08-descriptive-statistics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'> \n",
    "# Computational Statistics for Data Analysis\n",
    "</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <div class=\"alert alert-error\"><strong><center><small>\"Statistics is the discipline of using data samples to support claims about populations.\"<small></center></strong> </div>\n",
    "\n",
    "In this notebook, we will get familiar with Descriptive statistics that comprise  concepts, terms, measures and tools that help to describe, show and summarize the data in a meaningful way. When analysing data, such as the price of flats renting per year, it is possible to use both descriptive and inferential statistics in order to analyse the results and draw some conclusions. We will discuss basic concepts,  terms and procedures, like mean, median, variance, correlation, etc.,  to explore, describe and summarize the given set of data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statistics is based on 2 main concepts:\n",
    "\n",
    "* A **population** is a collection of objects, items (“units”) about which information is sought.\n",
    "\n",
    "* A **sample** is a part of the population that is observed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'>\n",
    "# 1 Descriptive Statistics.\n",
    "* 1.1 Getting data\n",
    "* 1.2 Data preparation\n",
    "* 1.3 Improving data as a pandas DataFrame\n",
    "* 1.4 Data cleaning \n",
    " <font\\>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### \"Are the men more likely to become high income professionals i.e. to receive income bigger than 50K?\"\n",
    "\n",
    "Some people believe it is true, but **without data analysis** to support it, this claim is a case of **anecdotal evidence**:\n",
    "\n",
    "* There are a **small number of samples** (personal experience, friends, etc.).\n",
    "* There is a **selection bias**: most *believers* are interested in this claim because their first babies were late.\n",
    "* There is a **confirmation bias**: believers might be more likely to contribute data that confirm it.\n",
    "* Sources are **innaccurate**: personal stories are subject to memory deformations. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Getting Data\n",
    "\n",
    "Let us consider a public database, called “Adult” dataset hosted on the UCI’s Machine Learning Repository (https://archive.ics.uci.edu/ml/datasets/Adult), that contains approximately 32.000 observations about different financial parameters of US population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Data preparation\n",
    "\n",
    "One of the reasons we are using a general-purpose language such as Python rather than a stats language like R is that for many projects the *hard* part is preparing the data, not doing the analysis.\n",
    "\n",
    "The most common steps are:\n",
    "\n",
    "1. **Getting the data**. Data can be directly read from a file or it might be necessary to scrap the web.\n",
    "2. **Parsing the data**.  Of course, this depends on what format it is in: plain text, fixed columns, CSV, XML, HTML, etc.\n",
    "3. **Cleaning the data**.  Survey responses and other data files are almost always incomplete.  Sometimes there are multiple codes for things like, *not asked*, *did not know*, and *declined to answer*. And there are almost always errors. A simple strategy is to remove or ignore incomplete records.\n",
    "4. **Building data structures**. Once you read the data, you usually want to store it in a data structure that lends itself to the analysis you want to do.\n",
    "\n",
    "If the data fits into memory, building a data structure is usually the way to go.   If not, you could build a database, which is an out-of-memory data structure. Most databases provide a mapping from keys to values, so they are like dictionaries.\n",
    "\n",
    "Let us read the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "file = open('files/ch03/adult.data', 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def chr_int(a):\n",
    "    if a.isdigit():\n",
    "        return int(a)\n",
    "    else:\n",
    "        return 0\n",
    "                \n",
    "data=[]\n",
    "for line in file:\n",
    "     data1=line.split(', ')\n",
    "     if len(data1)==15:\n",
    "        data.append([chr_int(data1[0]),data1[1],chr_int(data1[2]),data1[3],chr_int(data1[4]),data1[5],data1[6],\\\n",
    "            data1[7],data1[8],data1[9],chr_int(data1[10]),chr_int(data1[11]),chr_int(data1[12]),data1[13],\\\n",
    "            data1[14]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[50, 'Self-emp-not-inc', 83311, 'Bachelors', 13, 'Married-civ-spouse', 'Exec-managerial', 'Husband', 'White', 'Male', 0, 0, 13, 'United-States', '<=50K\\n']]\n"
     ]
    }
   ],
   "source": [
    "print(data[1:2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Importing data as a pandas DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>age</th>\n",
       "      <th>type_employer</th>\n",
       "      <th>fnlwgt</th>\n",
       "      <th>education</th>\n",
       "      <th>education_num</th>\n",
       "      <th>marital</th>\n",
       "      <th>occupation</th>\n",
       "      <th>relationship</th>\n",
       "      <th>race</th>\n",
       "      <th>sex</th>\n",
       "      <th>capital_gain</th>\n",
       "      <th>capital_loss</th>\n",
       "      <th>hr_per_week</th>\n",
       "      <th>country</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>39</td>\n",
       "      <td>State-gov</td>\n",
       "      <td>77516</td>\n",
       "      <td>Bachelors</td>\n",
       "      <td>13</td>\n",
       "      <td>Never-married</td>\n",
       "      <td>Adm-clerical</td>\n",
       "      <td>Not-in-family</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>2174</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>50</td>\n",
       "      <td>Self-emp-not-inc</td>\n",
       "      <td>83311</td>\n",
       "      <td>Bachelors</td>\n",
       "      <td>13</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Exec-managerial</td>\n",
       "      <td>Husband</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>38</td>\n",
       "      <td>Private</td>\n",
       "      <td>215646</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Divorced</td>\n",
       "      <td>Handlers-cleaners</td>\n",
       "      <td>Not-in-family</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>53</td>\n",
       "      <td>Private</td>\n",
       "      <td>234721</td>\n",
       "      <td>11th</td>\n",
       "      <td>7</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Handlers-cleaners</td>\n",
       "      <td>Husband</td>\n",
       "      <td>Black</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>28</td>\n",
       "      <td>Private</td>\n",
       "      <td>338409</td>\n",
       "      <td>Bachelors</td>\n",
       "      <td>13</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Prof-specialty</td>\n",
       "      <td>Wife</td>\n",
       "      <td>Black</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>Cuba</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age     type_employer  fnlwgt  education  education_num  \\\n",
