fRQ45/KA/GK+ZzmgLfCKc64NkMlhh4qccw5wha3snBvtnEt3zqXXrFmzmBEkFJyDvQ//jUT2A7C61lnUvPEij1OJyPEoalHINLPqBD6ozexsYFcx33MdsM45NzUwPw5/kdhsZrUCr18LyCjm64tHvv/XanpufC04n/Ss9hJEIk1Ri8IDwASgvpn9CLwJ3FOcN3TObQLWmlmjQNN5wILA6/cNtPUFPirO64t3Mh9+inhyAViW0pGTruvucSIROV5FGmTHOTfTzLoAjfAPlrjYOZdbgve9B/iPmcUDK4Cb8Reo9wInsFcDV5fg9aWUrVzhmLOuGl1JJIlsyg/TXoJIJDpqUTCz3kd4qqGZ4Zx7vzhv6pybDaQX8tR5xXk98d7wEcaLDGUkA3m04bvccX1XryOJSDEca0/hkqM854BiFQWJLhs3wuuv+6c3UYv6L9zn358UkYhz1KLgnLu5tIJI5Prb3yDbf1sCbdvC+ed7m0dEiu9Yh4/6OOf+bWYPFPa8c254aGJJpNixYR8f/2Mv4L88eMgQdXonEsmO9eebHPhZsZBHhRDmkggxpd8YFmSm8hJ30rXuMnr29DqRiJTEsQ4fHbg1dZJz7seCz5lZx5ClkoiQnZlPsy+Hk0Q2d/IKZ53biJiYgV7HEpESKOqO/gtFbJMy5IcHP6K+bxkAu2Kq0ObFYnWHJSJh5FjnFNoDHYCah51XqARo1PUyzDmoMXZYcH7huXdwdiUdURSJdMe6JDUe/7mDcvjPIxywG7gyVKEk/M166SfaZv0MwH7iafJSsW5wF5Ewc6xzCt8B35nZGOfc6lLKJBEg+8mDewm/NuxDp8a1PEwjIidKkbq5ABLMbDSQVnAd51y3UISS8LZ53hbO3PxxcL7O8EKvWBaRCFTUovBfYBTwOsXvMluixNIn36UTeQDMrdSBFj2beZxIRE6UohaFPOfcKyFNIhGj8if/Dk5v7dHHwyQicqIV9ZLUj83sTjOrZWbVDjxCmkzC0vLPl9Ii0z8URg5xtHpKndmKRJOi7ikcGOfgwQJtDjjtxMaRcDf2q1NYzRj68G8qnFKJ9g2qex1JRE6goo6nUC/UQST85efDa28ls4m+vElfPnxBp5dEok2RDh+ZWXkzeyRwBRJm1sDM/hDaaBJuJk+GTZv80ykpcPElun9RJNoU9ZzCP4Ec/Hc3A6wHngxJIglbb755cPrKKyEuzrssIhIaRS0K9Z1zfwf/ALzOuSw0jEqZkr07h23jv8XwAXDTTd7mEZHQKGpRyDGzJPwnlzGz+sD+kKWSsPPbM5/zaVZXVpHGX6uN4IwzvE4kIqFQ1KuPHgM+B+qa2X+AjsBNoQol4ceNHw9AKmvp1DAD036iSFQq6tVHX5nZTOBs/IeNBjrntoY0mYQNl5NL46UHu7VI6nOFh2lEJJSKevXR5fjvav7UOfcJkGdmvUKaTMLGsn98TxXfDgDWWV3a3KpjRyLRqqjnFB5zzu06MOOc24n/kJKUAdtefz84Pb9BL+ITdOxIJFoVtSgUtlxRz0dIJPP5qPfbh8HZ8n16e5dFREKuqEVhupkNN7P6gcdwYEYog0l4WDP+V1LyNgCwleqcMbCTx4lEJJSKWhTuwX/z2rvAO0A2cFeoQkn42PDiwUNHv6VeSvlK2kEUiWbH/As3s1jgE+dc11LII2HE+Ry1fjlYFOitQ0ci0e6YewrOuXzAZ2aVSyGPhJGF4+Zzas4yAPZQgfRB53ucSERCrajHAvYCc83sKyDzQKNz7t6QpJKw8NkPlfgvj3Ihn+NLrUf7lESvI4lIiBW1KLwfeEgZMuabVObzOEN4nHHDfF7HEZFSUNQ7mscG+j5Kdc4tDnEmCQOrVsH8+f7phAS48OKiXpMgIpGsqHc0XwLMxt//EWbW2swmlOSNzSzWzGaZ2SeB+XpmNtXMlpnZu2YWX5LXl5L5+GCvFnTtCsnJ3mURkdJT1K9/Q4B2wE4A59xsSj4U50BgYYH5Z4ARzrnTgR1AvxK+vpTA159mB6cvvdTDICJSqopaFHILdnMRUOyDzGZWB+gJvB6YN6AbMC6wyFigV3FfX0omZ79j+JfNmMaZPMFgLuyw2+tIIlJKinqieb6ZXQfEmlkD4F7gpxK873PAn4CKgfnqwE7nXF5gfh1Qu7AVzaw/0B8gNTW1BBHkSOaMW0K6W8FprKCxLaZi00e9jiQipeR47mhuhn9gnbeAXcB9xXnDwNjOGc65YnWT4Zwb7ZxLd86l16xZszgvIcew4+3Pg9NLUs/XuJsiZchR9xTMLBG4HTgdmAu0L/Btvrg6Apea2cVAIlAJGAlUMbNygdevg38caPFA5V8OFoX9517oYRIRKW3H2lMYC6TjLwgXAcNK+obOuT875+o459KAa4BvnHPXA5OBKwOL9QU+Kul7yfHL3plNi23fBudP7d/DuzAiUuqOdU6hqXOuBYCZvQFMC2GWh4B3zOxJYBbwRgjfS45g2b9+pjn+K49WxDXktA6nepxIRErTsYpC7oEJ51yeneCBeZ1z3wLfBqZX4L/sVTy0ffzk4PSq07qV+LpjEYksxyoKrczswPWIBiQF5g1wzrlKIU0npa7SjG+C0wk91DGuSFlz1KLgnIstrSDive1rM2m2d2pwvtld53oXRkQ8oQ5tJGjR6z8Qh//ismVJzanS8CSPE4lIaVNRkKCVM7azkZMB2Nikm8dpRMQLKgoSNDLjWk5hA01YwL7bBnodR0Q8oAF3BYCdO2HGDABjsTUh/WqPA4mIJ7SnIAB8/z34Al0ctm4N1ap5GkdEPKKiIAB8+eXB6fPO8y6HiHhLRUEAaPHeYG7lNRqwhO7nO6/jiIhHdE5B2L5qN7dueZoB+PBh7Gu+HajidSwR8YD2FITF//iR2MCYSUvLtyK5dhVvA4mIZ1QUhH2ffxec3ty4i4dJRMRrKgpC9fkHi0JSDxUFkbJMRaGM27Uhk6ZZ04PzjW/r7GEaEfGaikIZt/ifPwX7O1qa2JyK9Wp4nEhEvKSiUMbt+WxKcHpTw3M8TCIi4UBFoYyrvODn4HR8t04eJhGRcKCiUIbl7Mun0c5fgvNp13X0MI2IhAMVhTJs0bh5VGQvABtja5OSXtfjRCLiNd3RXIZ9s+o0BvMhHfiJhs0SufwEj8EtIpFHRaEM+/LnikzkMiZwGa/d43UaEQkHOnxURjl3YPwEv446nSAiqCiUWStXQkaGf7pqVWjY0Ns8IhIeVBTKqMU/byeBbMA/qE5srLd5RCQ8qCiUUZVHPsEuKjOFTlxd+Quv44hImNCJ5jKq+oIpJJBDJ37ENfF5HUdEwoT2FMqgfZt3c3rmbAB8GA1v6uBtIBEJGyoKZdCSsT8HB9VZHN+SlIaVPU4kIuFCRaEM2vHxD8HpTQ3UVbaIHKSiUAZVnX+wZ9S481QUROSgUi8KZlbXzCab2QIzm29mAwPt1czsKzNbGvhZtbSzlQX7t+6h4Y6pwflTr1PPqCJykBd7CnnAH51zTYGzgbvMrCkwCPjaOdcA+DowLyfYymfHkRS4P2FxfHPqtDvF40QiEk5KvSg45zY652YGpvcAC4HawGXA2MBiY4FepZ2tLEj+75jg9G+tb0J94IlIQZ6eUzCzNKANMBVIcc5tDDy1CUg5wjr9zWy6mU3fsmVL6QSNFsuXU3fl9wDkEUvW5dd7HEhEwo1nRcHMKgDjgfucc7sLPuecc4ArbD3n3GjnXLpzLr1mzZqlkDR6zFsYyygGsJPKTOQiOvQ+2etIIhJmPCkKZhaHvyD8xzn3fqB5s5nVCjxfC8jwIls0u39kGncwilps5OOLXlEneCLyO15cfWTAG8BC59zwAk9NAPoGpvsCH5V2tmj2zTcwaZJ/OicmifuG1fE2kIiEJS/6PuoI3ADMNbPZgba/AEOB98ysH7AauNqDbFHJ54M//eng/M03Q9Om3uURkfBV6kXBOfcDcKRrXs4rzSxlxU8D34UZ9YF0EhNhyBCvE4lIuFIvqVFu9/y1tH7pVqaSxQvcw/a7nqZOnfJexxKRMKVuLqKZcyy/6G4quL3E4uOi2K/430H6HiAiR6aiEMVmPfoBbdZOCM6vf+xVKtWI9zCRiIQ7FYUotWv1Tmo9fU9wftJp