Lecture10_Statistics_In_Data_Science_1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "pd.options.display.max_columns=None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 미국인구 데이터"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>state/region</th>\n",
       "      <th>ages</th>\n",
       "      <th>year</th>\n",
       "      <th>population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AL</td>\n",
       "      <td>under18</td>\n",
       "      <td>2012</td>\n",
       "      <td>1117489.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AL</td>\n",
       "      <td>total</td>\n",
       "      <td>2012</td>\n",
       "      <td>4817528.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>AL</td>\n",
       "      <td>under18</td>\n",
       "      <td>2010</td>\n",
       "      <td>1130966.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>AL</td>\n",
       "      <td>total</td>\n",
       "      <td>2010</td>\n",
       "      <td>4785570.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>AL</td>\n",
       "      <td>under18</td>\n",
       "      <td>2011</td>\n",
       "      <td>1125763.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  state/region     ages  year  population\n",
       "0           AL  under18  2012   1117489.0\n",
       "1           AL    total  2012   4817528.0\n",
       "2           AL  under18  2010   1130966.0\n",
       "3           AL    total  2010   4785570.0\n",
       "4           AL  under18  2011   1125763.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state_pop_dataset = pd.read_csv('state-population.csv')\n",
    "state_pop_dataset.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 미국 살인기록 데이터"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>state</th>\n",
       "      <th>abb</th>\n",
       "      <th>region</th>\n",
       "      <th>population</th>\n",
       "      <th>total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Alabama</td>\n",
       "      <td>AL</td>\n",
       "      <td>South</td>\n",
       "      <td>4779736</td>\n",
       "      <td>135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alaska</td>\n",
       "      <td>AK</td>\n",
       "      <td>West</td>\n",
       "      <td>710231</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Arizona</td>\n",
       "      <td>AZ</td>\n",
       "      <td>West</td>\n",
       "      <td>6392017</td>\n",
       "      <td>232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Arkansas</td>\n",
       "      <td>AR</td>\n",
       "      <td>South</td>\n",
       "      <td>2915918</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>California</td>\n",
       "      <td>CA</td>\n",
       "      <td>West</td>\n",
       "      <td>37253956</td>\n",
       "      <td>1257</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        state abb region  population  total\n",
       "0     Alabama  AL  South     4779736    135\n",
       "1      Alaska  AK   West      710231     19\n",
       "2     Arizona  AZ   West     6392017    232\n",
       "3    Arkansas  AR  South     2915918     93\n",
       "4  California  CA   West    37253956   1257"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = pd.read_csv('./inputs/murders.csv')\n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 독일 신용 데이터"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# German credit data를 살펴보자.\n",
    "german_dataset = pd.read_csv('./inputs/german_credit_data.csv',  index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 데이터에는 돈을 갚을 능력(Good/Bad)에 대한 데이터가 없다. \n",
    "# 따라서 해당 data를 concat 하도록 하겠다.\n",
    "\n",
    "# Label 만 가지고 온다.\n",
    "path = 'https://archive.ics.uci.edu/ml/machine-learning-databases/statlog/german/german.data'\n",
    "dataset = pd.read_csv(path, delimiter=' ', header=None)\n",
    "\n",
    "# 데이터를 concat\n",
    "german_dataset = pd.concat([german_dataset, dataset.iloc[:,-1] - 1], axis=1)\n",
    "\n",
    "# 컬럼 이름 변경\n",
    "german_dataset.columns.values[-1] = 'Risk'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Job</th>\n",
       "      <th>Housing</th>\n",
       "      <th>Saving accounts</th>\n",
       "      <th>Checking account</th>\n",
       "      <th>Credit amount</th>\n",
       "      <th>Duration</th>\n",
       "      <th>Purpose</th>\n",
       "      <th>Risk</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>67</td>\n",
       "      <td>male</td>\n",
       "      <td>2</td>\n",
       "      <td>own</td>\n",
       "      <td>NaN</td>\n",
       "      <td>little</td>\n",
       "      <td>1169</td>\n",
       "      <td>6</td>\n",
       "      <td>radio/TV</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>22</td>\n",
       "      <td>female</td>\n",
       "      <td>2</td>\n",
       "      <td>own</td>\n",
       "      <td>little</td>\n",
       "      <td>moderate</td>\n",
       "      <td>5951</td>\n",
       "      <td>48</td>\n",
       "      <td>radio/TV</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>49</td>\n",
       "      <td>male</td>\n",
       "      <td>1</td>\n",
       "      <td>own</td>\n",
       "      <td>little</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2096</td>\n",
       "      <td>12</td>\n",
       "      <td>education</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>45</td>\n",
       "      <td>male</td>\n",
       "      <td>2</td>\n",
       "      <td>free</td>\n",
       "      <td>little</td>\n",
       "      <td>little</td>\n",
       "      <td>7882</td>\n",
       "      <td>42</td>\n",
       "      <td>furniture/equipment</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>53</td>\n",
       "      <td>male</td>\n",
       "      <td>2</td>\n",
       "      <td>free</td>\n",
       "      <td>little</td>\n",
       "      <td>little</td>\n",
       "      <td>4870</td>\n",
       "      <td>24</td>\n",
       "      <td>car</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age     Sex  Job Housing Saving accounts Checking account  Credit amount  \\\n",
       "0   67    male    2     own             NaN           little           1169   \n",
       "1   22  female    2     own          little         moderate           5951   \n",