       "0   39         State-gov   77516  Bachelors             13   \n",
       "1   50  Self-emp-not-inc   83311  Bachelors             13   \n",
       "2   38           Private  215646    HS-grad              9   \n",
       "3   53           Private  234721       11th              7   \n",
       "4   28           Private  338409  Bachelors             13   \n",
       "\n",
       "              marital         occupation   relationship   race     sex  \\\n",
       "0       Never-married       Adm-clerical  Not-in-family  White    Male   \n",
       "1  Married-civ-spouse    Exec-managerial        Husband  White    Male   \n",
       "2            Divorced  Handlers-cleaners  Not-in-family  White    Male   \n",
       "3  Married-civ-spouse  Handlers-cleaners        Husband  Black    Male   \n",
       "4  Married-civ-spouse     Prof-specialty           Wife  Black  Female   \n",
       "\n",
       "   capital_gain  capital_loss  hr_per_week        country   income  \n",
       "0          2174             0           40  United-States  <=50K\\n  \n",
       "1             0             0           13  United-States  <=50K\\n  \n",
       "2             0             0           40  United-States  <=50K\\n  \n",
       "3             0             0           40  United-States  <=50K\\n  \n",
       "4             0             0           40           Cuba  <=50K\\n  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame(data) #  Two-dimensional size-mutable, potentially heterogeneous tabular data structure with labeled axes \n",
    "\n",
    "df.columns = ['age', 'type_employer', 'fnlwgt', 'education', \n",
    "                \"education_num\",\"marital\", \"occupation\", \"relationship\", \"race\",\"sex\",\n",
    "                \"capital_gain\", \"capital_loss\", \"hr_per_week\",\"country\",\"income\"]\n",
    "df.head()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>age</th>\n",
       "      <th>type_employer</th>\n",
       "      <th>fnlwgt</th>\n",
       "      <th>education</th>\n",
       "      <th>education_num</th>\n",
       "      <th>marital</th>\n",
       "      <th>occupation</th>\n",
       "      <th>relationship</th>\n",
       "      <th>race</th>\n",
       "      <th>sex</th>\n",
       "      <th>capital_gain</th>\n",
       "      <th>capital_loss</th>\n",
       "      <th>hr_per_week</th>\n",
       "      <th>country</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>32556</td>\n",
       "      <td>27</td>\n",
       "      <td>Private</td>\n",
       "      <td>257302</td>\n",
       "      <td>Assoc-acdm</td>\n",
       "      <td>12</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Tech-support</td>\n",
       "      <td>Wife</td>\n",
       "      <td>White</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>38</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>32557</td>\n",
       "      <td>40</td>\n",
       "      <td>Private</td>\n",
       "      <td>154374</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Machine-op-inspct</td>\n",
       "      <td>Husband</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&gt;50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>32558</td>\n",
       "      <td>58</td>\n",
       "      <td>Private</td>\n",
       "      <td>151910</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Widowed</td>\n",
       "      <td>Adm-clerical</td>\n",
       "      <td>Unmarried</td>\n",
       "      <td>White</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>32559</td>\n",
       "      <td>22</td>\n",
       "      <td>Private</td>\n",
       "      <td>201490</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Never-married</td>\n",
       "      <td>Adm-clerical</td>\n",
       "      <td>Own-child</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K\\n</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>32560</td>\n",
       "      <td>52</td>\n",
       "      <td>Self-emp-inc</td>\n",
       "      <td>287927</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Exec-managerial</td>\n",
       "      <td>Wife</td>\n",
       "      <td>White</td>\n",
       "      <td>Female</td>\n",
       "      <td>15024</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&gt;50K\\n</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       age type_employer  fnlwgt   education  education_num  \\\n",
       "32556   27       Private  257302  Assoc-acdm             12   \n",
       "32557   40       Private  154374     HS-grad              9   \n",
       "32558   58       Private  151910     HS-grad              9   \n",
       "32559   22       Private  201490     HS-grad              9   \n",
       "32560   52  Self-emp-inc  287927     HS-grad              9   \n",
       "\n",
       "                  marital         occupation relationship   race     sex  \\\n",
       "32556  Married-civ-spouse       Tech-support         Wife  White  Female   \n",
       "32557  Married-civ-spouse  Machine-op-inspct      Husband  White    Male   \n",
       "32558             Widowed       Adm-clerical    Unmarried  White  Female   \n",
       "32559       Never-married       Adm-clerical    Own-child  White    Male   \n",
       "32560  Married-civ-spouse    Exec-managerial         Wife  White  Female   \n",
       "\n",
       "       capital_gain  capital_loss  hr_per_week        country   income  \n",
       "32556             0             0           38  United-States  <=50K\\n  \n",
       "32557             0             0           40  United-States   >50K\\n  \n",
       "32558             0             0           40  United-States  <=50K\\n  \n",
       "32559             0             0           20  United-States  <=50K\\n  \n",
       "32560         15024             0           40  United-States   >50K\\n  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32561, 15)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's count the number of items per country:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "country\n",
      "?                               583\n",
      "Cambodia                         19\n",
      "Canada                          121\n",
      "China                            75\n",
      "Columbia                         59\n",
      "Cuba                             95\n",
      "Dominican-Republic               70\n",
      "Ecuador                          28\n",
      "El-Salvador                     106\n",
      "England                          90\n",
      "France                           29\n",
      "Germany                         137\n",
      "Greece                           29\n",
      "Guatemala                        64\n",
      "Haiti                            44\n",
      "Holand-Netherlands                1\n",
      "Honduras                         13\n",
      "Hong                             20\n",
      "Hungary                          13\n",
      "India                           100\n",
      "Iran                             43\n",
      "Ireland                          24\n",
      "Italy                            73\n",
      "Jamaica                          81\n",
      "Japan                            62\n",
      "Laos                             18\n",
