statkclee/chap05ex-kor.ipynb

## chap05ex-kor.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "통계적 사고 (2판) 연습문제 ([thinkstats2.com](thinkstats2.com), [think-stat.xwmooc.org](http://think-stat.xwmooc.org))<br>\n",
    "Allen Downey / 이광춘(xwMOOC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "import thinkstats2\n",
    "import thinkplot\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 연습문제 5.1\n",
    "\n",
    "BRFSS 데이터셋에서 (5.4절 참조), 신장 분포는 대략 남성에 대해 모수 µ = 178 cm, σ = 7.7cm을 갖는 정규분포이며, 여성에 대해서 µ = 163 cm, σ = 7.3 cm 을 갖는다.\n",
    "\n",
    "블루맨 그룹에 가입하기 위해서, 남성은 5’10”에서 6’1”사이여야 된다. ([http://bluemancasting.com](http://bluemancasting.com) 참조). US 남성 인구의 몇 퍼센티지가 해당 범위에 있을까? 힌트: scipy.stats.norm.cdf를 사용하라."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<tt>scipy.stats</tt> 모듈은 해석분포(analytic distributions)를 나타내는 객체를 담고 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "예를 들어, <tt>scipy.stats.norm</tt>은 정규분포를 나타낸다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "scipy.stats._distn_infrastructure.rv_frozen"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu = 178\n",
    "sigma = 7.7\n",
    "dist = scipy.stats.norm(loc=mu, scale=sigma)\n",
    "type(dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"고정된 확률변수(frozen random variable)\"는 평균과 표준편차를 계산할 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(178.0, 7.7000000000000002)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist.mean(), dist.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CDF도 평가할 수 있다. 평균아래 1 표준편차를 벗어난 사람은 얼마나 될까? 약 16%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15865525393145741"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist.cdf(mu-sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5'10\"과 6'1\" 사이 얼마나 많은 사람이 분포하고 있는가?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 연습문제 5.2\n",
    "\n",
    "파레토 분포에 대한 감각을 갖기 위해서, 만약 사람 신장의 분포가 파레토라면 세상이 얼마나 달라지는지 살펴보자. $x_m = 1$ m, $α = 1.7$ 모수로, 일리있는 최소값 1 m, 중위수 1.5 m 를 갖는 분포가 된다.\n",
    "\n",
    "상기 분포를 도식화하세요. 파레토 세상에서 평균 사람 신장은 얼마인가? 인구의 얼마나 평균보다 더 적은가? 만약 파레토 세상에 70억 사람이 있다면, 얼마나 많은 사람들이 1 km 보다 더 클 것으로 예상하는가? 가장 작은 사람은 신장이 얼마나 될 것으로 예상하는가?\n",
    "\n",
    "<tt>scipy.stats.pareto</tt>는 파레토 분포를 나타낸다. 파레토 세상에서, 사람 키 분포는 모수 $x_m = 1$ m, $α = 1.7$을 갖는다. 그래서 가장 키가 작은 사람은 100 cm이고, 중위수는 150cm이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5034066538560549"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = 1.7\n",
    "xmin = 1\n",
    "dist = scipy.stats.pareto(b=alpha, scale=xmin)\n",
    "dist.median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ISGRxTCAcONjZXDRGzUUiIiHnmECoOtQQmB49Kt3GSkREIpNjAuFgdWcg5Oop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\nEREREREREREREREREREJlf8PpNNclz5JfdEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ca5002410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs, ps = thinkstats2.RenderParetoCdf(xmin, alpha, 0, 10.0, n=100) \n",
    "thinkplot.Plot(xs, ps, label=r'$\\alpha=%g$' % alpha)\n",
    "thinkplot.Config(xlabel='height (m)', ylabel='CDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "파레토 세상에서 평균신장이 얼마인가?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "평균보다 더 키가 작은 사람의 비율은 얼마나 될까?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "70억 사람중에서, 1 km 보다 더 키가 클 것으로 예상되는 사람은 얼마나 될까? <tt>dist.cdf</tt> 혹은 <tt>dist.sf</tt>을 사용한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "가장 키가 큰 사람은 얼마나 키가 클 것으로 예상되는가? 힌트: 한 사람에 대한 신장을 찾아본다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 연습문제 5.3\n",
    "\n",
    "와이불 분포(Weibull distribution)는 고장 분석에서 나오는 지수분포를 일반화한 것이다 ([http://wikipedia.org/wiki/Weibull_distribution](http://wikipedia.org/wiki/Weibull_distribution) 참조). CDF는 다음과 같다.\n",
    "\n",
    "$CDF(x) = 1 − \\exp(−(x / λ)^k)$ \n",
    "\n",
    "와이블 분포를 직선처럼 보이게 하는 변환을 찾을 수 있을까요? 직선의 기울기와 절편은 무엇을 나타내는가?\n",
    "<tt>random.weibullvariate</tt>을 사용해서 와이블 분포에서 표본을 생성하시오. 그리고 이를 사용해서 분포를 테스트하시오."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 연습문제 5.4\n",
    "\n",
    "`n`의 적은 값으로, 정확하게 해석 분포에 적합되는 경험분포를 기대하지 못한다. 적합 품질을 평가하는 한 방법이 해석적 분포로부터 표본을 생성하고 데이터와 얼마나 잘 매칭되는지 살펴보는 것이다.\n",
    "예를 들어, 5.1 절에서, 출생사이 시간 분포를 도식화했고 근사적으로 지수분포라는 것을 보았다. 하지만, 분포는 단지 데이터가 44에 불과하다. 데이터가 지수분포에서 나왔는지 살펴보기 위해서, 출생사이 약 33분인, 데이터와 동일한 평균을 갖는 지수분포에서 데이터를 44개 생성한다.\n",
    "\n",
    "임의 확률 표본의 분포를 도식화하고, 실제 분포와 비교한다. `random.expovariate` 을 사용해서 값을 생성한다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ca5369950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import analytic\n",
    "\n",
    "df = analytic.ReadBabyBoom()\n",
    "diffs = df.minutes.diff()\n",
    "cdf = thinkstats2.Cdf(diffs, label='actual')\n",
    "thinkplot.Cdf(cdf, complement=True)\n",
    "thinkplot.Config(yscale='log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}