CH4/templates/04_stat.bootstrap_intervals.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Доверительные интервалы на основе bootstrap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Загрузка данных"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Время ремонта телекоммуникаций"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verizon — основная региональная телекоммуникационная компания (Incumbent Local Exchange Carrier, ILEC) в западной \n",
    "части США. В связи с этим по закону она обязана предоставлять сервис ремонта телекоммуникационного оборудования \n",
    "не только для своих клиентов, но и для клиентов других локальных телекоммуникационых компаний (Competing Local Exchange Carriers, CLEC). При этом в случаях, когда время ремонта оборудования для клиентов других компаний существенно выше, чем для собственных клиентов, Verizon может быть оштрафована. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1687, 2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('verizon.txt', sep='\\t')\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ILEC    1664\n",
       "CLEC      23\n",
       "Name: Group, dtype: int64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Group.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>Group</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.50</td>\n",
       "      <td>ILEC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.40</td>\n",
       "      <td>ILEC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.00</td>\n",
       "      <td>ILEC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.65</td>\n",
       "      <td>ILEC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>22.23</td>\n",
       "      <td>ILEC</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Time Group\n",
       "0  17.50  ILEC\n",
       "1   2.40  ILEC\n",
       "2   0.00  ILEC\n",
       "3   0.65  ILEC\n",
       "4  22.23  ILEC"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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hcHuSq4EddK7gQVVtSXI7nXeEPwO890BBWpIkSZotejnNg6paD6zfb/gxOqeAHGj764Dr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12a14a5a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.figure(figsize(12,5))\n",
    "pylab.subplot(1,2,1)\n",
    "pylab.hist(data[data.Group == 'ILEC'].Time, \n",
    "           bins=20,color='b',range=(0,100), \n",
    "           label = 'ILEC')\n",
    "pylab.legend()\n",
    "pylab.subplot(1,2,2)\n",
    "pylab.hist(data[data.Group == 'CLEC'].Time, \n",
    "           bins=20,color='r',range=(0,100), \n",
    "           label = 'CLEC')\n",
    "\n",
    "pylab.legend()\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_bootstrap_samples(data, n_samples):\n",
    "    indices = np.random.randint(0, len(data), (n_samples, len(data)))\n",
    "    samples = data[indices]\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def stat_intervals(stat, alpha):\n",
    "    boundaries = np.percentile(stat, [100 * alpha / 2., 100 * (1 - alpha / 2.)])\n",
    "    return boundaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Интервальная оценка медианы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ilec_time = data[data.Group == 'ILEC'].Time.values\n",
    "clec_time = data[data.Group == 'CLEC'].Time.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval for the ILEC median repair time: [ 3.18     3.82525]\n",
      "95% confidence interval for the CLEC median repair time: [  5.79125  20.     ]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "\n",
    "ilec_median_scores = map(np.median, get_bootstrap_samples(ilec_time, 1000))\n",
    "clec_median_scores = map(np.median, get_bootstrap_samples(clec_time, 1000))\n",
    "\n",
    "print \"95% confidence interval for the ILEC median repair time:\",  stat_intervals(ilec_median_scores, 0.05)\n",
    "print \"95% confidence interval for the CLEC median repair time:\",  stat_intervals(clec_median_scores, 0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Точечная оценка разности медиан"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "delta median 10.74\n"
     ]
    }
   ],
   "source": [
    "print \"delta median\", np.median(clec_time) - np.median(ilec_time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Интервальная оценка разности медиан"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "median_scores = zip(map(np.median, ilec_median_scores), map(np.median, clec_median_scores))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "delta_median_scores = map(lambda x: x[1] - x[0], median_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% confidence interval for the difference between median repair times: [  2.04975  16.63   ]\n"
     ]
    }
   ],
   "source": [
    "print \"95% confidence interval for the difference between median repair times:\",  stat_intervals(delta_median_scores, 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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