      "Mexico                          643\n",
      "Nicaragua                        34\n",
      "Outlying-US(Guam-USVI-etc)       14\n",
      "Peru                             31\n",
      "Philippines                     198\n",
      "Poland                           60\n",
      "Portugal                         37\n",
      "Puerto-Rico                     114\n",
      "Scotland                         12\n",
      "South                            80\n",
      "Taiwan                           51\n",
      "Thailand                         18\n",
      "Trinadad&Tobago                  19\n",
      "United-States                 29170\n",
      "Vietnam                          67\n",
      "Yugoslavia                       16\n",
      "dtype: int64\n"
     ]
    }
   ],
   "source": [
    "counts = df.groupby('country').size()\n",
    "\n",
    "print(counts) \n",
    "# also: df.outcome.value_counts()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "age\n",
      "17    395\n",
      "18    550\n",
      "19    712\n",
      "20    753\n",
      "21    720\n",
      "     ... \n",
      "85      3\n",
      "86      1\n",
      "87      1\n",
      "88      3\n",
      "90     43\n",
      "Length: 73, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "counts = df.groupby('age').size() # grouping by age\n",
    "print(counts) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21790, 15)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml = df[(df.sex == 'Male')] # grouping by sex\n",
    "ml.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6662, 15)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml1 = df[(df.sex == 'Male')&(df.income=='>50K\\n')]\n",
    "ml1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's separate male from female according to the income. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10771, 15)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm =df[(df.sex == 'Female')]\n",
    "fm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1179, 15)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm1 =df[(df.sex == 'Female')&(df.income=='>50K\\n')]\n",
    "fm1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The rate of people with high income is:  24 %.\n",
      "The rate of men with high income is:  30 %.\n",
      "The rate of women with high income is:  10 %.\n"
     ]
    }
   ],
   "source": [
    "df1=df[(df.income=='>50K\\n')]\n",
    "\n",
    "print('The rate of people with high income is: ', int(len(df1)/float(len(df))*100), '%.') \n",
    "print('The rate of men with high income is: ', int(len(ml1)/float(len(ml))*100), '%.') \n",
    "print('The rate of women with high income is: ', int(len(fm1)/float(len(fm))*100), '%.') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Data Cleaning\n",
    "\n",
    "The most common steps are:\n",
    "\n",
    "+ **Sample the data**. If the amount of raw data is huge, processing all of them may require an extensive amount of processing power which may not be practical.  In this case, it is quite common to sample the input data to reduce the size of data that need to be processed.\n",
    "\n",
    "+ **Impute missing data**. It is quite common that some of the input records are incomplete in the sense that certain fields are missing or have input error.  In a typical tabular data format, we need to validate each record contains the same number of fields and each field contains the data type we expect. In case the record has some fields missing, we have the following choices: \n",
    "<small>\n",
    "* (a) Discard the whole record if it is incomplete; \n",
    "* (b) Infer the missing value based on the data from other records.  A common approach is to fill the missing data with the average, or the median.\n",
    "<small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Normalize numeric value**. Normalize data is about transforming numeric data into a uniform range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Reduce dimensionality**. High dimensionality can be a problem for some machine learning methods.  There are two ways to reduce the number of input features.  One is about $removing$ $irrelevant$ input variables, another one is about $removing$ $redundant$ input variables.\n",
    "+ **Add derived features**. In some cases, we may need to compute additional attributes from existing attributes (f.e. converting a geo-location to a zip code, or converting the age to an age group).\n",
    "+ **Discretize numeric value into categories**. Discretize data is about cutting a continuous value into ranges and assigning the numeric with the corresponding bucket of the range it falls on.  For numeric attribute, a common way to generalize it is to discretize it into ranges, which can be either constant width (variable height/frequency) or variable width (constant height).\n",
    "+ **Binarize categorical attributes**. Certain machine learning models only take binary input (or numeric input).  In this case, we need to convert categorical attribute into multiple binary attributes, while each binary attribute corresponds to a particular value of the category. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ **Select, combine, aggregate data**. Designing the form of training data is the most important part of the whole predictive modeling exercise because the accuracy largely depends on whether the input features are structured in an appropriate form that provide strong signals to the learning algorithm. Rather than using the raw data as it is, it is quite common that multiple pieces of raw data need to be combined together, or aggregating multiple raw data records along some dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Exploratory Data Analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Summarizing the data: \n",
    "#### 2.1.1 Sample Mean \n",
    "\n",
    "If you have a sample of $n$ values, $x_i$, the **sample mean** is the sum of the values divided by the number of values:\n",
    "\n",
    "$$ \\mu = \\frac{1}{n} \\sum_i x_i$$\n",
    "\n",
    "The **mean** is the most basic and important summary statistic. It describes the central tendency of a sample. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a small difference!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average age of men is:  39.43354749885268 .\n",
      "The average age of women is:  36.85823043357163 .\n"
     ]
    }
   ],
   "source": [
    "print('The average age of men is: ', ml['age'].mean(), '.') \n",
    "print('The average age of women is: ', fm['age'].mean(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This difference in sample means can be considered a first evidence of our hypothesis!\n",
    "\n",
    "\n",
    "**Comment: ** *Later, we will work with both concepts: the population mean and the sample mean. Do not confuse them! Remember, the first one is the mean of samples taken from the population and the second one is the mean of the whole population.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average age of high-income men is:  44.62578805163614 .\n",
      "The average age of high-income women is:  42.125530110262936 .\n"
     ]
    }
   ],
   "source": [
    "print('The average age of high-income men is: ', ml1['age'].mean(), '.') \n",