       "2   49    male    1     own          little              NaN           2096   \n",
       "3   45    male    2    free          little           little           7882   \n",
       "4   53    male    2    free          little           little           4870   \n",
       "\n",
       "   Duration              Purpose  Risk  \n",
       "0         6             radio/TV     0  \n",
       "1        48             radio/TV     1  \n",
       "2        12            education     0  \n",
       "3        42  furniture/equipment     0  \n",
       "4        24                  car     1  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "german_dataset.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### House price 데이터"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "      <th>housing_median_age</th>\n",
       "      <th>total_rooms</th>\n",
       "      <th>total_bedrooms</th>\n",
       "      <th>population</th>\n",
       "      <th>households</th>\n",
       "      <th>median_income</th>\n",
       "      <th>median_house_value</th>\n",
       "      <th>ocean_proximity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-122.23</td>\n",
       "      <td>37.88</td>\n",
       "      <td>41.0</td>\n",
       "      <td>880.0</td>\n",
       "      <td>129.0</td>\n",
       "      <td>322.0</td>\n",
       "      <td>126.0</td>\n",
       "      <td>8.3252</td>\n",
       "      <td>452600.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-122.22</td>\n",
       "      <td>37.86</td>\n",
       "      <td>21.0</td>\n",
       "      <td>7099.0</td>\n",
       "      <td>1106.0</td>\n",
       "      <td>2401.0</td>\n",
       "      <td>1138.0</td>\n",
       "      <td>8.3014</td>\n",
       "      <td>358500.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-122.24</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1467.0</td>\n",
       "      <td>190.0</td>\n",
       "      <td>496.0</td>\n",
       "      <td>177.0</td>\n",
       "      <td>7.2574</td>\n",
       "      <td>352100.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-122.25</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1274.0</td>\n",
       "      <td>235.0</td>\n",
       "      <td>558.0</td>\n",
       "      <td>219.0</td>\n",
       "      <td>5.6431</td>\n",
       "      <td>341300.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-122.25</td>\n",
       "      <td>37.85</td>\n",
       "      <td>52.0</td>\n",
       "      <td>1627.0</td>\n",
       "      <td>280.0</td>\n",
       "      <td>565.0</td>\n",
       "      <td>259.0</td>\n",
       "      <td>3.8462</td>\n",
       "      <td>342200.0</td>\n",
       "      <td>NEAR BAY</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
       "0    -122.23     37.88                41.0        880.0           129.0   \n",
       "1    -122.22     37.86                21.0       7099.0          1106.0   \n",
       "2    -122.24     37.85                52.0       1467.0           190.0   \n",
       "3    -122.25     37.85                52.0       1274.0           235.0   \n",
       "4    -122.25     37.85                52.0       1627.0           280.0   \n",
       "\n",
       "   population  households  median_income  median_house_value ocean_proximity  \n",
       "0       322.0       126.0         8.3252            452600.0        NEAR BAY  \n",
       "1      2401.0      1138.0         8.3014            358500.0        NEAR BAY  \n",
       "2       496.0       177.0         7.2574            352100.0        NEAR BAY  \n",
       "3       558.0       219.0         5.6431            341300.0        NEAR BAY  \n",
       "4       565.0       259.0         3.8462            342200.0        NEAR BAY  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing_data = pd.read_csv('./inputs/housing.csv')\n",
    "housing_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 빅데이터 시대가 되면서 더이상 표본추출(표집, 샘플링)이 필요 없을 거라는 오해\n",
    "- 데이터의 질과 적합성을 일정 수준 이상으로 담보할 수 없으면서 데이터 크기만 늘어나는 것이 오늘날 상황\n",
    "- 오히려, 다양한 데이터를 효과적으로 다루고 데이터 편향을 최소화하기 위한 방법으로 표본추출의 필요성이 더 커짐"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 전통적인 통계학에서는 강력한 가정에 기초한 이론을 통해 모집단을 밝혀내는 데 초점\n",
    "- 현대 통계학에서는 이러한 가정이 더 이상 필요하지 않은, 즉 효과적인 표본추출에 대한 연구로 방향이 옮겨지기 시작\n",
    "- 데이터 과학자들은 이론적 측면에 대해 걱정하기보다, 표본추출 과정과 주어진 데이터에 집중할 필요가 있음. 하지만 이론적인 측면을 알아야 함."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Random Sampling과 Sample Bias\n",
    "\n",
    "---\n",
    "\n",
    "- 표본(sample) : 모집단 또는 큰 데이터 집합으로부터 얻은 부분집합\n",
    "- 모집단(population) : 어떤 데이터 집합을 구성하는 전체 대상 혹은 전체 집합\n",
    "- $N$ : 모집단의 크기\n",
    "- $n$ : 표본의 크기\n",
    "- 랜덤표본추출(random sampling, 임의표집) : 무작위로 표본을 추출하는 것\n",
    "- 층화표본추출(stratified sampling) : 모집단을 층으로 나눈 뒤, 각 층에서 무작위로 표본을 추출하는 것\n",
    "- 단순랜덤표본 : 모집단 층화(stratified) 없이 랜덤표본추출로 얻은 표본\n",
    "- 표본편향(sample bias) : 모집단을 잘못 대표하는(misrepresents) 표본\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 랜덤표본추출(Random sampling, 임의표집)은 무작위로 표본을 추출하는 것, 각 추첨에서 모든 원소는 동일한 확률로 뽑힘.\n",
    "  - 복원추출(With replacement) : 추출 후, 다음번에도 중복 추출이 가능하도록 해당 샘플을 다시 모집단에 포함\n",
    "  - 비복원추출(Without replacement) : 한번 뽑힌 원소는 추후 추첨에 사용하지 않음\n",
    "- 샘플 기반의 추청이나 모델링에서 **데이터 품질은 데이터 양보다 더욱 중요함**\n",
    "- 데이터 과학에서 <U>데이터 품질</U>\n",
    "    - 완결성(completeness)\n",
    "    - 형식의 일관성(consistency of format)\n",
    "    - 깨끗함(cleanliness)\n",
    "    - 각 데이터 값의 정확성(accuracy of individual data points)\n",
    "    - 대표성(representativeness) $\\to$ 통계에서 중요시 생각하는 것\n",
    "- 표본편향(Sample bias)은 모집단을 잘못 대표하는 표본을 의미하며, 유의미한 nonrandom(비임의 방식)으로 표본이 추출될 때 발생. 이 경우 랜덤표본이라고 해도 어떤 표본도 모집단을 정확하게 대표할 수 없다는 것을 의미.\n",
    " - 대표적인 예가 review 데이터가 될 수 있다.\n",
    " - 대표적인 예가 대선 설문 조사시에, 특정 지역, 특정 계층에 대해서만 표본을 추출하는 경우"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (Sample) Bias\n",
    "- (통계) Bias : 측정 과정 혹은 표본추출 과정에서 발생하는 systematic 오차를 의미\n",
    "- (머신러닝) Bias : 모델의 예측값과 실제값의 차이"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random selection\n",
    " - Bias, 즉 표본편향 문제를 피하고, 데이터의 representativeness(대표성)을 담보하기 위한 핵심\n",
    " - Random sampling을 위해 고려해야 할 2가지\n",
    "     - 접근 가능한 모집단의 적절한 정의 \n",
    "         - ex) 고객의 정의 : 구매 금액이 0보다 큰 고객이 대상일 때, 모든 과거 고객을 포함? 제품을 환불한 고객 포함? 사업자 포함?\n",
    "     - 표본추출 절차를 선택\n",
