{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [],
   "source": [
    "path_data = '../../../../data/'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling from a Population ###\n",
    "\n",
    "The law of averages also holds when the random sample is drawn from individuals in a large population.\n",
    "\n",
    "As an example, we will study a population of flight delay times. The table `united` contains data for United Airlines domestic flights departing from San Francisco in the summer of 2015. The data are made publicly available by the [Bureau of Transportation Statistics](http://www.transtats.bts.gov/Fields.asp?Table_ID=293) in the United States Department of Transportation.\n",
    "\n",
    "There are 13,825 rows, each corresponding to a flight. The columns are the date of the flight, the flight number, the destination airport code, and the departure delay time in minutes. Some delay times are negative; those flights left early."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>Date</th>\n",
       "      <th>Flight Number</th>\n",
       "      <th>Destination</th>\n",
       "      <th>Delay</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>73</td>\n",
       "      <td>HNL</td>\n",
       "      <td>257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>217</td>\n",
       "      <td>EWR</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>237</td>\n",
       "      <td>STL</td>\n",
       "      <td>-3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>250</td>\n",
       "      <td>SAN</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6/1/15</td>\n",
       "      <td>267</td>\n",
       "      <td>PHL</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13820</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>1978</td>\n",
       "      <td>LAS</td>\n",
       "      <td>-4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13821</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>1993</td>\n",
       "      <td>IAD</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13822</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>1994</td>\n",
       "      <td>ORD</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13823</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>2000</td>\n",
       "      <td>PHX</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13824</th>\n",
       "      <td>8/31/15</td>\n",
       "      <td>2013</td>\n",
       "      <td>EWR</td>\n",
       "      <td>-2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>13825 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          Date  Flight Number Destination  Delay\n",
       "0       6/1/15             73         HNL    257\n",
       "1       6/1/15            217         EWR     28\n",
       "2       6/1/15            237         STL     -3\n",
       "3       6/1/15            250         SAN      0\n",
       "4       6/1/15            267         PHL     64\n",
       "...        ...            ...         ...    ...\n",
       "13820  8/31/15           1978         LAS     -4\n",
       "13821  8/31/15           1993         IAD      8\n",
       "13822  8/31/15           1994         ORD      3\n",
       "13823  8/31/15           2000         PHX     -1\n",
       "13824  8/31/15           2013         EWR     -2\n",
       "\n",
       "[13825 rows x 4 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united = pd.read_csv(path_data + 'united_summer2015.csv')\n",
    "united"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One flight departed 16 minutes early, and one was 580 minutes late. The other delay times were almost all between -10 minutes and 200 minutes, as the histogram below shows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-16"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united['Delay'].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "580"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united['Delay'].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delay_bins = np.append(np.arange(-20, 301, 10), 600)\n",
    "\n",
    "unit = 'minute'\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "\n",
    "ax1.hist(united['Delay'], bins=delay_bins, density=True, alpha=0.8, ec='white')\n",
    "\n",
    "y_vals = ax1.get_yticks()\n",
    "\n",
    "y_label = 'Percent per ' + (unit if unit else 'unit')\n",
    "\n",
    "x_label = 'Delay' + (unit if unit else '(unit)')\n",
    "\n",
    "ax1.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
    "\n",
    "plt.ylabel(y_label)\n",
    "\n",
    "plt.xlabel(x_label)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purposes of this section, it is enough to zoom in on the bulk of the data and ignore the 0.8% of flights that had delays of more than 200 minutes. This restriction is just for visual convenience; the table still retains all the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008390596745027125"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united_delay_more_than_200 = united[united['Delay']>200]\n",
    "\n",
    "len(united_delay_more_than_200)/len(united)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delay_bins = np.arange(-20, 201, 10)\n",
    "\n",
    "unit = 'minute'\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "\n",
    "ax1.hist(united['Delay'], bins=delay_bins, density=True, alpha=0.8, ec='white')\n",
    "\n",
    "y_vals = ax1.get_yticks()\n",
    "\n",
    "y_label = 'Percent per ' + (unit if unit else 'unit')\n",
    "\n",
    "x_label = 'Delay' + (unit if unit else '(unit)')\n",
    "\n",
    "ax1.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
    "\n",
    "plt.ylabel(y_label)\n",
    "\n",
    "plt.xlabel(x_label)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The height of the [0, 10) bar is just under 3% per minute, which means that just under 30% of the flights had delays between 0 and 10 minutes. That is confirmed by counting rows: \n",
    "\n",
    "**Notice** the height of the bar depends upon bin size, for bin size the upper limit of 10 in not included hence we are using records where the delay is equal to or greater than 0 and less than 10 i.e. [0,100)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2935985533453888"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united_delay_between_0_and_10 = united[(united['Delay']>=0) & (united['Delay']<10)]\n",
    "\n",
    "len(united_delay_between_0_and_10)/len(united)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Empirical Distribution of the Sample ###\n",
    "\n",
    "Let us now think of the 13,825 flights as a population, and draw random samples from it with replacement. It is helpful to package our code into a function. The function `empirical_hist_delay` takes the sample size as its argument and draws an empiricial histogram of the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def empirical_hist_delay(n):\n",
    "    \n",
    "    unit = 'minute'\n",
    "\n",
    "    fig, ax1 = plt.subplots()\n",
    "\n",
    "    ax1.hist(united['Delay'].sample(n), bins=delay_bins, density=True, alpha=0.8, ec='white')\n",
    "\n",
    "    y_vals = ax1.get_yticks()\n",
    "\n",
    "    y_label = 'Percent per ' + (unit if unit else 'unit')\n",
    "\n",
    "    x_label = 'Delay' + (unit if unit else '(unit)')\n",
    "\n",
    "    ax1.set_yticklabels(['{:g}'.format(x * 100) for x in y_vals])\n",
    "\n",
    "    plt.ylabel(y_label)\n",
    "\n",
    "    plt.xlabel(x_label)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw with the dice, as the sample size increases, the empirical histogram of the sample more closely resembles the histogram of the population. Compare these histograms to the population histogram above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most consistently visible discrepancies are among the values that are rare in the population. In our example, those values are in the the right hand tail of the distribution. But as the sample size increases, even those values begin to appear in the sample in roughly the correct proportions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convergence of the Empirical Histogram of the Sample ###\n",
    "What we have observed in this section can be summarized as follows:\n",
    "\n",
    "For a large random sample, the empirical histogram of the sample resembles the histogram of the population, with high probability.\n",
    "\n",
    "This justifies the use of large random samples in statistical inference. The idea is that since a large random sample is likely to resemble the population from which it is drawn, quantities computed from the values in the sample are likely to be close to the corresponding quantities in the population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
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