    "print('The average age of high-income women is: ', fm1['age'].mean(), '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.2 Sample Variance\n",
    "\n",
    "Usually, mean is not a sufficient descriptor of the data, we can do a little better with two numbers: mean and **variance**:\n",
    "\n",
    "$$ \\sigma^2 = \\frac{1}{n} \\sum_i (x_i - \\mu)^2 $$\n",
    "\n",
    "**Variance** $\\sigma^2$ describes the *spread* of data. The term $(x_i - \\mu)$ is called the *deviation from the mean*, so variance is the mean squared deviation.\n",
    "\n",
    "The square root of variance, $\\sigma$, is called the **standard deviation**. We define standard deviation because variance is hard to interpret (in the case the units are grams, the variance is in grams squared). Let's get the basic statistics for our example data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics of age for men: mu: 39.43354749885268 var: 178.77375174529985 std: 13.370630192526448\n",
      "Statistics of age for women: mu: 36.85823043357163 var: 196.3837063948063 std: 14.013697099438332\n"
     ]
    }
   ],
   "source": [
    "ml_mu = ml['age'].mean()\n",
    "fm_mu = fm['age'].mean()\n",
    "ml_var = ml['age'].var()\n",
    "fm_var = fm['age'].var()\n",
    "ml_std = ml['age'].std()\n",
    "fm_std = fm['age'].std()\n",
    "print('Statistics of age for men: mu:', ml_mu, 'var:', ml_var, 'std:', ml_std)\n",
    "print('Statistics of age for women: mu:', fm_mu, 'var:', fm_var, 'std:', fm_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics of hours per week for men: mu: 42.42808627810923 var: 146.88846717140746 std: 12.11975524387384\n",
      "Statistics  of hours per week for women: mu: 36.410361154953115 var: 139.50679700047422 std: 11.811299547487323\n"
     ]
    }
   ],
   "source": [
    "ml_mu_hr = ml['hr_per_week'].mean()\n",
    "fm_mu_hr = fm['hr_per_week'].mean()\n",
    "ml_var_hr = ml['hr_per_week'].var()\n",
    "fm_var_hr = fm['hr_per_week'].var()\n",
    "ml_std_hr = ml['hr_per_week'].std()\n",
    "fm_std_hr = fm['hr_per_week'].std()\n",
    "print('Statistics of hours per week for men: mu:', ml_mu_hr, 'var:', ml_var_hr, 'std:', ml_std_hr)\n",
    "print('Statistics  of hours per week for women: mu:', fm_mu_hr, 'var:', fm_var_hr, 'std:', fm_std_hr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.3 Sample Median\n",
    "\n",
    "The statistical median is an order statistic that gives the *middle* value of a sample. It is a value more robust to ouliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median age per men and women:  38.0 35.0\n",
      "Median age per men and women with high-income:  44.0 41.0\n"
     ]
    }
   ],
   "source": [
    "ml_median= ml['age'].median()\n",
    "fm_median= fm['age'].median()\n",
    "print(\"Median age per men and women: \", ml_median, fm_median)\n",
    "\n",
    "ml_median_age= ml1['age'].median()\n",
    "fm_median_age= fm1['age'].median()\n",
    "print(\"Median age per men and women with high-income: \", ml_median_age, fm_median_age)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median hours per week per men and women:  40.0 40.0\n"
     ]
    }
   ],
   "source": [
    "ml_median_hr= ml['hr_per_week'].median()\n",
    "fm_median_hr= fm['hr_per_week'].median()\n",
    "print(\"Median hours per week per men and women: \", ml_median_hr, fm_median_hr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1.4 Summarizing the data: Quantiles & Percentiles\n",
    "\n",
    "Order the sample $\\{ x_i \\}$, then find $x_p$ so that it divides the data into two parts where:\n",
    "\n",
    "+ a fraction $p$ of the data values are less than or equal to $x_p$ and\n",
    "+ the remaining fraction $(1 − p)$ are greater than $x_p$.\n",
    "\n",
    "That value $x_p$ is the pth-quantile, or 100×pth percentile.\n",
    "\n",
    "**5-number summary**: $x_{min}, Q_1, Q_2, Q_3, x_{max}$, where $Q_1$ is the 25×pth percentile,\n",
    "$Q_2$ is the 50×pth percentile and $Q_3$ is the 75×pth percentile."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most common representation of a distribution is a **histogram**, which is a graph that shows the frequency of each value. Let us visualize the histogram for the age of the male and female populations in our example: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/pandas/plotting/_matplotlib/hist.py:316: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  ax.hist(values, bins=bins, **kwds)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "ml_age=ml['age']\n",
    "ml_age.hist(normed=0, histtype='stepfilled', bins=20)\n",
    "\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Male samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age=fm['age']\n",
    "\n",
    "fm_age.hist(normed=0, histtype='stepfilled', bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Female samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare both populations: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting seaborn\n",
      "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/a8/76/220ba4420459d9c4c9c9587c6ce607bf56c25b3d3d2de62056efe482dadc/seaborn-0.9.0-py3-none-any.whl (208kB)\n",
      "\u001b[K     |████████████████████████████████| 215kB 791kB/s eta 0:00:01\n",
      "\u001b[?25hRequirement already satisfied: scipy>=0.14.0 in /home/sitthichok/anaconda3/lib/python3.7/site-packages (from seaborn) (1.3.1)\n",
      "Requirement already satisfied: matplotlib>=1.4.3 in /home/sitthichok/.local/lib/python3.7/site-packages (from seaborn) (3.1.1)\n",
      "Requirement already satisfied: pandas>=0.15.2 in /home/sitthichok/anaconda3/lib/python3.7/site-packages (from seaborn) (0.25.1)\n",
      "Requirement already satisfied: numpy>=1.9.3 in /home/sitthichok/anaconda3/lib/python3.7/site-packages (from seaborn) (1.16.4)\n",
      "Requirement already satisfied: cycler>=0.10 in /home/sitthichok/.local/lib/python3.7/site-packages (from matplotlib>=1.4.3->seaborn) (0.10.0)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in /home/sitthichok/.local/lib/python3.7/site-packages (from matplotlib>=1.4.3->seaborn) (2.8.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /home/sitthichok/.local/lib/python3.7/site-packages (from matplotlib>=1.4.3->seaborn) (1.1.0)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /home/sitthichok/.local/lib/python3.7/site-packages (from matplotlib>=1.4.3->seaborn) (2.4.2)\n",
      "Requirement already satisfied: pytz>=2017.2 in /home/sitthichok/anaconda3/lib/python3.7/site-packages (from pandas>=0.15.2->seaborn) (2019.2)\n",
      "Requirement already satisfied: six in /home/sitthichok/anaconda3/lib/python3.7/site-packages (from cycler>=0.10->matplotlib>=1.4.3->seaborn) (1.12.0)\n",
      "Requirement already satisfied: setuptools in /home/sitthichok/anaconda3/lib/python3.7/site-packages (from kiwisolver>=1.0.1->matplotlib>=1.4.3->seaborn) (41.0.1)\n",
      "Installing collected packages: seaborn\n",
      "Successfully installed seaborn-0.9.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/pandas/plotting/_matplotlib/hist.py:316: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  ax.hist(values, bins=bins, **kwds)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "!pip install seaborn\n",