    "         - ex) 고객을 추출 : 무작위로 100명의 고객을 선택? 평일 오전 10시의 방문자들만?(주말 오전 10시의 방문자와 같을까?)\n",
    " - <font color=green>Stratified sampling (층화표본추출)</font> : 모집단을 여러 층으로 나누고 각 층(strata)에서 무작위로 샘플을 추출"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Size vs Quality\n",
    "\n",
    "빅데이터 시대라 할지라도, 데이터 개수가 적을수록 더 유리한 경우도 존재한다. 랜덤표본추출에 시간과 노력을 기울일수록 편향이 줄어들 뿐만 아니라 데이터 탐색 및 데이터 품질에 더 집중할 수 있다. \n",
    "\n",
    "Missing value 또는 outlier를 통하여 유용한 정보를 얻을 수 있다. 몇백만 개 데이터 중에서 missing value 및 outlier를 추적하고 평가하는 것은 어렵지만 수천개의 데이터 샘플에서는 가능할 수 있다. 이처럼 데이터가 많은 경우에는 데이터를 일일이 손으로 조사하고 검사하기 매우 어렵다.\n",
    "\n",
    "그렇다면 대량의 데이터가 필요할 때는 언제일까? 빅데이터가 가치 있을 때는, 데이터가 크고 동시에 sparse 할 때이다. 구글 검색 쿼리를 생각해보자. word - document matrix를 생각할 수 있고, 행렬의 대부분의 entry가 0가 될 것이다. 아주 방대한 데이터가 누적될 때에 대부분에 쿼리에 대해 효과적인 검색 결과를 반환할 수 있게 될 것이다. 정확한 검색 결과는 데이터가 많은 양이 누적되어 있을 때 가능한 것이지, 랜덤표본추출을 잘 한다고 해서 도움이 되는 것이 아니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Sampling Distribution of Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 용어정리\n",
    "    - Sample statistic(표본통계량) : 더 큰 모집단에서 추출된 표본(a sample) 데이터들로부터 얻은 측정 지표 (예를 들어, 표본평균)\n",
    "    - Data distribution(데이터 분포) : 어떤 데이터 집합에서의 각 개별 값의 도수분포\n",
    "    - Sampling distribution(표본분포) : 여러 표본들(samples) 혹은 재표본(resamples)들로부터 얻은 표본통계량의 도수분포\n",
    "    - Central limit theorem(중심극한정리) : 표본크기가 커질수록 표본분포가 정규분포를 따르는 경향\n",
    "    - Standard error(표준오차) : 여러 표본들(samples)로부터 얻은 표본통계량의 변량(개별 데이터 값들의 변량을 뜻하는 표준편차와 다름)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "일반적으로 우리는 측정 및 통계 or 머신러닝 모델링을 위해 표본을 추출한다. 표본을 통한 추정이나 모델링은 오류가 있다. 다른 표본을 추출했다면 결과가 다를 수 있다. 과연 결과가 얼마나 달라졌을까에 대한 관심사가 <font color=green>sampling variability(표본의 변동성)</font>이다.\n",
    "\n",
    "우리가 많은 양의 데이터를 가지고 있다면 추가로 표본을 얻어서 통계의 분포를 직접 관찰할 수 있다. 하지만 보통은 이미 최대한 많은 데이터를 사용하여 추정치 또는 모델을 계산했을 것이므로, 모집단에서 추가 표본을 얻는 옵션은 쉽게 이용할 수 없다. 표본의 변동성을 확인하는 것은 결국 표본통계량의 분포를 살펴보는 것이다. \n",
    "\n",
    "대표적인 표본통계량인 표본평균의 분포는, 특히나 표본의 크기가 커질수록, 데이터 자체의 분포보다 규칙적이고 종 모양일 가능성(정규분포일 가능성)이 높다. (물론 중심극한정리를 알기에 받아들이는 사실이지만 직관적으로도 그렇다.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Central limit theorem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "plt.rcParams[\"figure.figsize\"] = (10,20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "캘리포니아 집 값 데이터에 대하여, 집 값의 median에 대한 표본분포를 살펴보자."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Sample mean of 100 data points : 1000 samples')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107912978>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. 전체 표본에 대한 분포\n",
    "ax1 = plt.subplot(411)\n",
    "sns.distplot(housing_data['median_house_value'])\n",
    "plt.title('Dataset')\n",
    "\n",
    "# 2. 데이터를 5개씩 추출해서 표본을 만들고, 표본평균을 구한다. 즉, 표본의 크기는 5이다. 이 과정을 1000번 반복한다. \n",
    "sample_5 = []\n",
    "for _ in range(1000):\n",
    "    sample_5.append(housing_data.median_house_value.sample(5).mean())\n",
    "ax2 = plt.subplot(412, sharex = ax1)\n",
    "sns.distplot(sample_5)\n",
    "plt.title('Sample mean of 5 data points : 1000 samples')\n",
    "\n",
    "# 3. 데이터를 20개씩 추출해서 표본을 만들고, 표본평균을 구한다. 즉, 표본의 크기는 20이다. 이 과정을 1000번 반복한다.\n",
    "sample_20 = []\n",
    "for _ in range(1000):\n",
    "    sample_20.append(housing_data.median_house_value.sample(20).mean())\n",
    "ax3 = plt.subplot(413, sharex = ax1)\n",
    "sns.distplot(sample_20)\n",
    "plt.title('Sample mean of 20 data points : 1000 samples')\n",
    "\n",
    "# 4. 데이터를 100개씩 추출해서 표본을 만들고, 표본평균을 구한다. 즉, 표본의 크기는 100이다. 이 과정을 1000번 반복한다.\n",
    "sample_100 = []\n",
    "for _ in range(1000):\n",
    "    sample_100.append(housing_data.median_house_value.sample(100).mean())\n",
    "ax4 = plt.subplot(414, sharex = ax1)\n",
    "sns.distplot(sample_100)\n",
    "plt.title('Sample mean of 100 data points : 1000 samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "중심극한정리는 모집단이 정규분포가 아니더라도, 표본크기가 충분하고 데이터가 정규성을 크게 이탈하지 않는 경우 여러 표본에서 추출한 평균은 종 모양의 정규곡선을 따른다는 것을 보여준다. 중심극한정리 덕분에, 추론을 위한 표본분포에, 즉 신뢰구간이나 가설검정을 계산하는 데에 $t$ 분포 같은 정규근사 공식을 사용할 수 있다.\n",
    "\n",
    "데이터 과학에서는 형식적인 가설검정이나 신뢰구간이, 통계에서의 중요성만큼, 중요하지 않기 때문에(이 2개의 밑바탕이 바로 중심극한정리이다) 중식극한정리가, 통계에서의 중요성만큼, 중요하지는 않다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 표준오차는 표본분포의 변동성을 나타내는 측정 지표\n",
    "- 표본 값들의 표준편차가 $s$이고 표본크기가 $n$일 때, $\\text{Standard error} = \\frac{s}{\\sqrt{n}}$ \n",
    "- 표본크기가 커지면 표준오차가 줄어들며, 표준오차와 표본크기 사이의 관계를 때로는 $n$ 제곱근의 법칙(square root of $n$ rule)이라고 한다. 표준오차를 2배로 줄이려면 표본 크기를 4배 증가시켜야 한다.\n",
    "- 표준오차를 측정할 때 고려해야 할 사항\n",
    "    1. 모집단에서 완전히 새로운 샘플들을 많이 수집한다.\n",
    "    2. 각각의 새 샘플에 대해 통계량(예, 평균)을 계산한다.\n",
    "    3. 2번째 단계에서 얻은 통계량의 표준편차를 계산한다. 이것을 표준오차의 추정치로 사용한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "현대 통계에서는 새로운 샘플을 뽑을 필요 없이, **bootstrap(부트스트랩) 재표본**을 사용하여 표준 오차를 추정한다. 현대 통계에서 부트스트랩은 표준 오차를 추정하는 표준 방법이 되었다. <U>사실상 모든 통계에 사용할 수 있으며 중심극한정리 또는 기타 분포 가정에 의존하지 않는다.</U>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. <font color=red>Bootstrap</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 통계량이나 모델 파라미터(모수)의 표본분포를 추정하는 쉽고 효과적인 방법\n",
    "- 현재 있는 표본에서 추가적으로 표본을 **복원추출**하고 각 표본에 대한 통계량과 모델을 다시 계산하는 것\n",
    "- 데이터나 표본통계량이 정규분포를 따라야 한다는 가정은 꼭 필요하지 않음\n",
    "- 표본을 많이 복제하고(수천, 수백만 번) 이를 통해 원래 표본으로부터 얻어지는 모든 정보를 포함하는 가상 모집단을 얻게 된다고 가정할 수 있음"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "- Bootstrap sample(부트스트랩 표본) : 관측 데이터 집합으로부터 얻은 복원추출 표본\n",
    "- Resampling(재표본추출, 리샘플링) : 관측 데이터로부터 반복해서 표본추출하는 과정이며, bootstrap과 shuffling(순열) 과정을 포함\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "(**Bootstrap 알고리즘**)\n",
    "1. 샘플 값을 하나 뽑아서 기록하고 제자리에 놓는다.\n",
    "2. $n$ 번 반복한다.(resampling)\n",
    "3. $n$ 번 재표본추출된(resampled) 값의 평균을 기록한다.\n",
    "4. 1~3단계를 $R$번 반복한다.\n",
    "4. $R$개의 결과를 사용하여 (총 $nR$번 추출)\n",
    " - 결과들의 표준편차(표본평균의 표준오차)를 계산한다.\n",
    " - 히스토그램 또는 상자그림을 그린다.\n",
    " - 신뢰구간을 찾는다.\n",
    "        \n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "부트스트랩의 반복 횟수는 임의로 설정한다. 반복 횟수가 많을수록 표준오차나 신뢰구간에 대한 추정이 더 정확해진다. 이런 절차를 통해 표본통계량 혹은 추정한 모델 파라미터의 부트스트랩 집합을 얻게 되고, 결과적으로 이 집합이 얼마나 변하는지를 조사할 수 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**(예제) Bootstrap을 이용하여 미국 인구의 median을 추정하라**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dataset의 median : 1597005.0\n"
     ]
    }
   ],
   "source": [
