{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![MLU Logo](../../data/MLU_Logo.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install -q -r ../../requirements.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6895804522257558\n"
     ]
    }
   ],
   "source": [
    "# A single median of 1000 datapoints from a badly behaved distribution\n",
    "d = -np.log(np.random.rand(1000))\n",
    "print(np.median(d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  2.,  15.,  62., 196., 317., 242., 114.,  43.,   8.,   1.]),\n",
       " array([0.58034962, 0.60426511, 0.62818061, 0.6520961 , 0.67601159,\n",
       "        0.69992709, 0.72384258, 0.74775807, 0.77167357, 0.79558906,\n",
       "        0.81950456]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# histogram of 1000 independent medians of a long tailed distribution (like house prices)\n",
    "meds = [np.median(-np.log(np.random.rand(1000))) for x in range(1000)]\n",
    "\n",
    "plt.figure(figsize = (10,10))\n",
    "plt.hist(meds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  8.,  12.,  53., 138., 374., 229., 116.,  32.,  33.,   5.]),\n",
       " array([0.52400859, 0.5455968 , 0.56718501, 0.58877322, 0.61036144,\n",
       "        0.63194965, 0.65353786, 0.67512607, 0.69671428, 0.7183025 ,\n",
       "        0.73989071]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A single distribution of 1000 datapoints ›\n",
    "data = -np.log(np.random.rand(1000))\n",
    "\n",
    "# 1000 samples with replacement and histogram\n",
    "meds = [np.median(np.random.choice(data,1000)) for x in range(1000)]\n",
    "\n",
    "plt.figure(figsize = (10,10))\n",
    "plt.hist(meds)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "conda_python3",
   "language": "python",
   "name": "conda_python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}