    "import seaborn as sns\n",
    "fm_age.hist(normed=0, histtype='stepfilled', alpha=.5, bins=20)   # default number of bins = 10\n",
    "ml_age.hist(normed=0, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75), bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Samples',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(normed=1, histtype='stepfilled', alpha=.5, bins=20)   # default number of bins = 10\n",
    "ml_age.hist(normed=1, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75), bins=10)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('PMF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Data Distributions\n",
    "\n",
    "Summarizing can be dangerous: very different data can be described by the same statistics. It must be validated by inspecting the data.\n",
    "\n",
    "We can look at the **data distribution**, which describes how often (frequency) each value appears.\n",
    "\n",
    "\n",
    "We can normalize the frequencies of the histogram by dividing/normalizing by $n$, the number of samples. The normalized histogram is called **Probability Mass Function (PMF)**.\n",
    "\n",
    "Let's visualize and compare the MPF of male and female age in our example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(normed=1, histtype='stepfilled', bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(normed=1, histtype='stepfilled', bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **cumulative distribution function (CDF)**, or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found to have a value less than or equal to x. For our example, the CDFs will be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAELCAYAAAAybErdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAYzklEQVR4nO3df5TddX3n8efbRBLIEDGJzgZBE07RdhYqyJTIka2JYhNcJT01dclpWavSuKdmK5V2i8ctXdw9p7Xt6rpHSpMqtnJaJ9RfDZys4CqzXVyMEPyxZig1G6zySwSUOKMERt77x/c74Wa+M5kfufO93zvzfJxzT+b7/X7uva+5c+995/v5fr+fT2QmkiS1ek6nA0iSmsfiIEmqsDhIkiosDpKkCouDJKlicacDtMOqVatyzZo1tT3fyMgIy5Ytq+35ZqMbMoI5260bcnZDRlgYOfft2/doZr5gwo2Z2fW38847L+t022231fp8s9ENGTPN2W7dkLMbMmYujJzAXTnJ96rdSpKkCouDJKnC4iBJqrA4SJIqLA6SpAqLgySpotbiEBHXR8QjEfHNSbZHRPz3iDgQEd+IiFfUmU+SVKj7Iri/Aj4MfHyS7RcDZ5a3dcB15b+SNCeuuWk/Qw8eqqzfuHKE63bc0YFEM7Nx5Qj/66b9/OEb/2VbH7fW4pCZ/xARa47RZDPw8fLijC9HxCkRsTozH6oloKSOmexLeq7tve/xCddf2DM66bYmubBnlKHH2v+6RdY82U9ZHG7OzLMm2HYz8MeZeXu5/AXg9zPzrgnabgO2AfT29p43MDAwl7GPMjw8TE9PT23PNxvdkBHM2W7dkHOyjAcfHWHk8GgHEk2s90T43k86nWJqvSfC8DOLOWPVzIfQ2LBhw77M7J9oW9eOrZSZO4GdAP39/bl+/franntwcJA6n282uiEjmLPdOplzuv/z37hyhBseWFJZv/e+EZrwlbRu7QoANi55nNuHV3Q4zeSGHjrEj54c5cqzR7l9eAW7tlzQ1sfv/F/iaA8Ap7csn1auk1SD4+namW4XzHS7a8a+pOvUd+ryI333g4ODbf/Cbad/s+OOOe32alpx2A1sj4gBigPRT3i8QarP0IOHGtHPvm7tCna9o7lfzAtBrcUhIj4BrAdWRcT9wB8CzwXIzL8A9gCvBw4APwbeWmc+Se0z2f/8ly15fMq9gr5Tl89FJM1A3WcrbZ1iewLvrCmOpGM4eeli+lbP7ku6tXtmvKZ316jQtG4lScfpeI4bDD307P36Vi+3a2cBszhI80xTjhuouzm2kiSpwj0HaR473uMGWrgsDtI85nEDzZbdSpKkCouDJKnCbiWpgWZ7OurGlSMMPXR4DhJpobE4SA0029NRL+wZ5UdPzkEgLTh2K0mSKtxzkBpuJqejjh+3yNNRNVsWB6nhZnI6quMWqV3sVpIkVVgcJEkVditJc+B4RkaFo0dHlTrB4iDNAUdGVbezW0mSVOGegzTHjmdkVPB0VHWGxUGaY46Mqm5kt5IkqcLiIEmqsDhIkiosDpKkCouDJKnC4iBJqvBUVmkSrUNgbFw5wnU77pj2fR3+Qt3O4iBNonUIjAt7Rh0OQwuK3UqSpAr3HKRpWPScOGqGtZlw+At1I4uDNA1Ln7vIITC0oNitJEmqsDhIkipqLw4RsSki7o2IAxFx1QTbXxwRt0XEVyPiGxHx+rozStJCV2txiIhFwLXAxUAfsDUi+sY1+4/AjZl5LnAp8Od1ZpQk1b/ncD5wIDMPZuZTwACweVybBMZO73ge8GCN+SRJQGRmfU8WsQXYlJmXl8uXAesyc3tLm9XArcDzgWXARZm5b4LH2gZsA+jt7T1vYGCght+gMDw8TE9PT23PNxvdkBGanfPgoyOMHB4F4NSTYOXzn9fhRFNr8us5phsyQvNzjr0/e0+E4WcWc8aqZTN+jA0bNuzLzP6JtjXxVNatwF9l5n+NiAuAGyLirMx8prVRZu4EdgL09/fn+vXraws4ODhInc83G92QEZqd87oddxy5KvrqfnhTQ3O2avLrOaYbMkLzc469P688e5Tbh1ewa0t7T7Wuu1vpAeD0luXTynWt3g7cCJCZdwBLgVW1pJMkAfUXhzuBMyNibUScQHHAefe4Nt8BXgsQET9HURy+X2tKSVrgau1WyszRiNgO3AIsAq7PzP0R8T7grszcDVwJ/GVE/A7FwenfyDoPjGheaR1ZdaYcWVULWe3HHDJzD7Bn3LqrW34eAl5Vdy7NT60jq0qaPq+QliRVNPFsJWlOnLx0MX2rZzdC6onPfaLNaaRmszhowehbvXzWI6sODg62N4zUcHYrSZIqLA6SpAqLgySpwuIgSaqwOEiSKiwOkqQKi4MkqcLrHNR4jo8k1c/ioMZzfCSpfnYrSZIq3HNQVzme8ZH6Tp3d/aSFyOKgrnI84yNJmj67lSRJFRYHSVKFxUGSVGFxkCRVWBwkSRUWB0lShcVBklRhcZAkVVgcJEkVFgdJUoXFQZJUYXGQJFVYHCRJFRYHSVKFxUGSVOF8DqrFZPNAb1w5wnU77jjmfZ0HWqqfxUG1mGwe6At7Rp0fWmqg2ruVImJTRNwbEQci4qpJ2rw5IoYiYn9E/G3dGSVpoat1zyEiFgHXAq8D7gfujIjdmTnU0uZM4D3AqzLzBxHxwjozau61zgO9bMnjrFu7Ytr3dR5oqR51dyudDxzIzIMAETEAbAaGWtr8JnBtZv4AIDMfqTmj5ljrPNCDg4Ps2uKc0FLT1N2t9CLguy3L95frWr0UeGlEfCkivhwRm2pLJ0kCIDKzvieL2AJsyszLy+XLgHWZub2lzc3A08CbgdOAfwDOzswfjnusbcA2gN7e3vMGBgbq+SWA4eFhenp6anu+2WhaxoOPjjByeBSAZUsWc8aqZUDzck7GnO3TDRmh+TnHPlO9J8LwM89+pmZiw4YN+zKzf6JtdXcrPQCc3rJ8Wrmu1f3A3sx8GrgvIv4JOBO4s7VRZu4EdgL09/fn+vXr5ypzxeDgIHU+32w0LeN1O+44clbSurUrjnQlNS3nZMzZPt2QEZqfc+wzdeXZo9w+vKLt3bN1dyvdCZwZEWsj4gTgUmD3uDafBdYDRMQqim6mg3WGlKSF7pjFISJujYiXjVv3moiY+f4LkJmjwHbgFuAe4MbM3B8R74uIS8pmtwCPRcQQcBvwe5n52GyeT5I0O1N1K10EPG9soTwV9fPALwB3z+YJM3MPsGfcuqtbfk7g3eVNktQBs+lWirankCQ1igPvSZIqplMcJjrXtb7zXyVJtZvOqay3RMTouHVfmGAdmelQF5I0D0xVHK6pJYUkqVGOWRwy0+IgSQvQjK6QLk9lHRtC8/HM/Gn7I0mSOm1aZytFxGUR8X+AHwMPl7eRcnC8X5vLgJKk+k255xARHwHeBuwF3k8x9lFQjKb6S8DHI+LVmbltLoNKkupzzOIQEW8A3gq8PTM/NkGTqyPibcDOiPhsefWzJKnLTbXn8FZg1ySFAYDMvD4iXkexd2FxmKeuuWk/Qw8emvX9hx6a/X0l1W+q4tAP/P40HufvKbqcNE8NPXjoyJDbkua/qQ5Iv4CjZ26bzP1lW0nSPDDVnsNSilnZpvI0sOT446gbnLx0MX2rl8/6/n2nzv6+kuoxnesc3hQRE04j12JNG7KoS/StXs6ud7R31ilJzTKd4vB703wsB+OTpHliquEzHNJbkhagqaYJXR0Rn4qIjcdos7Fs44iskjRPTLVn8LvAGcCtx2hzK7AWuLJdoSRJnTVVcXgD8BflvM4TKrftADa3M5gkqXOmKg4vAYam8Tj34BlLkjRvTFUcfgJM56T0nrKtJGkemKo43A1cMo3H2Vy2lSTNA1MVhz8H3h4Rb5msQUT8W4oB+j7czmCSpM6Z6jqHT0XEh4CPRcR24HPAdygueHsxsJFicL4PZuZn5jqsJKkeU14hnZlXRsQgcAXFqa1jYygdBr4EbM7Mm+csoSSpdtOaQzozbwJuiojFwMpy9WOZOTpnySRJHTOt4jCmLAbfm6MskqSGmFFxUHc7ntncnMlNWlgsDguIs7lJmi5HXZUkVbjnsEAdz2xuzuQmzX8WhwXK2dwkHUvt3UoRsSki7o2IAxFx1THavSkichpTlEqS2qzW4hARi4BrgYuBPmBrRPRN0O5k4F3A3jrzSZIKde85nA8cyMyDmfkUMMDE80D8Z+D9wJN1hpMkFeIY8/i0/8kitgCbMvPycvkyYF1mbm9p8wrgvZn5pnLYjt/NzLsmeKxtwDaA3t7e8wYGBur4FQAYHh6mp6entuebjYkyHnx0hJHDxUXty5Ys5oxVyzoR7Sjd8FqCOdupGzJC83OOfZ57T4ThZ2b3ed6wYcO+zJyw675RB6Qj4jnAB4DfmKptZu4EdgL09/fn+vXr5zRbq8HBQep8vtmYKON1O+44cp3DurUr2LWl8weku+G1BHO2UzdkhObnHPs8X3n2KLcPt//zXHe30gPA6S3Lp5XrxpwMnAUMRsS3gVcCuz0oLUn1qrs43AmcGRFrI+IE4FJg99jGzHwiM1dl5prMXAN8Gbhkom4lSdLcqbU4lAP3bQduoZh3+sbM3B8R74uI6cw4J0mqQe3HHDJzD7Bn3LqrJ2m7vo5MkqSjObaSJKnC4iBJqrA4SJIqLA6SpAqLgySpwuIgSaqwOEiSKiwOkqQKi4MkqaJRo7JqatfctJ+hBw9N2W7jyhGu23HHUeuGHpr6fpIEFoeuM/TgoSPDbh/LhT2j02onSROxW0mSVOGeQxc7eeli+lYvn3DbsiWPs27tiknv23fqxPeTJLA4dLW+1cvZ9Y6JZ38aHBxsxExvkrqT3UqSpAqLgySpwuIgSaqwOEiSKiwOkqQKi4MkqcLiIEmqsDhIkiosDpKkCouDJKnC4iBJqrA4SJIqLA6SpAqLgySpwuIgSaqwOEiSKiwOkqQKZ4LrgGtu2s/Qg4dmdd+hh2Z3P0maidqLQ0RsAj4ELAI+kpl/PG77u4HLgVHg+8DbMvOf6845l4YePMTe+x7vdAxJmlSt3UoRsQi4FrgY6AO2RkTfuGZfBfoz8+eBTwJ/UmdGSVL9ew7nAwcy8yBARAwAm4GhsQaZeVtL+y8Dv15rwpqdvHQxfauXz+q+fafO7n6SNJXIzPqeLGILsCkzLy+XLwPWZeb2Sdp/GHg4M//LBNu2AdsAent7zxsYGJi74OMMDw/T09Mz6/sffHSEkcOjACxbspgzVi1rV7QjjjdjXczZXt2QsxsyQvNzjn2P9J4Iw8/M7ntkw4YN+zKzf6JtjT0gHRG/DvQDr55oe2buBHYC9Pf35/r162vLNjg4yPE833U77jhyzGHd2hXs2nJBm5I963gz1sWc7dUNObshIzQ/59j3yJVnj3L7cPu/R+ouDg8Ap7csn1auO0pEXAS8F3h1Zh6uKZskqVT3dQ53AmdGxNqIOAG4FNjd2iAizgV2AJdk5iM155MkUXNxyMxRYDtwC3APcGNm7o+I90XEJWWzPwV6gL+LiK9FxO5JHk6SNEdqP+aQmXuAPePWXd3y80V1Z5IkHc3hMyRJFRYHSVKFxUGSVGFxkCRVWBwkSRWNvUK66Rx2W9J8ZnGYJYfdljSf2a0kSapwz6ENHHZb0nxjcWiDvtXL2fWO9o+sKkmdYreSJKnC4iBJqrA4SJIqLA6SpAqLgySpwuIgSaqwOEiSKiwOkqQKi4MkqcLiIEmqsDhIkiosDpKkigU78N7xTNazceUIQw8dbnMiSWqOBVscjmeyngt7RvnRk20OJEkNYreSJKliwe45tJrpZD3LljzOurUrjiw7YY+k+cbiwMwn6xkcHGTXFif3kTR/2a0kSaqwOEiSKiwOkqQKi4MkqcLiIEmqsDhIkipqLw4RsSki7o2IAxFx1QTbl0TErnL73ohYU3dGSVroai0OEbEIuBa4GOgDtkZE37hmbwd+kJk/A3wQeH+dGSVJ9e85nA8cyMyDmfkUMABsHtdmM/DX5c+fBF4bEVFjRkla8Oq+QvpFwHdblu8H1k3WJjNHI+IJYCXwaGujiNgGbCsXhyPi3tmG+mfgxn83o7usGp+ngbohI5iz3bohZzdkhC7J+dtlzhl+h415yWQbunb4jMzcCezsxHNHxF2Z2d+J556ubsgI5my3bsjZDRnBnHV3Kz0AnN6yfFq5bsI2EbEYeB7wWC3pJElA/cXhTuDMiFgbEScAlwK7x7XZDbyl/HkL8MXMzBozStKCV2u3UnkMYTtwC7AIuD4z90fE+4C7MnM38FHghog4ADxOUUCapiPdWTPUDRnBnO3WDTm7ISMs8Jzhf8olSeN5hbQkqcLiIEmqsDgcQ0ScHhG3RcRQROyPiHeV61dExOcj4lvlv8/vcM6lEfGViPh6mfOacv3acgiSA+WQJCd0MmeZaVFEfDUibm5wxm9HxP+NiK9FxF3lukb9zctMp0TEJyPiHyPinoi4oGk5I+Jl5es4djsUEVc0MOfvlJ+db0bEJ8rPVBPfm+8qM+6PiCvKdXPyWlocjm0UuDIz+4BXAu8sh/u4CvhCZp4JfKFc7qTDwGsy8+XAOcCmiHglxdAjHyyHIvkBxdAknfYu4J6W5SZmBNiQmee0nD/etL85wIeAz2XmzwIvp3hdG5UzM+8tX8dzgPOAHwOfoUE5I+JFwG8D/Zl5FsXJMpfSsPdmRJwF/CbFSBMvB94QET/DXL2Wmeltmjfg74HXAfcCq8t1q4F7O52tJeNJwN0UV54/Ciwu118A3NLhbKeVb97XADcD0bSMZY5vA6vGrWvU35zi+p/7KE8qaWrOcdl+CfhS03Ly7KgMKyjO4LwZ2Ni09ybwq8BHW5b/APgPc/VauucwTeXosOcCe4HezHyo3PQw0NuhWEeU3TVfAx4BPg/8P+CHmTlaNrmf4kPQSf+N4s38TLm8kuZlBEjg1ojYVw7TAs37m68Fvg98rOym+0hELKN5OVtdCnyi/LkxOTPzAeDPgO8ADwFPAPto3nvzm8C/ioiVEXES8HqKC4bn5LW0OExDRPQAnwKuyMxDrduyKNcdPx84M3+axa77aRS7nT/b4UhHiYg3AI9k5r5OZ5mGCzPzFRSjB78zIn6xdWND/uaLgVcA12XmucAI47oTGpITgLK//hLg78Zv63TOso9+M0XBPRVYBmzqVJ7JZOY9FF1dtwKfA74G/HRcm7a9lhaHKUTEcykKw99k5qfL1d+LiNXl9tUU/1tvhMz8IXAbxW7wKeUQJDDxUCV1ehVwSUR8m2I03tdQ9Jk3KSNw5H+SZOYjFP3j59O8v/n9wP2Zubdc/iRFsWhazjEXA3dn5vfK5SblvAi4LzO/n5lPA5+meL828b350cw8LzN/keI4yD8xR6+lxeEYIiIorti+JzM/0LKpdYiPt1Aci+iYiHhBRJxS/nwixXGReyiKxJayWUdzZuZ7MvO0zFxD0b3wxcz8NRqUESAilkXEyWM/U/STf5OG/c0z82HguxHxsnLVa4EhGpazxVae7VKCZuX8DvDKiDip/MyPvZaNem8CRMQLy39fDPwK8LfM1WvZyQMsTb8BF1Lson2DYhfuaxT9fCspDqx+C/ifwIoO5/x54Ktlzm8CV5frzwC+Ahyg2J1f0unXtMy1Hri5iRnLPF8vb/uB95brG/U3LzOdA9xV/t0/Czy/oTmXUQye+byWdY3KCVwD/GP5+bkBWNK092aZ839TFK6vA6+dy9fS4TMkSRV2K0mSKiwOkqQKi4MkqcLiIEmqsDhIkiosDtIsRMR9EZHlwGfSvGNxkGYoIi4A1pSLWzsYRZozFgdp5rZSjGW0F4uD5imLgzQDEbEIeDPFkAXXAz8XES8f12Z9RHwjIp6MiDsj4vyIeDQi/tO4dpsj4q6y3cMR8SflWF5Sx1kcpJnZQDEk8gDFYHdP07L3UE4cs4di8LMtwA7gb4ATWx8kIt5MMcDbVyhGK70G2Ab80Zz/BtI0LJ66iaQWW4EfUszA9lRE3ApcGhHvyWIsmisoZjt7Y2b+BCAiDgG7xh6gHNztT4GPZ+Zvtaw/DFwbEX+UmY/V9ytJVe45SNNUzknwK8BnMvOpcvUA8BKKIdIBfgH4/FhhKO0e91AvBV4M3BgRi8duwBeBpcBZc/U7SNNlcZCm72LgFGBPRJxSDpM+SDGH91jX0r+gmKHtiMx8EhhuWbWq/HcPRbfU2O2+cv3pcxFemgm7laTpGysAldnMgF+NiCsopml8QeuGiFgK9LSserz8dxvFUOvj3TfBOqlWFgdpGsqJf95IMWHNznGbzwU+QDG73Z3AWyPixJaupUvGtb+XYlaxNZn5l3OXWpo9i4M0PZuBk4AP5bNTcwIQEV8C3kuxZ/EHwDuBmyLigxTdTFdRHKR+BiAzn4mIK4EbImI58D+Apygml/llYEtm/riW30qahMccpOnZCnxrfGEAyGLe4RspDlY/Cvxr4IUUp6r+e+BtwCLgUMt9dlEUnHMouqk+DfwWcDdFoZA6ypngpDkWERdSTO/4msy8rdN5pOmwOEhtFhHvpzjQ/DDwMoqupseAczPzmU5mk6bLYw5S+y2huMitF/gRcCvwbguDuol7DpKkCg9IS5IqLA6SpAqLgySpwuIgSaqwOEiSKv4/6AJ4A36lSr4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(normed=1, histtype='step', cumulative=True, linewidth=3.5, bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fm_age.hist(normed=1, histtype='step', cumulative=True, linewidth=3.5, bins=20)\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(bins=10, normed=1, histtype='stepfilled', alpha=.5)   # default number of bins = 10\n",
    "fm_age.hist(bins=10, normed=1, histtype='stepfilled', alpha=.5, color=sns.desaturate(\"indianred\", .75))\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml_age.hist(normed=1, histtype='step', cumulative=True,  linewidth=3.5, bins=20)\n",
    "fm_age.hist(normed=1, histtype='step', cumulative=True,  linewidth=3.5, bins=20, color=sns.desaturate(\"indianred\", .75))\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean sample difference is  2.5753170652810553\n"
     ]
    }
   ],
   "source": [
    "print(\"The mean sample difference is \", ml_age.mean() - fm_age.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Outliers\n",
    "\n",
    "**Ouliers** are data samples with a value that is far from the central tendency.\n",
    "\n",
    "We can find outliers by:\n",
    "\n",
    "+ Computing samples that are *far* from the median.\n",
    "+ Computing samples whose value *exceeds the mean* by 2 or 3 standard deviations.\n",
    "\n",
    "This expression will return a series of boolean values that you can then index the series by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['age'].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how many outliers we can detect in our example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df[(df.income == '>50K\\n') & (df['age'] < df['age'].median() - 15)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(df[(df.income == '>50K\\n') & (df['age'] > df['age'].median() + 35)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we think that outliers correspond to errors, an option is to trim the data by discarting the highest and lowest values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32492, 15)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = df.drop(df.index[(df.income=='>50K\\n') & (df['age']>df['age'].median() + 35) & (df['age'] > df['age'].median() -15)])\n",
    "df2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "ml1_age=ml1['age']\n",
    "fm1_age=fm1['age']\n",
    "\n",
    "ml2_age = ml1_age.drop(ml1_age.index[(ml1_age > df['age'].median() + 35) & (ml1_age > df['age'].median() - 15)])\n",
    "fm2_age = fm1_age.drop(fm1_age.index[(fm1_age > df['age'].median() + 35) & (fm1_age > df['age'].median() - 15)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Men statistics: Mean: 44.317982123920615 Std: 10.019749857171409 Median: 44.0 Min: 19 Max: 72\n"
     ]
    }
   ],
   "source": [
    "mu2ml = ml2_age.mean()\n",
    "std2ml = ml2_age.std()\n",
    "md2ml = ml2_age.median()\n",
    "# Computing the mean, std, median, min and max for the high-income male population\n",
    "print(\"Men statistics: Mean:\", mu2ml, \"Std:\", std2ml, \"Median:\", md2ml, \"Min:\", ml2_age.min(), \"Max:\", ml2_age.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Women statistics: Mean: 44.317982123920615 Std: 10.019749857171409 Median: 44.0 Min: 19 Max: 72\n"
     ]
    }
   ],
   "source": [
    "mu3ml = fm2_age.mean()\n",
    "std3ml = fm2_age.std()\n",
    "md3ml = fm2_age.median()\n",
    "# Computing the mean, std, median, min and max for the high-income female population\n",
    "print(\"Women statistics: Mean:\", mu2ml, \"Std:\", std2ml, \"Median:\", md2ml, \"Min:\", fm2_age.min(), \"Max:\", fm2_age.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean difference with outliers is: 2.58.\n",
      "The mean difference without outliers is: 2.44.\n"
     ]
    }
   ],
   "source": [
    "print('The mean difference with outliers is: %4.2f.' % (ml_age.mean() - fm_age.mean()))\n",
    "print(\"The mean difference without outliers is: %4.2f.\" % (ml2_age.mean() - fm2_age.mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare visually the age distributions before and after removing the outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Samples')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 964.8x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(13.4,5))\n",
    "\n",