    "# (미국 인구 데이터) median 원래 추정치\n",
    "print('dataset의 median :', state_pop_dataset.population.median())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (미국 인구 데이터) 부트스트랩 분포\n",
    "state_pop_sample_meds = []\n",
    "# 100개의 data가 1개의 sample set이다. 총 500번 반복\n",
    "for _ in range(500):\n",
    "    samp_med = state_pop_dataset.population.sample(100, replace=True).median()\n",
    "    state_pop_sample_meds.append(samp_med)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bootstrap median : 1675731.245\n",
      "bootstrap median의 표준오차(변동성) : 339939.30553654494\n"
     ]
    }
   ],
   "source": [
    "print('bootstrap median :', np.mean(state_pop_sample_meds))\n",
    "print('bootstrap median의 표준오차(변동성) :', np.std(state_pop_sample_meds))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Baggigng : 분류 및 회귀 트리를 사용할 때, 여러 부트스트랩 샘플을 가지고 트리를 여러 개 만든 다음 각 트리에서 나온 예측값을 평균 내는 것\n",
    "- Bootstrap은 표본크기가 작은 것을 보완하기 위한 것이 아니고, 새로운 데이터를 만들거나 기존 데이터 집합의 빈 곳을 채우는 것도 아니다. <U>모집단에서 추가적으로 표본을 뽑는다고 할 때, 그 표본이 얼마나 원래 표본과 비슷할지를 알려줄 뿐이다.</U> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "다시한번 정리하자면, 부트스트랩(데이터로부터 복원추출하는 기법)은 표본평균 또는 표본 중앙값과 같은 표본통계량의 변동성을 평가하는 강력한 도구이다. 부트스트랩은 수학적 근사치에 대한 엄청난 연구 없이도 다양한 환경에서 유사한 방식으로 적용될 수 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. 신뢰구간"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 신뢰구간은 구간 범위로 추정값을 표시하는 일반적인 방법이며, 우리가 구하고자 하는 관심 통계량을 포함할 것으로 예상되는 구간이다.\n",
    "- 신뢰구간은 항상 신뢰수준(confidence level)과 함께 나온다.\n",
    " - 90% 신뢰구간 : 표본통계량의 부트스트랩 표본분포의 90%를 포함하는 구간\n",
    "- 표본추정치의 주위의 $x$% 신뢰구간이란, 평균적으로 유사한 표본추정치 $x$% 정도(비슷한 샘플링 절차를 따랐을 때)가 포함되어야 한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "표본크기 $n$과 관심있는 표본통계량이 주어졌을 때, 부트스트랩 신뢰구간을 구하는 방법\n",
    "1. 데이터에서 복원추출 방식으로 크기 $n$인 표본을 뽑는다. (a resampling)\n",
    "2. Resampling 표본에 대해 원하는 통계량을 기록한다.\n",
    "3. 1 ~ 2 단계를 R번 반복한다.\n",
    "4. $x$% 신뢰구간을 구하기 위해, R개의 resampling 결과로부터 분포의 양쪽 끝에서 $\\frac{(100-x)}{2}$% 만큼 잘라낸다.\n",
    "5. 절단한 점들은 $x$% 부트스트랩 신뢰구간의 양 끝점이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 부트스트랩은 대부분의 통계량 혹은 모델 파라미터에 대한 신뢰구간을 생성하는 데 사용할 수 있는 일반적이고 효과적인 기법\n",
    "- 컴퓨터가 없던 시절에는 $t$-분포로 구한 신뢰구간을 사용\n",
    "\n",
    "신뢰구간과 관련된 백분율을 신뢰수준이라고 부른다. 신뢰수준이 넓을수록 구간이 넓어진다. 또한 표본이 작을수록 구간이 넓어진다. 즉 불확실성이 더 커진다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**(예제) 캘리포니아 지역의 평균 집 값에 대한 90% 신뢰구간을 부트스트랩을 이용하여 구하라.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (Housing data)\n",
    "house_prices = []\n",
    "for _ in range(1000):\n",
    "    mean_price = housing_data.median_house_value.sample(50, replace=True).mean()\n",
    "    house_prices.append(mean_price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x109267438>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e159b0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (6, 6)\n",
    "sns.distplot(house_prices, kde=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "90% CI lower: 181674.34\n",
      "90% CI upper: 235206.799\n"
     ]
    }
   ],
   "source": [
    "# 90% 구간\n",
    "ci_min = np.percentile(house_prices, 5)\n",
    "ci_max = np.percentile(house_prices, 95)\n",
    "\n",
    "print('90% CI lower:', ci_min)\n",
    "print('90% CI upper:', ci_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(예제) 미국 지역별 살인 발생 횟수의 평균에 대한 90% 신뢰구간을 부트스트랩을 이용하여 구하라.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. 정규분포"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 용어정리\n",
    "    - Error(오차) : 데이터 포인트와 예측값 혹은 평균 사이의 거리\n",
    "    - Standardize(표준화/정규화하다) : 평균을 빼고 표준편차로 나눈다.\n",
    "    - Z-score(z 점수) : 개별 데이터 포인트를 정규화한 결과\n",
    "    - Standard normal distribution : 평균=0, 표준편차=1인 정규분포\n",
    "    - QQ plot(QQ 그림) : 표본분포가 정규분포에 얼마나 가까운지를 보여주는 그림"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 대부분의 데이터가 정규분포를 따르기 때문에, 즉 이게 정상이기 때문에 정상적인(normal) 분포라고 부르는 것은 아니다. 실제로 전형적인 데이터 과학 프로젝트에서 사용되는 대부분의 변수들, 실제 대부분의 원시 데이터는 전체적으로 정규분포를 따르지 않는다. 표본분포에서 대부분의 통계량이 정규분포를 따른다는 점에서 정규분포의 유용함이 드러날 뿐이다. 설령 그렇다 해도 일반적으로 정규분포 가정은 경험적 확률분포나 부트스트랩 분포를 구할 수 없는 경우 사용되는 최후의 수단이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "표준정규분포는 $x$축의 단위가 평균의 표준편차로 표현되는 정규분포를 말한다. 데이터를 표준정규분포와 비교하려면 데이터에서 평균을 뺀 다음 표준편차로 나누면 된다. 이를 정규화(normalization) 또는 표준화(standardization)라고 한다. 이렇게 변환된 값을 $z$점수라고 하며, 정규분포를 $z$분포라고도 한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "데이터를 $z$점수로 변환(즉, 데이터를 표준화 또는 정규화)한다고 해서, 데이터가 정규분포가 되는 것은 아니다. 단지 비교를 목적으로 데이터를 표준정규분포와 같은 척도로 만드는 것이다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "QQ 그림은 표본이 정규분포에 얼마나 가까운지를 시각적으로 판별하는 데 사용된다. QQ 그림은 $z$점수를 오름차순으로 정렬하고 각 값의 $z$ 점수를 $y$축에 표시한다. $x$축은 정규분포에서의 해당 분위수를 나타낸다. 데이터가 표준화되었기 때문에, 단위는 평균으로부터 떨어진 데이터의 표준편차 수에 해당한다. 점들이 대략 대각선 위에 놓이면 표본분포가 정규분포에 가까운 것으로 간주할 수 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "QQ plot을 그리기 위해서는 `scipy.stats`의 `probplot`을 사용한다. 다른 라이브러리를 이용해서 그릴수도 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Normal distribution')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a169f5eb8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (Housing data)\n",
    "from scipy import stats\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (12, 6)\n",
    "\n",
    "# Housing data\n",
    "plt.subplot(121)\n",
    "stats.probplot(housing_data.median_house_value, plot=sns.mpl.pyplot)\n",
    "plt.title('Median house value in California')\n",
    "\n",
    "# Synthetic normal distribution data\n",
    "plt.subplot(122)\n",
    "stats.probplot(np.random.normal(5,5,250), plot=sns.mpl.pyplot)\n",
    "plt.title('Normal distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. 긴 꼬리 분포"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "- Tail(꼬리) : 적은 수의 극단값이 주로 존재하는, 도수분포의 길고 좁은 부분\n",
    "- Skewness : 분포의 한쪽 꼬리가 반대쪽 다른 꼬리보다 긴 정도\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 오차나 표본통계량의 분포를 볼 때 정규분포는 적절하고 유용하지만, 정규분포가 일반적으로 원시 데이터 분포의 특징을 나타내지는 않는다.\n",
    "- <font color=red>실무에서는 long tail 분포를 잘 들여다보는 것이 중요하다.</font>\n",
    "- 데이터는 가변적이며 보기에는 하나가 아닌 여러 유형의 분포와 일치할 수 있다.\n",
    "- 일반적으로 주어진 상황을 묘사하기에 적합한 분포 유형을 결정하기 위해서, 데이터만 들여다 보는것이 아니라, 분야 지식과 통계 지식을 모두 활용해야 한다.\n",