/ek2WP0cicjRqShEI+dY0nUAJ/s2AJBhKbSaONTjUCISCVQUotDs+8dy5sr3gvPL//gyNRuq01kROTYVhSiz6qulnD7y7uD8V2m30f7Z3h4mEpFIoqIQRbJ25rD7kuuoQCYAS2Ib0+zLER6nEpFIoqIQRV6/axb19y8AYD/xZL/xFqc0SPY4lYhEEhWFKDF7Njzw7lmcwQxm0Zpfew+lZd82XscSkQijO5miQH4+DBjg/7mYxgzq8gufvxfndSwRiUAqClFg1CiYNs0/HR8Pz7+agMV6m0lEIpMOH0W4pW9P57UHlwTn//IXaNTIw0AiEtFUFCJYxrwMEm64mp/3tWIgz9G4oY9Bg7xOJSKRTEUhQmVt3sOWdj1JzV9JEtkMYQgfvrqZhASvk4lIJFNRiEC+7ByWtuxNs33TAcgnhnl/HEOjc2t5nExEIp2KQoTJz/UxvVlfWmVMCrZ9d80oOg3r5V0oEYkaKgoR5odOD9FuxTvB+Y/P+itd37rNw0QiEk1UFCLIb/e+QZdpw4LzkxrdxcU/PIwdaXBTEZHjpPsUIsSS0d/S9IXbg/M/ntSLbnNHElNOFUFEThztKUSAWVNzqHBHH+LIA2B+XGsa/vIvYuJ0h5qInFgqCmHuxx+h83nx3Ot7Dh/GJjuZ+C8+pma9Cl5HE5EopKIQxiZPhp49ITMTxnMlDyW9wIZXJtCgax2vo4lIlNI5hTDk8n28/Nhm7v1bLXw+f1tKCtz8zV00beptNhGJbioKYSZnZxZzWvWhx5o5VOUXtlGDk0+Gzz9HBUFEQk6Hj8LI7Oe+ZdXJZ5G+5gNOZzkfcDldzt7P9OnQqpXX6USkLNCeQhjY8NMqNlz/v6SvGn9Ie1azdnz5TTnikzwKJiJljvYUPLR71XamtPsj1Ts2OqQgZFKer68aRfc5/0d8ki47FZHSo6LggR3LtzPpnCfwnVafzr8OJ4Gc4HPf1b2e3dMWc957A4jR/46IlDJ97JSSrCz46CPo0AGmNb6B86c8RhW3M/j8b0ln8+OzP9Flzb+pdaYuORURb+icQgg4n2PDtHVs+HgGu35dwssV/sSkSbBnj//5YdxHDz4DYGVcA9be8Tc6De9NTKy6rBARb4VVUTCzC4GRQCzwunNuqMeRjmjf7ly2LN7OziUZ7Fu0mtzFK3CLF5O8ZhGn7vqN2m4btQPLXs2t7KFacN1JnM+/6EODuy/kzGH/Q72EsPpvEJEyLGw+jcwsFngJ6A6sA341swnOuQUn8n1WroThw6HzzJHU2joXy8/D8nOJycvFfHnE5Of6H748YvNzifHl8kbKw0xK6El2Nuzb5//Gv3BPGqlsILUI79mOaXzBhTRsCJdfDj17Gh07/kvnDEQk7IRNUQDaAcuccysAzOwd4DLghBaFjAx48UXoyUQ680WR1tmzZxPzD2vbRnVqs+GI6+yiEisrt2Z7/XYMuLwuf78UWrRA3VyLSFgLp6JQG1hbYH4dcNbhC5lZf6A/QGpqUb6nH6pc4F+cS1zR1wn0TlrQFjuJbVaDPXHV2V4hlT3VTyWvXkOSz2hMnR7NqN2pHq1jVAFEJLKEU1EoEufcaGA0QHp6ujve9VNTYeRIsCV38f3uS7Fy5YhJiIP4OGLi/NMWH0dMvH86JiGOAaedzt11IDERkpIgORmqVP4KizGqA2kn+N8oIuKVcCoK64G6BebrBNpOqJo14d57AS4s4StpL0BEok84ner8FWhgZvXMLB64BpjgcSYRkTIlbPYUnHN5ZnY38AX+S1L/4Zw7/PyuiIiEUNgUBQDn3GcQuKtLRERKXTgdPhIREY+pKIiISJCKgoiIBKkoiIhIkDl33Pd/hQ0z2wKs9jBCDWCrh+9fEpGaPVJzg7J7Rdl/71TnXM3CnojoouA1M5vunEv3OkdxRGr2SM0Nyu4VZT8+OnwkIiJBKgoiIhKkolAyo70OUAKRmj1Sc4Oye0XZj4POKYiISJD2FEREJEhFQUREglQUisHMLjSzxWa2zMwGeZ3neJjZKjOba2azzWy613mOxsz+YWYZZjavQFs1M/vKzJYGflb1MuORHCH7EDNbH9j2s83sYi8zFsbM6prZZDNbYGbzzWxgoD3st/tRskfCdk80s2lm9lsg++OB9npmNjXwWfNuYFiB0GbROYXjY2axwBKgO/4hQ38FrnXOndCxpEPFzFYB6c65sL+Zx8zOAfYCbzrnmgfa/g5sd84NDRTkqs65h7zMWZgjZB8C7HXODfMy29GYWS2glnNupplVBGYAvYCbCPPtfpTsVxP+292AZOfcXjOLA34ABgIPAO87594xs1HAb865V0KZRXsKx68dsMw5t8I5lwO8A1zmcaao5Jz7Hth+WPNlwNjA9Fj8f/Rh5wjZw55zbqNzbmZgeg+wEP/46WG/3Y+SPew5v72B2bjAwwHdgHGB9lLZ7ioKx682sLbA/Doi5BcvwAFfmtkMM+vvdZhiSHHObQxMbwJSvAxTDHeb2ZzA4aWwOwRTkJmlAW2AqUTYdj8sO0TAdjezWDObDWQAXwHLgZ3OubzAIqXyWaOiUPZ0cs61BS4C7goc5ohIzn/sM5KOf74C1AdaAxuB//M0zVGYWQVgPHCfc253wefCfbsXkj0itrtzLt851xr/+PTtgMZe5FBROH7rgboF5usE2iKCc2594GcG8AH+X75Isjlw7PjAMeQMj/MUmXNuc+AP3we8Rphu+8Ax7fHAf5xz7weaI2K7F5Y9Urb7Ac65ncBkoD1QxcwOjJBZKp81KgrH71egQeCqgHjgGmCCx5mKxMySAyfgMLNk4AJg3tHXCjsTgL6B6b7ARx5mOS4HPlQDLicMt33ghOcbwELn3PACT4X9dj9S9gjZ7jXNrEpgOgn/hSwL8ReHKwOLlcp219VHxRC4pO05IBb4h3PuKW8TFY2ZnYZ/7wD843O/Fc7Zzext4Fz83QdvBh4DPgTeA1Lxd5t+tXMu7E7oHiH7ufgPYThgFTCgwHH6sGBmnYApwFzAF2j+C/5j82G93Y+S/VrCf7u3xH8iORb/l/X3nHNPBP5m3wGqAbOAPs65/SHNoqIgIiIH6PCRiIgEqSiIiEiQioKIiASpKIiISJCKgoiIBKkoiIhIkIqCiIgE/T9oGb4RoC1yxQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ps = 100 * ss.norm.cdf(np.linspace(-3, 3, 50))\n",
    "ps = np.insert(ps, 0, 0)\n",
    "ps = np.insert(ps, -1, 100)\n",
    "x_p = np.percentile(data, ps)\n",
    "\n",
    "xs = np.sort(data)\n",
    "ys = np.linspace(0, 1, len(data))\n",
    "\n",
    "plt.plot(xs, ys * 100, label=\"ECDF\", color=\"b\", lw=3)\n",
    "plt.plot(x_p, ps, label=\"Percentiles\", color=\"r\", lw=3, ls=\"--\")\n",
    "plt.ylabel(\"Percentile\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": [
    "from scipy.interpolate import interp1d\n",
    "\n",
    "n = int(1e6)\n",
    "u = np.random.uniform(size=n)\n",
    "samp_p = interp1d(ps / 100, x_p)(u)\n",
    "\n",
    "_, bins, _ = plt.hist(data, bins=50, density=True, alpha=0.3, label=\"Data\")\n",
    "plt.hist(samp_p, bins=bins, density=True, histtype=\"step\", label=\"percentile\")\n",
    "plt.ylabel(\"Percentile\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>sex</th>\n",
       "      <th>height</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>71.00</td>\n",
       "      <td>186.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>63.83</td>\n",
       "      <td>172.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>67.74</td>\n",
       "      <td>174.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>67.28</td>\n",
       "      <td>169.20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "</div>"
      ],
      "text/plain": [
       "   sex  height  weight\n",
       "0    1   71.74  259.88\n",
       "1    1   71.00  186.73\n",
       "2    2   63.83  172.17\n",
       "3    1   67.74  174.66\n",
       "4    2   67.28  169.20"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"../data/height_weight.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>height</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>18.602008</td>\n",
       "      <td>78.502181</td>\n",
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       "    <tr>\n",
       "      <th>weight</th>\n",
       "      <td>78.502181</td>\n",
       "      <td>1512.912088</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           height       weight\n",
       "height  18.602008    78.502181\n",
       "weight  78.502181  1512.912088"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"height\", \"weight\"]].cov()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>height</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.467945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>weight</th>\n",
       "      <td>0.467945</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
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       "</table>\n",
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      "text/plain": [
       "          height    weight\n",
       "height  1.000000  0.467945\n",
       "weight  0.467945  1.000000"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"height\", \"weight\"]].corr()"
   ]
  }
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