    "df.age[(df.income == '>50K\\n')].plot(alpha=.25, color='blue')\n",
    "df2.age[(df2.income == '>50K\\n')].plot(alpha=.45,color='red')\n",
    "\n",
    "plt.ylabel('Age')\n",
    "plt.xlabel('Samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what is happening near the mode:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:3: VisibleDeprecationWarning: Passing `normed=True` on non-uniform bins has always been broken, and computes neither the probability density function nor the probability mass function. The result is only correct if the bins are uniform, when density=True will produce the same result anyway. The argument will be removed in a future version of numpy.\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:4: VisibleDeprecationWarning: Passing `normed=True` on non-uniform bins has always been broken, and computes neither the probability density function nor the probability mass function. The result is only correct if the bins are uniform, when density=True will produce the same result anyway. The argument will be removed in a future version of numpy.\n",
      "  after removing the cwd from sys.path.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "countx,divisionx = np.histogram(ml2_age, normed=True) \n",
    "county,divisiony = np.histogram(fm2_age, normed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "val = [(divisionx[i]+divisionx[i+1])/2 for i in range(len(divisionx)-1)]\n",
    "plt.plot(val, countx-county, 'o-') \n",
    "plt.title('Differences in promoting men vs. women')\n",
    "plt.xlabel('Age',fontsize=15)\n",
    "plt.ylabel('Differences',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is still some evidence for our hypothesis!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Remember:\n",
      " We have the following mean values for men, women and the difference:\n",
      "Originally:  39.43354749885268 36.85823043357163 2.5753170652810553\n",
      "For high-income:  44.62578805163614 42.125530110262936 2.5002579413732064\n",
      "After cleaning:  44.317982123920615 41.877028181041844 2.440953942878771\n",
      "\n",
      "The same for the median:\n",
      "38.0 35.0 3.0\n",
      "44.0 41.0 3.0\n",
      "44.0 41.0 3.0 "
     ]
    }
   ],
   "source": [
    "print(\"Remember:\\n We have the following mean values for men, women and the difference:\\nOriginally: \", ml_age.mean(), fm_age.mean(),  ml_age.mean()- fm_age.mean()) # The difference between the mean values of male and female populations.\n",
    "print(\"For high-income: \", ml1_age.mean(), fm1_age.mean(), ml1_age.mean()- fm1_age.mean()) # The difference between the mean values of male and female populations.\n",
    "print(\"After cleaning: \", ml2_age.mean(), fm2_age.mean(), ml2_age.mean()- fm2_age.mean()) # The difference between the mean values of male and female populations.\n",
    "\n",
    "print(\"\\nThe same for the median:\")\n",
    "print(ml_age.median(), fm_age.median(), ml_age.median()- fm_age.median()) # The difference between the mean values of male and female populations.\n",
    "print(ml1_age.median(), fm1_age.median(), ml1_age.median()- fm1_age.median()) # The difference between the mean values of male and female populations.\n",
    "print(ml2_age.median(), fm2_age.median(), ml2_age.median()- fm2_age.median(), end=' ') # The difference between the mean values of male and female populations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.5 Measuring asymmetry (optional).\n",
    "\n",
    "**Skewness** is a statistic that measures the asymmetry of set of $n$ data samples $x_i$:\n",
    "\n",
    "$$ g_1 = \\frac{\\frac{1}{n} \\sum_i (x_i - \\mu)^2 }{\\frac{1}{n} \\sum_i (x_i - \\mu)^3 }$$\n",
    "\n",
    "The numerator is the mean squared deviation (or variance) and the denominator the mean cubed deviation.\n",
    "\n",
    "Negative deviation indicates that the distribution \"skews left\" (it extends farther to the left than to the right).\n",
    "\n",
    "**Skewness** can be affected by outliers!!! A simpler alternative is to look at the relationship between mean ($\\mu$) and median ($\\mu_{\\frac{1}{2}}$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The skewness of the male population is: 0.26644438384328223\n",
      "The skewness of the female population is: 0.3863335249128606\n"
     ]
    }
   ],
   "source": [
    "def skewness(x):\n",
    "    res=0\n",
    "    m=x.mean()\n",
    "    s=x.std()\n",
    "    for i in x:\n",
    "        res+=(i-m)*(i-m)*(i-m)\n",
    "    res/=(len(x)*s*s*s)\n",
    "    return res\n",
    "\n",
    "print(\"The skewness of the male population is:\", skewness(ml2_age))\n",
    "print(\"The skewness of the female population is:\", skewness(fm2_age))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.6 Pearson's median skewness coefficient** is a more robust alternative:\n",
    "\n",
    "$$ g_p = \\frac{3(\\mu - \\mu_{\\frac{1}{2}})}{\\sigma} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Write a function to compute $g_1$ and $g_p$ of the pregnancy length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson's coefficient of the male population is: 0.09520660549016392\n",
      "The Pearson's coefficient of the female population is: 0.2621531209596967\n"
     ]
    }
   ],
   "source": [
    "def pearson(x):\n",
    "    return 3*(x.mean()-x.median())/x.std()\n",
    "\n",
    "print(\"The Pearson's coefficient of the male population is:\", pearson(ml2_age))\n",
    "print(\"The Pearson's coefficient of the female population is:\", pearson(fm2_age))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.6 Relative Risk\n",
    "\n",
    "Let's say that a person is \"early\" promoted if he/she is promoted before the age of 41, \"on time\" if he/she is promoted of age 41, 42, 43 or 44, and \"late\" promoted if he/she is ascended to get income bigger than 50K after being 44 years old. Let us compute the probability of being early, on time and late promoted for men and women:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6601, 15) (1171, 15)\n"
     ]
    }
   ],
   "source": [
    "#ml1 = df[(df.sex == 'Male')&(df.income=='>50K\\n')]\n",
    "\n",
    "ml2 = ml1.drop(ml1.index[(ml1['age'] > df['age'].median() + 35) & (ml1['age'] > df['age'].median() - 15)])\n",
    "fm2 = fm1.drop(fm1.index[(fm1['age'] > df['age'].median() + 35) & (fm1['age'] > df['age'].median() - 15)])\n",
    "\n",
    "print(ml2.shape, fm2.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Men grouped in 3 categories:\n",
      "Young: 38 %.\n",
      "Elder: 48 %.\n",
      "Average age: 14 %.\n"
     ]
    }
   ],
   "source": [
    "print(\"Men grouped in 3 categories:\")\n",
    "print(\"Young:\",int(round(100*len(ml2_age[ml2_age<41])/float(len(ml2_age.index)))),\"%.\")\n",
    "print(\"Elder:\", int(round(100*len(ml2_age[ml2_age >44])/float(len(ml2_age.index)))),\"%.\")\n",
    "print(\"Average age:\", int(round(100*len(ml2_age[(ml2_age>40) & (ml2_age< 45)])/float(len(ml2_age.index)))),\"%.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Women grouped in 3 categories:\n",
      "Young: 48 %.\n",
      "Elder: 37 %.\n",
      "Average age: 15 %.\n"
     ]
    }
   ],
   "source": [
    "print(\"Women grouped in 3 categories:\")\n",
    "print(\"Young:\",int(round(100*len(fm2_age[fm2_age <41])/float(len(fm2_age.index)))),\"%.\")\n",