    "    - 예) 5초마다 연속적으로 서버의 인터넷 트래픽 수준에 대한 데이터를 얻는다고 할 때 적합한 분포 유형은? '시간 주기별 이벤트'를 모델링하는 데 가장 적합한 분포가 포아송 분포라는 사전 지식이 있다면 큰 도움이 된다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Total room number in California')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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S4LPHXJIkSeoA9phLkkaE7gUuySqps9ljLkkN6Fntc9So4rlSaXdEkqThxh5zSepFpVIsKLRkyQvLlywpVv8Ex5pLkgaPPeaSVEOlUiTf6yblPVatKpJ2SZIGS9MS84jYNCKuiYg/RsRNEfGVsny3iFgQEbdHxJyIGFOWb1JuLy7rJ1Qd64Sy/LaIOLCqfHJZtjgivtis9yJp5Jk5s0i+6+ltFVBJkgaimT3mzwD7ZebrgNcDkyNiH+Bk4JTM3B1YCRxTtj8GWJmZrwBOKdsREXsARwF7ApOBUyNidESMBr4LHATsARxdtpWkDdZI0u1qn5KkwdS0xDwLT5SbG5ePBPYDzi3LzwQOK19PKbcp6ydFRJTlZ2fmM5l5F7AY2Kt8LM7MOzPzWeDssq0kbbC+ku4IV/uUJA2upo4xL3u2rwceBOYDdwCPZObqsskyYOfy9c7APQBl/aPANtXl6+zTW3mtOKZHxMKIWLh8+fLBeGuShrlZs2Ds2Np1EfDJT3rjpyRpcDU1Mc/MNZn5emAcRQ/3a2o1K5+jl7r+lteKY3ZmTszMidttt13fgUsa8bq6YPZs2HXXYnv06OJ5113hxz+GU09tX2ySpOGpJdMlZuYjEXEVsA+wZURsVPaKjwPuK5stA3YBlkXERsBLgBVV5T2q9+mtXJI2WFeXveKSpNZp5qws20XEluXrzYD9gVuAK4EjymbTgAvK1/PKbcr6KzIzy/KjyllbdgN2B64BrgV2L2d5GUNxg+i8Zr0fSZIkqZma2WO+I3BmOXvKKGBuZl4YETcDZ0fE14E/AKeX7U8HfhwRiyl6yo8CyMybImIucDOwGjguM9cARMSngEuB0cAZmXlTE9+PJEmS1DRNS8wz8wbgDTXK76QYb75u+dPAkb0caxaw3vwHmXkRcNEGBytJkiS1mSt/SpIkSR3AxFySJEnqACbmkiRJUgcwMZekGioVmDABRo0qniuVdkckSRruWjKPuSQNJZUKTJ8Oq1YV20uWFNvgvOaSpOaxx1yS1jFz5vNJeY9Vq4pySZKaxcRcktaxZEnt8qVLWxuHJGlkMTGXpCozZvReN3586+KQJI08JuaSVKpU4Hvfq10XAbPWW+ZMkqTBY2IuSaWZMyGzdl2mN35KkprLxFySSvXGkO+6a+vikCSNTCbmklTqbQy5w1gkSa1gYi5JpVmzYOzYF5ZFwCc/6TAWSVLzmZhLUqmrC2bPLoatRBTPP/4xnHpquyOTJI0ErvwpSVW6uuwdlyS1hz3mkiRJUgcwMZekUqUCEybAqFHFc6XS7ogkSSOJQ1kkiSIJnz4dVq0qtpcsKbbBoS2SpNawx1ySKBYX6knKe6xaVZRLktQKJuaSRNFDXku9RYckSRpMJuaSRrxKpZgesZbeFh0aaSJidET8ISIuLLd3i4gFEXF7RMyJiDFl+Sbl9uKyfkLVMU4oy2+LiAPb804kqXOZmEsa8WbOhMz1y13x8wWOB26p2j4ZOCUzdwdWAseU5ccAKzPzFcApZTsiYg/gKGBPYDJwakSMblHskjQkmJhLGvF6G66S6Y2fABExDngP8INyO4D9gHPLJmcCh5Wvp5TblPWTyvZTgLMz85nMvAtYDOzVmncgSUODibmkEa+34Sq77traODrYfwKfB9aW29sAj2Tm6nJ7GbBz+Xpn4B6Asv7Rsv1fy2vs8wIRMT0iFkbEwuXLlw/m+5CkjmZiLmlEq1TgoYfWLx871mEsABFxCPBgZi6qLq7RNPuoq7fPCwszZ2fmxMycuN122/UrXkkaypzHXNKIVanAxz4Gzz23ft20aQ5jKe0LHBoRBwObAi+m6EHfMiI2KnvFxwH3le2XAbsAyyJiI+AlwIqq8h7V+0iSsMdc0gg2c2btpBzgootaG0unyswTMnNcZk6guHnziszsAq4EjiibTQMuKF/PK7cp66/IzCzLjypnbdkN2B24pkVvQ5KGBHvMJY1Y9eYod/7yPn0BODsivg78ATi9LD8d+HFELKboKT8KIDNvioi5wM3AauC4zFzT+rAlqXOZmEsascaP731hIecvX19mXgVcVb6+kxqzqmTm08CRvew/C3DkviT1wqEskkasWbNg443XLx8zxhs/JUmtZ2IuacTq6oL/+R/YZpvny7bZBs44wxs/JUmtZ2IuacSqVIobQFesKOYs/8lPiqkTTcolSe3gGHNJI1KlAtOnw6pVxfaSJcU2mJhLktrDHnNJI9Lxxz+flPdYtaroQZckqR1MzCWNOJUKPPxw7breZmmRJKnZTMwljTj1esVHj25dHJIkVTMxlzTi1Fs8aI1L3kiS2sTEXNKIs/XWvdftumvr4pAkqZqJuSRVcWEhSVK7mJhLGnFWrOi9zqkSJUntYmIuacQZP752ucNYJEnt5AJDkkacWbNeuLgQwNixDmPR87oX1L5DeOrevfyvTpIGQb96zCNiq4h4bbOCkaRW6OqC2bOLHvKI4nn2bIexSJLaq88e84i4Cji0bHs9sDwifpWZn21ybJLUNF1dJuKSpM7SSI/5SzLzMeB9wP9k5puA/ZsbliRJkjSyNJKYbxQROwIfAC5scjyS1HSVCkyYAKNGFc+VSrsjkiSpsZs/vwpcCvw2M6+NiJcBtzc3LElqjv33h8svf357yZLiRlBwaIskqb367DHPzHMy87WZeWy5fWdmvr/5oUnS4Jox44VJeY9Vq2DmzNbHI0lStT4T84h4ZURcHhE3ltuvjYgvNz80SRpcs2f3Xre09ux4kiS1TCNjzP8bOAF4DiAzbwCOamZQktQMa9b0XtfbokOSJLVKI4n52My8Zp2y1c0IRpKaaVSdK56LC0mS2q2RxPyhiHg5kAARcQRwf1OjkqQm2KiX293HjPHGT0lS+zUyK8txwGzg1RFxL3AX8KGmRiVJg2z//eHZZ2vXPfdca2ORJKmWPhPzzLwT2D8iNgdGZebjzQ9LkgbPnnvCzTf3Xu/4cklSJ+gzMY+If15nG4DM/GqTYpKkQTNjRv2kHBxfLknqDI0MZXmy6vWmwCHALc0JR5IGV70pEns4vlyS1AkaGcry79XbEfEtYF7TIpKkQVRvikSAbbZpTRySJPWlkVlZ1jUWeNlgByJJg61SqV8fAd/+dmtikSSpL42s/PmniLihfNwE3Ab0+U9ZROwSEVdGxC0RcVNEHF+Wbx0R8yPi9vJ5q7I8IuI7EbG4PNcbq441rWx/e0RMqyp/Uxnf4nLfGMiHIGl4+vjH69f/+McOY5EkdY5GxpgfUvV6NfBAZjaywNBq4HOZeV1EvAhYFBHzgY8Cl2fmSRHxReCLwBeAg4Ddy8fewGnA3hGxNXAiMJFiLvVFETEvM1eWbaYDVwMXAZOBixuITdIwV6nA00/3Xh9hUi5J6iy99piXPdtbA49XPZ4CXlyW15WZ92fmdeXrxyluGN0ZmAKcWTY7EzisfD0F+FEWrga2jIgdgQOB+Zm5okzG5wOTy7oXZ+bvMzOBH1UdS9IIN3Nm/XqnSJQkdZp6PeaLKHqoaw0PSfoxzjwiJgBvABYAO2Tm/VAk7xGxfdlsZ+Ceqt2WlWX1ypfVKJckli6tX+8UiZKkTtNrYp6Zuw3GCSJiC+CnwGcy87E6w8B7+w9Af8trxTCdYsgL4+0mk0aE8eNhyZLadZMmOYxFktR5GpqVJSK2ioi9IuLtPY8G99uYIimvZOZ5ZfED5TAUyucHy/JlwC5Vu48D7uujfFyN8vVk5uzMnJiZE7fbbrtGQpc0xM2aBWPHrl8+aRJcdlnr45EkqS+NzMryceDXwKXAV8rnf2lgvwBOB27JzP+oqpoH9MysMg24oKr8I+XsLPsAj5ZDXi4FDij/c7AVcABwaVn3eETsU57rI1XHkjTCdXXBtGkwenSxPXo0HHusSbkkqXM10mN+PPBmYElmvotirPjyBvbbF/gwsF9EXF8+DgZOAt4dEbcD7y63oZhV5U5gMfDfwAyAzFwBfA24tnx8tSwDOBb4QbnPHTgji6TSjBlw2mnPLzC0Zg2cfnrfc5tLktQujUyX+HRmPh0RRMQmmXlrRLyqr50y8zfUHgcOMKlG+wSO6+VYZwBn1ChfCPxNX7FIGlkqlSIpX9ezz8Lxxzu+XJLUmRpJzJdFxJbAz4D5EbGSXsZyS1InqLew0MMPty4OSZL6o8/EPDMPL1/+S0RcCbwEuKSpUUnSAPW1sJAkSZ2q18Q8In4BdAM/y8wnATLzV60KTJIG4pOfrF+/zTatiUOSpP6qd/PnbOAQ4O6ImBMRh0XEmBbFJUkD8sQT9eu//e3WxCFJUn/1mphn5gWZeTQwHjiPYmrDpRFxRkS8u1UBSlKjZsyoX+/CQpKkTtbndImZ+VRmzinHmh9AMV2iY8wldZzZs+vXO4e5JKmTNbLA0A4R8Q8R8VuKmVl+Cbyp6ZFJUj/1zFley+abty4OSZIGot7Nn58AjgZeRTGU5fOZ+dtWBSZJ/dHXwkHf/35r4pAkaaDq9Zi/lWJVzl0y8x9MyiV1sg9/uH69Y8sHLiI2jYhrIuKPEXFTRHylLN8tIhZExO3lJAFjyvJNyu3FZf2EqmOdUJbfFhEHtucdSVJnqnfz58cy85eZubaVAUlSf+25J2T2Xj96dOtiGaaeAfbLzNcBrwcmR8Q+wMnAKZm5O7ASOKZsfwywMjNfAZxStiMi9gCOAvYEJgOnRoTfjiSV+hxjLkmdrFKBm2+u32b69NbEMlxloWciyo3LRwL7AeeW5WcCh5Wvp5TblPWTIiLK8rMz85nMvAtYDOzVgrcgSUOCibmkIe2jH+27zamnNj2MYS8iRkfE9cCDwHzgDuCRzFxdNlkG7Fy+3hm4B6CsfxTYprq8xj7V55oeEQsjYuHy5cub8XYkqSPVu/lz63o7ZuaKwQ9Hkvpn9er69ZMmtSaO4S4z1wCvj4gtgfOB19RqVj5HL3W9la97rtkUi9wxceLEOoOUJGl46TUxBxbx/IV0PMX4wQC2BJYCuzU9Okmqo6+ZWMC5ywdbZj4SEVcB+wBbRsRGZa/4OOC+stkyYBdgWURsBLwEWFFV3qN6H0ka8erd/LlbZr4MuBR4b2Zum5nbAIdQTJ8oSW318Y/Xrz/22NbEMdxFxHZlTzkRsRmwP3ALcCVwRNlsGnBB+XpeuU1Zf0VmZll+VDlry27A7sA1rXkXktT56vWY93hzZn6yZyMzL46IrzUxJknqU6UCTz/de/2WWzq2fBDtCJxZzqAyCpibmRdGxM3A2RHxdeAPwOll+9OBH0fEYoqe8qMAMvOmiJgL3AysBo4rh8hIkmgsMX8oIr4M/IRiaMuHgIebGpUk9aGvmz5XrmxJGCNCZt4AvKFG+Z3UmFUlM58GjuzlWLOAWYMdoyQNB43MynI0sB3FzT7nl6+PbmZQklRPpdL3TZ+SJA01ffaYl7OvHB8RW1TNYytJbdPX2HJJkoaiPnvMI+Kt5TjCm8vt10WEIzcltU29seXgTZ+SpKGpkaEspwAHUo4rz8w/Am9vZlCS1Jv99++7jTd9SpKGooZW/szMe9Yp8i56SW1x+eX16+0tlyQNVY3MynJPRLwVyIgYA3yaYv5aSeo49pZLkoaqRnrMPwkcB+xMsWrb68ttSWqpGTPq10+a1Jo4JElqhro95uViEh/OzK4WxSNJvTrttPr1l13WmjgkSWqGuj3m5YpsU1oUiyT1qq/eckmShrpGxpj/NiL+C5gDPNlTmJnXNS0qSVpHX73lDmORJA11jSTmby2fv1pVlsB+gx+OJK2vkSkSHcYiSRrqGln5812tCESSetPXFImSJA0Hjaz8uUNEnB4RF5fbe0TEMc0PTZIa49zlkqThoJHpEn8IXArsVG7/GfhMswKSpP5y7nJJ0nDQSGK+bWbOBdYCZOZqXPlTUovsuWf9+p12ql8vSdJQ0Uhi/mREbENxwycRsQ/waFOjkqTSzTfXr7/33tbEIUlSszUyK8tngXnAyyPit8B2wBFNjUqSgEql3RFIktQ6jczKcl1EvAN4FRDAbZn5XNMjkzTizZxZv36bbVoThyRJrdBrYh4R7+ul6pURQWae16SYJAmAJUvq13/7262JQ5KkVqjXY/7e8nl7ikWGrii33wVcBZiYS2qaGTP6btPhYDuZAAAgAElEQVTV1fw4JElqlV4T88z8GEBEXAjskZn3l9s7At9tTXiSRqrvf79+/aRJrYlDkqRWaWRWlgk9SXnpAeCVTYpHkgBYu7Z+/WWXtSYOSZJapZFZWa6KiEuBsyimTDwKuLKpUUka0ZyNRZI0EjUyK8unIuJw4O1l0ezMPL+5YUkayT760fr1DmORJA1HdRPziBgNXJqZ+wMm45JaYvXq+vUOY5EkDUd1x5hn5hpgVUS8pEXxSBrh9t+/3RFIktQejYwxfxr4U0TMB57sKczMTzctKkkj1uWX16/fY4/WxCFJUqs1kpj/onxIUtvddFO7I5AkqTkaScznAK+gmJHljsx8urkhSRqp9tyz3RFIktQ+vY4xj4iNIuIbwDLgTOAnwD0R8Y2I2LhVAUoaOW6+uX79T37SmjgkSWqHejd/fhPYGtgtM9+UmW8AXg5sCXyrFcFJGjlmzOi7TVdX8+OQJKld6iXmhwCfyMzHewoy8zHgWODgZgcmaWQ57bR2RyBJUnvVS8wzM7NG4RqK8eaSNCgaWenz2GObH4ckSe1ULzG/OSI+sm5hRHwIuLV5IUkaaT7+8b7bnHpq8+OQJKmd6s3KchxwXkT8H2ARRS/5m4HNgMNbEJukEeLpPuZ6mjSpNXFIktROvSbmmXkvsHdE7AfsCQRwcWb2sfyHJDWukZs+L7us+XFIktRufc5jnplXAFe0IBZJI9D3vle/fqedWhOHJEntVm+MuSQ13fq3mL/Qvfe2Jg5JktrNxFxS22y1VbsjkCSpc5iYS2qbRx6pX+8wFknSSGJiLqktxozpu43DWCRJI4mJuaS2eO65dkcgSVJnaVpiHhFnRMSDEXFjVdnWETE/Im4vn7cqyyMivhMRiyPihoh4Y9U+08r2t0fEtKryN0XEn8p9vhMR0az3ImlwNfLb6tzlkqSRppk95j8EJq9T9kXg8szcHbi83AY4CNi9fEwHToMikQdOBPYG9gJO7EnmyzbTq/Zb91ySOlCj/4V27nJJ0kjTtMQ8M38NrFineApwZvn6TOCwqvIfZeFqYMuI2BE4EJifmSsycyUwH5hc1r04M3+fmQn8qOpYkjpUo7Ow9DWFoiRJw1Grx5jvkJn3A5TP25flOwP3VLVbVpbVK19Wo7ymiJgeEQsjYuHy5cs3+E1IGpi+ZmEZ9h59FM44A/7t39odScMiYpeIuDIibomImyLi+LJ80IYmSpIKfa782SK1/ridAyivKTNnA7MBJk6caF+c1AaNDmEZdmPLn34aLroIKhX4xS/gmWfgta+FL3wBRg2J++9XA5/LzOsi4kXAooiYD3yUYmjiSRHxRYqhiV/ghUMT96YYdrh31dDEiRTX60URMa/8a+iQ0b1g6XplU/ce34ZIJA1Hrf5X4YFyGArl84Nl+TJgl6p244D7+igfV6NcUgcaPbqxdhtvPEzGlq9ZA5dfDsccAy99Kbz//fCb38Df/z0sWADXXz9UknIy8/7MvK58/ThwC8VfKAdlaGIL34okdbxW/8swD+j58+U04IKq8o+UfwLdB3i0HOpyKXBARGxV/pn0AODSsu7xiNinnI3lI1XHktRh1q5trN2zzzY3jqbKhEWL4HOfg/HjYf/94Zxz4LDD4NJLi0nZv/1t2Guvxv980GEiYgLwBmABgzc0UZJUatpQlog4C3gnsG1ELKP4E+ZJwNyIOAZYChxZNr8IOBhYDKwCPgaQmSsi4mvAtWW7r2Zmzw2lx1LM/LIZcHH5kNRhGs1Bh+wNn4sXQ3d38bjttqLb/+CDoasLDjkENtus3REOiojYAvgp8JnMfKzODLUbPAQxIqZTzLrF+PEOE5E0cjQtMc/Mo3upWm8EaTmzynG9HOcM4Iwa5QuBv9mQGCU1184N9of+5CfNjWPQPfAAzJlTjBu/5prifx/veEfRW37EEY1PPzNERMTGFEl5JTPPK4sfiIgdM/P+fgxNfOc65VfVOp/3BUkaqYbGIEdJQ9J9Dd750dXV3DgGxWOPwY9+BAceCDvtBMcfX4y9+cY3YMkSuPJK+MQnhmNSHsDpwC2Z+R9VVYMyNLElb0KShohOmZVF0jAzZkxj7Tp6CMuzz8LFFxfDVObNK2ZY2W03OOEEmDoV9tij3RG2wr7Ah4E/RcT1ZdmXGNyhiZIkTMwlNclzz/Xd5thjmx9Hv61dC//7v8UwlXPPhZUrYdttixlWurpgn32G7M2bA5GZv6H2+HAYpKGJkqSCibmkQddo3nrqqc2No2GZ8Mc/Fj3jZ50Fy5bB5pvD4YcXPeP771/c1ClJUhOZmEsaVI0Ose6IISx33VUk4pUK3HwzbLQRTJ5cjBs/9NAiOZckqUVMzCUNqkce6btNW9fWWb4c5s4tesd/97ui7G1vg9NOK2ZU2XbbNgYnSRrJTMwlDZpGh7CsWdPcONbzxBNwwQVFz/gvf1kE8Dd/A//2b3D00bDrri0OSJKk9ZmYSxoUjSblLZvI5LnnihU3u7uLpHzVqmJFzn/8x+Imzr/92xYFIklSY0zMJbXUTTc18eBr1xbDUyoVOOccePhh2Hpr+MhHips49923zeNoJEnqnYm5pA3WaG950274vPHGIhk/66xisZ/NNoMpU4qe8QMOaHxSdUmS2sjEXNIGaTQpH/TZBpcufX5GlT/9CUaPhne/G77+9SIpf9GLBvmEkiQ1l4m5pAHrzzo7zz47CCd8+OFiiEp3d7EIEMBb3gL/7//BBz4A228/CCeRJKk9TMwlDUh/Rods0BCWVatg3ryiZ/ySS2D1anjNa4qe8aOPhpe9bAMOLklS5zAxl9Rve+5ZTHrSiAEl5atXw/z5Rc/4+efDk0/CzjvDZz5TjBt/3ev6110vSdIQYGIuqV96FskcdJlw9dVFMj5nTrEQ0JZbFr3iXV3wd39XjCOXJGmYMjGX1C8f+lDjbRvqLb/lliLb7+6Gu+6CTTeF9763mN7woINgk00GHKskSUOJibmkhoweXUwT3qi6SfmyZXD22UVCfv31xdzikybBiSfC4YfDi1+8wfFKkjTUmJhL6lN/h3PXTMpXroSf/rRIxn/1q6LRXnvBf/4nfPCD8NKXDkqskiQNVSbmkuraoKT8qafgwguLYSoXXVTMmbj77kXP+NSpxWtJkgSYmEuqY0BJ+erVcOWVRc/4eefB44/DjjvCcccVyfib3uSMKpIk1WBiLqmm/uXOybu2WAifqRRjxx94oBgnfsQRxYwq73ynM6pIktQHE3NJ62k0Kd+dPzOVbqbSzSufuB1OGwOHHFL0jL/nPcUMK5IkqSEm5pL+qlLpezrEl3I/R3E2U+nmzSxkLcGo/d4FU78A739/Mfe4JEnqNxNzSUD9XvIX8yjv4zy6qPAurmQ0a1nEG+Hf/51RH/xgsSqnJEnaICbmkmom5ZvwNAdzEVPp5hAuZFOeYTEvZxYz6WYqt+arWx+oJEnDmIm5NMJVJ+WjWMM7+BVT6eYIzmVLHuUBtuf7/D3dTOUa9gKisRU9JUlSv5iYSyPUjBlw2mkAyRv4A11UOIqz2Zn7eJwtOI/3UaGLK9iPNVWXCpNyDQXdC5a2OwRJ6jcTc2kEioCXcQdfppsuKrya23iWjbmYg/i/dHEhh/AUY9fbz6RckqTmMTGXRpIHHuDTL53D7+lmHxYAcBXv4D/4LOdyBCvZutddTcolSWouE3NpuHv8cTj/fC6dVmF/LuM7rOV6XsfnOZmzOJpl7FJ3dxNySZJaw8RcGo6efRYuuQQqFZ6aO4/NeJpXMoGT+CLdTOVm9mzoMCblkiS1jom5NFysXQv/+7/Q3Q3nnAMrV7KcbZnL/6FCF7/nLUCDS3piUi5JUquZmEtDWSbccEOxZOdZZ8GyZTzJWH7GYVToYj7vZjUbD+iwkiSptUzMpaHorruKRLxSgZtvho024sLVB9LNyVzAFFax+YAOa0IuSVL7mJhLQ8Xy5cUQlUoFfve7omzffTmWUzln9ZE8zLYbdHiTckmS2svEXOpkTzwBF1xQjBv/5S9h9WrYc0/4139lwpeOZslvJwzKaUzKJUlqPxNzqdM891yRhFcqRVK+ahXssgt87nO89uSp/Omm18KXBudUJuSSJHUOE3OpE6xdC7//fZGMz50LDz8MW28NH/4wTJ3KqHe8jTx51KCdzoRckqTOY2IutdONNxbDVLq7YckS2GwzOPRQ6OpizKEH8tz3x8D3B+90JuSSJHUuE3Op1ZYuLWZU6e4upjocPRre/W742td40UcO44k5L4I5g3tKE3JJkjqfibnUCitWFDOqdHfDr39dlO2zD3znO+zw6Q/w4CU7wCWDf1oTckmShg4Tc6lZVq2Cn/+8GDd+ySXFTZ2vfjVf5mucxdHcefXL4ermnNqEXJKkocfEXBpMq1fDZZcVPePnn19Md7jTTnzruU9ToYvrb309EE07vQm5JElDl4m5tKEyYcGComd8zhxYvpyVbMm5HEU3U/n1fW9nLaObenpJkjT0mZhLA3XLLc/PqHLnnTzNJvyc91Khi4s5iGfZpKmnNyGXJGl4MTGX+uPee+Gss7jun7p5I39gDaO4gv2o8P9xPofzGC9p6ulNxiVJGr5MzKU+bBUreT8/ZSrdvJOrGEWymjfzGU5hDh/kL+zY1PObjEuSNDKYmEtVorwvc1Oe4j38gi4q/IWL2IRn+TO78xVO5CyO5nZe2dQ4TMaloaN7wdKa5VP3Ht/iSCQNdSbmGpGixsQoo1jD/lzBVLp5H+fxEh7jfl7KqcygQheLeBPNmlHFRFySJI1qdwBSM0XUfjwvmci1nMJnWMY45nMA7+ennMf72J/5jGMZn+UUFjGRwU7KM59/SJ0sIs6IiAcj4saqsq0jYn5E3F4+b1WWR0R8JyIWR8QNEfHGqn2mle1vj4hp7XgvktTJ7DHXsFCrB7yeV3A7XVSYSjev5HaeYQy/4D10M5Vf8B6eZrNBj9EEXEPYD4H/An5UVfZF4PLMPCkivlhufwE4CNi9fOwNnAbsHRFbAycCE4EEFkXEvMxc2bJ3IUkdzsRcQ0p/E/BqL+V+PsgcuqjwZhayluAq3snJfIHzeB+PsNXgBYqJuIaPzPx1RExYp3gK8M7y9ZnAVRSJ+RTgR5mZwNURsWVE7Fi2nZ+ZKwAiYj4wGTiryeFL0pBhYq6OtCEJeLUX8yjv4zym0s1+XMFo1nIdb+BzfIs5fJB7GTc4J8JEXCPODpl5P0Bm3h8R25flOwP3VLVbVpb1Vi5JKpmYq60GKwGvNoZnOJiL6KLCIVzIpjzDHbyMf+VLdDOVW3nNBp/DJFzqVa3f6qxTvv4BIqYD0wHGj3dmE0kjh4m5WqIZCXi1Uazh7fyaLiocwblsyaM8yHbMZjrdTGUBezPQmzdNwqWaHoiIHcve8h2BB8vyZcAuVe3GAfeV5e9cp/yqWgfOzNnAbICJEyf6GyhpxDAx16BqdgL+Qskb+ANT6eZozmJn7uNxtuB8DqebqVzG/qzpx4+4CbjUL/OAacBJ5fMFVeWfioizKW7+fLRM3i8F/rVn9hbgAOCEFscsSR3NxFz91trke30v4w6m0s1UunkNt/IcG3ExB/FZ/oOf816eYmzd/U3Apf6JiLMoeru3jYhlFLOrnATMjYhjgKXAkWXzi4CDgcXAKuBjAJm5IiK+Blxbtvtqz42gkqSCibnW0+7Eu5bteJAPMoepdPMWrgbgV7yd/+QznMsRrGCb9fYxAZcGR2Ye3UvVpBptEziul+OcAZwxiKFJ0rAy5BPziJgMfBsYDfwgM09qc0gdYexYeOqpdkexYbbgcQ7jZ3RRYX8uYyPW8Edey+c5mbM5insobgozAZckScPBkF75MyJGA9+lWNBiD+DoiNhjsI5fqcCECTBqVPFcqdSvnzHj+e1tty0eEbDRRsXzqFG9r0Q52I+hmpRvzLO8l3mcxVE8wA78mI/wam7lG3we/vQnXpd/5Bv5eZbmeFfNlCRJw8pQ7zHfC1icmXcClDcbTQFu3tADVyowfTqsWlVsL1lSbAN0ddWuP+205/d/+OHnX69ZUzybRNYWrOVt/IYuKhzJOWzNSthmG/jAR6GriwlveQtfGjWk/w8pSZLUp6GemNdasGLvwTjwzJnPJ909Vq0qyru6aterP5L845+K/+GcdRbcc08x/uaww2DqVDjgANh443YHKUmS1DJDPTFvaMGKgSxWsXRp/fLe6rW+F/yl4O67i0S8UoHX3QSjR8OBB8JJJ8Ghh8IWW7QrTEmSpLYa6ol5bwtZvMBAFqsYP74YnlKrvF79SFV3mM5DD8HcudDdDb/9bVH21rfCd78LRx4J223XkhglSZI62VAfuHstsHtE7BYRY4CjKBa32GCzZhUjK6qNHVuU91Y/XE2axF9vtOztsZ4nnywS8fe8B3bcEY47DlauLD64O+8sEvQZM0zKJUmSSkO6xzwzV0fEp4BLKaZLPCMzbxqMY3d1Fc8zZxbDVsaPL3LKnvJa9QcfDBddVGxvvXVR//DDxWiNNWuK2VLacQPoZpu1aDz8c8/B/PnFMJWf/aw46bhx8NnPFuPGX/vazpwkXZIkqQMM6cQcIDMvolhpbtB1dT2fgA+kfkTIhN/9rugdnzu3GLay1VbwoQ8VH87b3lbMEylJkqS6hnxirja56abnZ1S5+27YdNPi5s2uLpg8GcaMaXeEkiRJQ4qJuRq3dCmcfXaRkN9wQ9ET/u53w1e+AocfDi96UbsjlCRJGrJMzFXfihVwzjnFUJVf/7oo23tv+M534AMfgB12aG98kiRJw4SJuda3ahX8/OdFz/gllxQ3db7qVfDVrxY3cb785e2OUJIkadgxMVdh9Wq4/PIiGT//fHjiCdhpJ/j0p4tk/A1vcEYVSZKkJjIxH8kyYcGCYpjKnDnw4IPwkpfABz9YJOPveEcx16MkSZKazsR8JLr11qJnvLu7WOxnk03gkEOKGVUOOqiYYUWSJEktZWI+Utx7bzGjSnc3XHddMSxlv/3gy1+G972v6CmXJElS25iYD2ePPAI//WnRO37VVcXQlYkT4T/+A446Cnbcsd0RStKw1b1g6XplU/ce34ZIJA0VJubDzdNPw4UXFj3jv/gFPPssvOIV8M//DEcfXcyuIkmSpI5jYj4crFkDV15ZJOM//Sk89lgxv/ixxxY3cb75zc6oIkmS1OFMzIeqTFi0qBimcvbZ8Je/FCtvvu99xU2c73oXbOTXK0mSNFSYuQ01t99e9Ix3d8Of/wxjxsDBBxc944ccAptt1u4IJUmSNAAm5kPBX/7y/Iwq115bDEt5xzvgn/4J3v9+2GqrdkcoSZKkDWRi3qkeewzOO68YqnLFFbB2Lbz+9fDNbxYzqowb1+4IJUmSNIhMzDvJM8/AxRcXyfjPf15s77YbnHBCMVRljz3aHaEkSZKaxMS83dauhV/9qhimcu65xdzj220Hn/hEkYzvs48zqkiSJI0AJubtkAnXX//8jCr33gubbw6HH17MqDJpEmy8cbujlCRJUguZmLfSHXfAWWcVCfmttxbTGU6eDN/6Fhx6KIwd2+4IJUmS1CYm5s324IMwd26RjF99dVH2d38Hxx8PRx4J22zT3vgkSS3TvWBpzfKpe49vcSSSOpGJeTM8/jj87GfFuPH584uVOf/2b+Gkk4oZVXbdtd0RSpIkqcOYmA+WZ5+FSy8tesbnzYOnnoLx44u5xqdOLRJzSZIkqRcm5hti7Vr4zW+KnvFzzoEVK4qhKR/9aJGMv/WtMGpUu6OUJEnSEGBiPhA33FD0jJ91FtxzD2y2GRx2WJGMH3AAjBnT7gglSZI0xJiYN2rJkqJnvLsbbrwRRo8ukvB/+zeYMgW22KLdEUqSJGkIMzHvy69/DV/6Evz2t8X2W98K//Vf8IEPFAsBSZIkSYPAxLwvo0bBypUwaxYcfTTstlu7I5IkDTO1plF0CkVp5DEx78u++xZDVyLaHYkkSZKGMRPzvpiQS5IkqQWcy0+SJEnqACbmkiRJUgcwMZckSZI6gGPMJUnqQLVmagFna5GGM3vMJUmSpA5gj7kkSUOIPenS8GWPuSRJktQB7DGXJGkY6K0nvRZ716XOZI+5JKllImJyRNwWEYsj4ovtjkeSOok95pKkloiI0cB3gXcDy4BrI2JeZt7c3shGnlq96/aiS+1nYi5JapW9gMWZeSdARJwNTAFMzDuAQ2Gk9jMxlyS1ys7APVXby4C92xSLNkB/kvhO4H8kNFSMuMR80aJFD0XEkn7uti3wUDPiGYBOiaVT4gBjqaVT4gBj6c1AYtm1GYG0UNQoy/UaRUwHppebT0TEbQM411D/rptlRMbS1XeTTvpcoLPiMZbaGoml39fsEZeYZ+Z2/d0nIhZm5sRmxNNfnRJLp8QBxtLJcYCx9KaTYmmhZcAuVdvjgPvWbZSZs4HZG3KiTvp8jaU2Y+ldJ8VjLLU1KxZnZZEktcq1wO4RsVtEjAGOAua1OSZJ6hgjrsdcktQembk6Ij4FXAqMBs7IzJvaHJYkdQwT88Zs0J9UB1mnxNIpcYCx1NIpcYCx9KaTYmmZzLwIuKgFp+qkz9dYajOW3nVSPMZSW1Niicz17ruRJEmS1GKOMZckSZI6gIl5P0XEP0ZERsS2bTr/1yLihoi4PiJ+GRE7tSOOMpZvRsStZTznR8SWbYzlyIi4KSLWRkTL79julGXGI+KMiHgwIm5sVwxVsewSEVdGxC3ld3N8m+LYNCKuiYg/lnF8pR1xrBPT6Ij4Q0Rc2O5YhptW/S5GxN0R8afyWrywLNs6IuZHxO3l81ZleUTEd8qYboiIN1YdZ1rZ/vaImNbgudf7PR/Mc0fEm8r3trjct9Y0l33F8y8RcW/5+VwfEQdX1Z1QHvu2iDiwqrzmd1feLLygjHNOeeNwrThqXnPa9dnUiacdn03N62Bv+0fEJuX24rJ+wkBj7EcsP4yIu6o+l9e34nsq27/gmtyOz+WvMtNHgw+Kab4uBZYA27YphhdXvf408L02fh4HABuVr08GTm5jLK8BXgVcBUxs8blHA3cALwPGAH8E9mjT5/B24I3Aje36Lqpi2RF4Y/n6RcCf2/G5UMydvUX5emNgAbBPmz+bzwLdwIXt/p6G06OVv4vA3ev+OwB8A/hi+fqLPddE4GDg4vJncR9gQVm+NXBn+bxV+XqrBs693u/5YJ4buAZ4S7nPxcBBA4jnX4B/rNF2j/J72QTYrfy+Rtf77oC5wFHl6+8Bx/YSR81rTrs+mzrxtOOzqXkd7G1/YAZlfkExe9KcgcbYj1h+CBxRo30rfoZfcE1ux+fS87DHvH9OAT5PjQUxWiUzH6va3LzNsfwyM1eXm1dTzEncrlhuycyBLEIyGP66zHhmPgv0LDPecpn5a2BFO869rsy8PzOvK18/DtxCsfJjq+PIzHyi3Ny4fLTt9yYixgHvAX7QrhiGsXb/Lk4BzixfnwkcVlX+o/Jn8Wpgy4jYETgQmJ+ZKzJzJTAfmNzXSXr5PR+Uc5d1L87M32eRcfyo6lj9iac3U4CzM/OZzLwLWEzxvdX87sqezv2Ac2u8t/+/vXMPvqqq4vjnK6BSmKSiQ6SSjI0Kwk/FJ2Y/U/MRA0NqNGENatOYisrETDoUPcwGNdMxLEtHKUUHEW18TIqvn1qWIMhLy1JxJg0hNbQyHYXVH3tdOL/LPffx8/7uucL6zJy5++57zlnfs849+6679t7nlOvIa3MK8U0P2sDe9E1eO5i3fdZntwPHuL2GNDaopZpfeu08lbfJNfzaa34pEYF5nUgaB7xiZsvaQMslkv5OepjZjKL1OGeQ/pVujVR6zHjLA9B2xrv7DiBlRoqw30fSUmAtqSEvRIdzFekP/oYCNWyptPJaNGCBpMVKTyoF2M3MVkMKyoBda+hqpt5m2R7i5WZoOteHHtwgHz7SAz07A+sySaC69JS1OYX7pkIb2HLflLeDpExu3vYbbfrnb7q9pnyXq7TJl7hfrpS0XbmWOm02ep7K2+Rqfu1Vv0AE5t2Q9KCklRWW8cB0WhQE19CBmU03s92BOcC5RWrxdaYD77ueQrUURF2PGd9akTQAmA9cUNbj0zLMbL2ZdZB6dQ6RNKIIHZLGAmvNbHER9rcCWnktjjGzA4ETgXMkHVVl3TxdrdDbqO1mafoFMAzoAFYDV7RKTwNtTkt8U0FPIb4pbwdJQ0Dztm+pFm+TLwL2AQ4mDU/5dm9ryWmTq23f69+ZuI95BjM7tlK9pP1JY4aW+fyBTwJLJB1iZq+2SkcFbgHuBb7XbA31avHJFmOBY7zLqNdowC+tpq7HjG+NSOpH+kGaY2Z3FK3HzNZJ6iINFyhiguwYYJzSZK/tgY9JutnMTitAy5ZIy65FM/uHv66VdCcp0FkjabCZrfbu9LU1dL0MdJbVd/VQUrNsv0z3YYk98qGZrSmVJV0HlCY6VztHlepfIw1d6OsZyqp6ctqcwnxTSU9RvimRaQcPq7J9ScvLkvoCO5KGKzWqsV4tJ5jZT7z6XUk3AtPKtJTvuxnnabM2mZRBL84v1guTYrb0hQqTflpoe+9MeQpwe4F+OAF4FhhU9DnJaOqi9ZM/+5ImnXyKTZM7hhfog6G0x+RPkcb2XVWwjkHAQC/3Bx4HxraBfzqJyZ/N9mlLrkXS/J4dMuUnvD28nO6TDC/z8hfoPnltodfvBKwiTVz7uJd3qlNDt+u8mbaBRb5uaeLcST3QMzhTnkoafwswnO6T5F4kTZDLPXfAPLpPxDs7R0PFNqco31TRU4RvKraDedsD59B9kuNtPdXYgJbBGb9dBcxs8Xe4k02TP1vul406mt1gbQ0LxQbm80mZvuXA3cCQAv3wPGns1FJfirxDzATSP9Z3gTXA/S22fxJpxv0LwPQC/XArqWv0PffHmQVqOZLUZbc88x2p2Tj2go6RwNOuYyUwoyiflOna+CMQS1P92uvXIukOC8t8eTLpwOUAAAbMSURBVKZkhzTW9CHgb/5aChIEXOOaVpBJHpDm5zzvy+l12t/sOm+mbWC0XysvALPwhxE2qOcmt7ccuIvuweh03/dzZO6WkXfu3N8LXec8YLscHRXbnKJ8U0VPEb6p2A7mbU/KHs/z+oXAXj3V2ICWh90vK4Gb2XTnll7/Dvs2nWwKzFvul9IST/4MgiAIgiAIgjYgJn8GQRAEQRAEQRsQgXkQBEEQBEEQtAERmAdBEARBEARBGxCBeRAEQRAEQRC0ARGYB0EQBEEQBEEbEIF5UBiSdpa01JdXJb3i5XWSnm2xlg5/wEDp/ThJF/ZwXy9J2qV56hqyPVnSJzLvr5e0X9G6giAIgiCoTQTmQWGY2etm1mHpsbzXAld6uQPY0Gx7/pSuPDpI9xotabvLzGY2W0MLmAxsDMzN7Otm1tI/OUEQBD1B0kBJZ9dYZ6ikr9Sxr6GSini6bxB8ICIwD9qVPpKuk/SMpAWS+gNIGibpPkmLJT0uaR+v31PSQ5KW++seXj9b0k8lPQJcKumjkm6QtEjS05LGS9oW+CEw0TP2Ez3zPMv3sZukOyUt8+UIr/+t63hG0jdqHZCk0yX9VdKjfmyl/c+WdEpmvf/46wA/liWSVkga7/VDJf253D++j9HAHD+O/pK6JI2uoOU0SQt9vV9K6uPLbEkr3d7UD3D+giAIGmUgUDUwJz1htGZg3gg1kjZB0FIiMA/alb2Ba8xsOLAOONnrfwVMMbODgGnAz71+FvAbMxsJzAGuzuzr08CxZvYt0pO5Hjazg4GjSY9q7gfMAOZ6Bn9umZargUfNbBRwIOlJfwBnuI7RwHmSds47GEmDgR8AY4DjgP3q8ME7wAQzO9C1XiFJef4xs9uBp4BJfhz/y9GyLzARGOM9FOuBSaRegyFmNsLM9gdurENjEARBs5gJDPOEweW+lBIFEzPrfMbXmeqJisc9gbGklDiphSdf5km6G1igxGb2qtR3epLlNk+4zJQ0yRMeKyQN8/VO9W2XSXqs+S4LtjTiX2LQrqwys6VeXgwMlTQAOAKYtyk+ZTt/PRz4opdvAi7L7Guema338ueBcZKm+fvtgT1qaPkc8DUA38+bXn+epAle3p0ULL+es49DgS4z+yeApLmkPwzVEPBjSUeRhvYMAXbzzzbzT419ZTkGOAhY5H7sD6wF7gb2kvQz4F5gQQP7DIIg+KBcCIwwsw5JJwNnAaOAXUjt1WO+zjQzGwsg6SPAcWb2jqS9gVtJyZJ6OBwYaWZvuL2OCvaOyKnH6/YF3gBeBK43s0MknQ9MAS4gJX2ON7NXJA3suWuCrYUIzIN25d1MeT0peNwGWOdZ3lpYpvzfTFmk7PJz2ZUlHdqIOEmdwLHA4Wb2tqQuUpBfr6Ys7+O9V54R39brJwGDgIPM7D1JL2VsVPJP3fKBX5vZRZt9II0CjgfOAb4EnNHAfoMgCJrFkcCtngxZI+lR4GDgrbL1+gGzJJV6/2olPLI8YGZv1LBXTcciM1sNIOkFNiUzVpB6OQH+AMyWdBtwRwPagq2UGMoSfGgws7eAVZJOhY1djKP84yeAL3t5EvD7nN3cD0wpDQmRdIDX/xvYIWebh4Bv+vp9JH0M2BH4lwfl+wCH1ZD/JNCpdCeafsCpmc9eImWwAcaTfmhwG2s9KD8a2LOGjVrHkT2eUyTt6se0k9IY/V2AbcxsPvBd0rCdIAiCIlDtVQCYCqwhZa9HsymxUQ/lSZtGdWQTJBsy7zfgiU8zOwv4DqlXdWm1IY9BABGYBx8+JgFnSlpGGus93uvPA06XtBz4KnB+zvYXkwLf5Uoz9i/2+keA/Xzc4sSybc4Hjpa0gjRsZDhwH9DX7V0M/KmaaM+qfB/4I/AgsCTz8XXAZyUtJA15Kf1YzAFGS3rKj/sv1Ww4s4FrS5M/c7Q8S/qhWOD6HwAGk4bKdEla6vvZLKMeBEHQi2QTC4+RJuT3kTQIOApYyObJhx2B1Wa2gdT29+mh7Tx7efV1IWmYmT1pZjOA10gBehDkIrO83vUgCHoLSZOB0WZ2btFagiAI2gVJtwAjgd951YmkYYA/MrO53uN4H2m892zgHmA+8DYpwTLFzAZIGgrcY2YjcuxMJtMGey/qZRXs5dV30n2se5e/fyr7maQ7SPOPROqtvMAi8AqqEIF5EBRABOZBEARBEJQTgXkQBEEQBEEQtAFxV5YgCIIgCLZIJB0PXFpWvcrMJlRaPwiKJjLmQRAEQRAEQdAGxF1ZgiAIgiAIgqANiMA8CIIgCIIgCNqACMyDIAiCIAiCoA2IwDwIgiAIgiAI2oAIzIMgCIIgCIKgDfg/3fJeC2+HP64AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1705bdd8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (Housing dataset) 긴꼬리 분포와 그것의 QQ 그림을 비교\n",
    "plt.subplot(121)\n",
    "stats.probplot(housing_data.total_rooms, plot=sns.mpl.pyplot)\n",
    "plt.title('Total room number in California')\n",
    "\n",
    "plt.subplot(122)\n",
    "sns.distplot(housing_data.total_rooms, kde=False)\n",
    "plt.title('Total room number in California')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "예제에서 왼쪽 그래프를 보면, 높은 값은 직선보다 훨씬 위에 위치하기 때문에, 이것은 데이터가 정규분포를 따른다고 할 때 예상되는 것보다 훨씬 더 많은 극단값을 관찰할 가능성이 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. 스튜던트의 $t$분포"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "- $n$ : 표본 크기\n",
    "- Degrees of freedom(자유도) : 다른 표본크기, 통계량, 그룹의 수에 따라 $t$분포를 조절하는 변수\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $t$분포는 정규분포와 생김새가 비슷하지만, 꼬리 부분이 약간 더 두껍고 길기 때문에, 표본통계량의 분포를 설명하는 데 광범위하게 사용된다.\n",
    "- <U>표본평균의 분포는 일반적으로 $t$분포와 같은 형태이며 표본이 클수록 더욱 정규분포를 닮은 $t$분포가 형성된다.</U>\n",
    "- 표준화된 여러 통계 자료를 $t$분포와 비교하여 신뢰구간을 추정할 수 있다.\n",
    "- 표본평균이 $x$인, 크기 $n$의 표본이 있다고 가정할 때, $s$가 표본 표준편차라면, 표본평균 주위의 90% 신뢰구간은 [$\\bar{x}-t_{n-1}(.05)\\times \\frac{s}{\\sqrt{n}}$, $\\bar{x}+t_{n-1}(.05)\\times \\frac{s}{\\sqrt{n}}$]\n",
    "- 사실, 지금과 같은 성능의 컴퓨터가 1908년($t$분포 논문이 나왔던 시기)부터 널리 보급됐다면, 처음부터 통계학은 계산을 많이 필요로 하는 resampling 방법을 더 많이 이용했을 것이다. 컴퓨터가 없었던 시절, 통계학자들은 표본분포를 근사화하기 위한 수학적 기법과 $t$분포와 같은 함수로 눈을 돌렸다.\n",
    "- 표본평균, 두 표본평균 간의 차이, 회귀 파라미터, 그 외 다른 통계량들의 분포를 구할 때 $t$ 분포를 사용한다.\n",
    "- 표본통계량의 상태를 묘사할 때 $t$ 분포의 정확도는 표본에 대한 통계량의 분포가 정규분포를 따른다는 조건을 필요로 한다. 모집단이 정규분포를 따르지 않을 때조차도, 표본통계량은 보통 정규분포를 따르는 것으로 나타났다. ($t$ 분포가 널리 적용되는 이유이며 이런 현상을 *중심극한정리*라고 부른다.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "데이터 과학자가 $t$분포와 중심극한정리에 대해 알아야 할 것은 무엇일까? 사실, 별로 없다. 이러한 분포는 고전적인 통계적 추론에 사용되기는 하지만, 데이터 과학이 주로 추구하는 목적과는 조금 거리가 있다. 데이터 과학자에게는 불확실성과 변동성을 이해하고 정량화하는 것이 중요하다. 이러한 목적을 위해서라면, 경험적 부트스트랩 표본추출을 통해서도 표본 오차에 대한 대부분의 질문에 답을 얻을 수 있다. 하지만 데이터 과학자들은 회귀분석 같은 통계 절차를 통해 나온 $t$통계량을 자주 만나게 되니 알아두면 도움이 된다.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. 이항분포\n",
    "---\n",
    "- Trial(시행) : 독립된 결과를 가져오는 하나의 사건(동전 던지기)\n",
    "- Success(성공) : 시행에 대한 관심의 결과(1, 즉 0의 반대)\n",
    "- Binomial(이항식) : 2가지 결과를 갖는다.(이진, Y/N, 0/1)\n",
    "- Binomial trial(이항시행) : 2가지 결과를 가져오는 시행(베르루이 시행)\n",
    "- Binomial distribution(이항분포) : 각 시행마다 성공확률 $p$가 정해져 있을 때, $x$번 시행에서 성공한 횟수에 대한 분포\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이항분포란 각 시행마다 그 성공 확률($p$)가 정해져 있을 때, 주어진 시행 횟수($n$) 중에서 성공한 횟수($x$)의 도수분포를 의미한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "한 번의 클릭이 판매로 이어질 확률이 0.1일 때, 5회 클릭으로 2번 판매될 확률을 구해보자."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0729"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.pmf(2, 5, 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "한 번의 클릭이 판매로 이어질 확률이 0.1일 때, 5회 클릭으로 2번 이하로 판매될 확률을 구해보자."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99144"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.cdf(2, 5, 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 시행 횟수가 충분할 경우(특히 p가 0.5에 가까울 때) 이항분포는 사실상 정규분포와 구별이 어렵다.\n",
    "- 실제로 표본크기가 커질수록 이항 확률을 구하기 위해선 많은 계산이 필요하다 보니, 대부분의 통계 절차에서는 평균과 분산으로 근사화한 정규분포를 사용한다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. 포아송 분포와 그 외 관련 분포들"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "- Lambda : 단위 시간이나 단위 면적당 사건이 발생하는 비율(평균적인 사건의 수)\n",
    "- Poisson distribution : 단위 시간 혹은 단위 공간에서 발생한 사건의 도수분포\n",
    "- Exponential distribution : 한 사건에서 그 다음 사건까지의 시간이나 거리에 대한 도수분포\n",
    "- Weibull distribution : 사건 발생률이 시간에 따라 변화하는, 지수분포의 일반화된 버전\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.1. 포아송 분포"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 포아송 분포는 시간 단위 또는 공간 단위로 표본들을 수집할 때, 그 사건들의 분포를 알려준다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 포아송 분포를 사용할 수 있는 다양한 예\n",
    "    - 일정한 시간동안 웹사이트에 방문한 방문객 수\n",
    "    - 일정한 시간동안 톨게이트에 들어오는 자동차\n",
    "    - 1제곱미터당 건물의 결함\n",
    "    - 코드 100줄당 오타"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 포아송 분포의 핵심 파라미터 $\\lambda$ : 일정 시간 / 공간 구간 안에서 발생한 평균 사건 수. 포아송 분포의 분산 역시 $\\lambda$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.2. 지수분포"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 포아송 분포에 사용된 것과 동일한 변수 $\\lambda$를 사용하여 사건과 사건 간의 시간 분포를 모델링"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 지수분포를 사용할 수 있는 다양한 예\n",
    "    - 웹사이트 방문이 일어나는 시간 사이\n",
    "    - 톨게이트에 자동차가 도착하는 시간 사이\n",
    "    - 기계에서 고장이 발생하는 시간\n",
    "    - 프로세스 관리에서 개별 고객 상담에 소요되는 시간"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "포아송이나 지수분포의 핵심은 $\\lambda$가 해당 기간 동안 일정하게 유지된다는 가정이다. 시간 주기 또는 공간을 일정 기간 충분히 동일하도록(homogeneous) 영역을 잘 나눈다면, 해당 기간 내의 분석 및 시뮬레이션이 가능하다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "(Advanced)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 9.3. 베이불 분포 (Weibull distribution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 사건 발생률이 시간에 지속적으로 변할 때(예를 들어 증가하는 고장률) 베이불 분포를 사용\n",
    "- Shape parameter $\\beta$에 따라 발생률이 달라짐\n",
    "    - $\\beta > 1$일 경우, 발생률은 시간이 자남에 따라 증가\n",
    "    - $\\beta < 1$일 경우, 발생률은 시간이 지남에 따라 감소\n",
    "- Scale parameter $\\eta$은 특수 수명을 표현"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    " - 수리통계학(송성주, 전명식)\n",
    " - 데이터 과학을 위한 통계, 데이터 분석에서 머신러닝까지 50가지 핵심 개념\n",
    " - The elements of statistical learning\n",
    " - An Introduction to Statistical Learning (https://www-bcf.usc.edu/~gareth/ISL/)"
   ]
  }
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