    "print(\"Elder:\", int(round(100*len(fm2_age[fm2_age >44])/float(len(fm2_age.index)))),\"%.\")\n",
    "print(\"Average age:\", int(round(100*len(fm2_age[(fm2_age>40) & (fm2_age< 45)])/float(len(fm2_age.index)))),\"%.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **relative risk** is the ratio of two probabilities. In order to get the relative risk \\cite{Downey} of early promotion, we need to consider the  fraction of both probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The male mean: 44.317982123920615\n",
      "The female mean: 41.877028181041844\n"
     ]
    }
   ],
   "source": [
    "print(\"The male mean:\", ml2_age.mean())\n",
    "print(\"The female mean:\", fm2_age.mean())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The relative risk of female early promotion is:  21.125440082163816\n"
     ]
    }
   ],
   "source": [
    "ml2_young = len(ml2_age[(ml2_age<41)])/float(len(ml2_age.index))\n",
    "fm2_young  = len(fm2_age[(fm2_age<41)])/float(len(fm2_age.index))\n",
    "print(\"The relative risk of female early promotion is: \", 100*(1-ml2_young/fm2_young))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means that women are 21% more likely to get high gains before 41 years than men."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The relative risk of male late promotion is:  128.9715708971242\n"
     ]
    }
   ],
   "source": [
    "ml2_elder = len(ml2_age[(ml2_age>44)])/float(len(ml2_age.index))\n",
    "fm2_elder  = len(fm2_age[(fm2_age>44)])/float(len(fm2_age.index))\n",
    "print(\"The relative risk of male late promotion is: \", 100*ml2_elder/fm2_elder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means that men are 29% more likely to get high gains after 44 years than women."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussions.\n",
    "\n",
    "After exploring the data, we obtained some apparent effects that seem to support our first assumption:\n",
    "\n",
    "+ **Data description:** The mean age for ascending male professionals is 44 years old while for female professionals it is 41 years.\n",
    "\n",
    "+ **Relative risk:** Female professionals are 21%  more likely to be ascended before 41 years of age, while men are 29% more likely to be ascended being at least 45 years old.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Continous distributions\n",
    "\n",
    "So far, we have built **empirical distributions** (which represent the distributions of values in a sample), based on observations, but many real problems are well approximated by fitting **continous distributions functions (CDF)**. \n",
    "\n",
    "They are called in this way because the distribution is described by an analytical continous function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.1 The exponential distribution\n",
    "\n",
    "The CDF of the exponential distribution is:\n",
    "\n",
    "$$ CDF(x) = 1 -  \\exp^{- \\lambda x}$$ \n",
    "\n",
    "And its PDF is:\n",
    "\n",
    "$$ PDF(x) = \\lambda \\exp^{- \\lambda x}$$\n",
    "\n",
    "The parameter $\\lambda$ determines the shape of the distribution, the mean of the distribution is $1/\\lambda$ and its variance is $1/\\lambda^2$. The median is $ln(2)/\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = 3\n",
    "x=np.arange(0,2.5,0.1)\n",
    "y= 1 - np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential CDF: $\\lambda$ =%.2f' % l ,fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('CDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "\n",
    "l = 3\n",
    "x=np.arange(0,2.5,0.1)\n",
    "y= l * np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential PDF: $\\lambda$ =%.2f' % l, fontsize=15)\n",
    "plt.xlabel('x', fontsize=15)\n",
    "plt.ylabel('PDF', fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a lot of real world events that can be described with this distribution.\n",
    "* The time until a radioactive particle decays,\n",
    "* The time it takes before your next telephone call,\n",
    "* The time until default (on payment to company debt holders) in reduced form credit risk modeling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The random variable $X$ of the lifelengths of some batteries is associated with a probability density function of the form:\n",
    "\n",
    "$$ PDF(x) = \\frac{1}{4} \\exp^{- \\frac{x}{4}}$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = 0.25\n",
    "x=np.arange(0,25,0.1)\n",
    "y= l * np.exp(-l*x)\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Exponential: $\\lambda$ =%.2f' % l ,fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('PDF',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.2 The normal distribution\n",
    "\n",
    "The **normal, or Gaussian distribution** is the most used one because it describes a lot of phenomena and because it is amenable for analysis. \n",
    "\n",
    "Its CDF has no closed-form expression and its more common representation is the PDF:\n",
    "\n",
    "$$ PDF(x) = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp \\left(-\\frac{(x-\\mu)^2}{2 \\sigma^2} \\right)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAEfCAYAAACEbivCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOzdd3xV9f348dc7O2FDwkjCCHuDEAEVcCs4wFn3qLPD1m/tt1W/bdXa2l9brXZotWrdWuoWEEUEt1IJkLBH2BmMsEd23r8/zom9XjJOSO49N8n7+XjcR+79nHHfN5DzvuczRVUxxhhjGiPK7wCMMcY0f5ZMjDHGNJolE2OMMY1mycQYY0yjWTIxxhjTaJZMjDHGNJolE2OMMY1mycQYY0yjWTJppUTkAhH5QER2i0iZiOSLyOsiMsXv2IKJyHMikhXG97tPRDTgUSAib4hIv1r2qRKRvSKySEQeEJHuHs5Z/fgwXJ+rPiISIyJ3ich6ESkVkTwRecTjsUNFZL6IHHF/X/eLSHSoY/ZKRC4VkZnu//NDIrJYRK7weGxEf7ZIEeN3ACb83AvEj4EXgMeB3UBv4HLgPRHpr6obfAwx2G+AxDC/536gOrH2dWOYLyLDVPVwDft0AMYA3wduEZEpqrq4jnMGlkWK54DTgF8Da4CewND6DhKRTsCHwCpgOtAP+BPOl9VfhijWhroD2AT8BCgCzgFeEZFkVf1bbQc1k88WGVTVHq3ogfMHocD1tWw/H0j1O06ff0f3AUVBZRPd39ulte3jlncElgHrgei6zhlJD5wkVw4MPYZj7wb2Au0Dyn4OHAks8/nzJddQ9gqwqbl/tkh5WDVX6/M/wCJVfa6mjao6S1ULAETkBLdqoFBEDotItohcFbi/iHwsIq8HlZ3iVuEMDygbJiLvi8ge91yrReSHXrbXVM3lMbbnRCRLRM4UkWXufp+LyLBj+L1V32X0qWsnVd2Hc7HpD5x5DO9TJxFJdn+3ZwSVPyIi/2nEqW8AFqjqqmM4diowV1UPBJTNwLmbPLmhJxOR7iLyvIjscKsQA6sFg+/2PFHVohqKlwKp9RzapJ+tJbNk0oqISAxwAvCBx0N6A18AN+LcsbwBPOu1rjnILKASuBqYBvwNaNeA7ccaWy/gQeAB4AqgK/BvEZEGxt/H/bndw74fAxXAhOANbrtE4EPc8uoEfEo95x7l/sypoXxZwPtIDe911CPg+PHAOhF5VEQOuO0Db4pIfRdbgME41WLfUNWtON/eB3s4/hsikoBTrTQZJymfD3zmbn4SePAYPlttTgDW1bNPk322ls7aTFqXLkA8sC2w0L2gBTYoVqpjRtA+nwLpwM3Av7y+qYgkAxnAdFVd7hbP97q9Jg2IrTNwkqqud/eNAt4CBhF0kagh7uq/j77A34GDOBe6OqlqiYgUAd2CNnXBqUoKdKZ7TsVJpvVN4z0KKFTVXTWUvxXw+jrg2fpiBaqTanfgepwkdTlOIv8j8JaITFC3fqcWnYB9NZTvdbc1xC9x22pUNR9ARNYAucDnqjpDRK6nYZ/t6A0ipwMX4NyR1aUpP1uLZsmkdQq+MPwU59t7tR8Bj7qNj7/GaWdJ478JJ7+B77cHJ4E9ISJ/BT5S1Z0N2H6UBsS2uTqRuKqrcdKpO5kEX/i3ApepamFdcQWGWEPZfuCMoLK1AKr6Cd7+HkcTdFciIuk4SXNZQPEs4HiPsYITr+Ak9N3ueQuBT3Aa5etM7k3oKuCp6kTi2ojzf7aj+7qhn+1bRKQPTnvJO7VV95qGs2TSuuwGSnEupIFexKmaAVgUUP4cTlXNb3AuwgdweitNb8ibqmqViJyFU9X0DJAoIl8AP1bVpfVtr+W0XmML/lZZ5v5MqCfs6gu/4lRtFdTz7fwbblVNF2BH0KYKVW1sF+dRwHs1lMG3k8keGtZTbC+wsTqRuD7H+X0Npe5kshenN1uwTu42T0RkME51YvDdXwpOoqtO5A39bIHv0Rnn97cFJ3HVp0k+W2tgbSatiKpWAF8BZwWV71DVrMALnXtBPA+4V1UfVdUF7vbg/zMlQFxQ2VG3/6q6RlUvxvl2eQbOxfxdt9qp3u2BGhBbY1S4v5PFqprvNZG4TsX5ovZVE8aDiMQBQ4AVQZtOAvJVNfDidh3OnVV9j2qrqfluSoCqekJbQ1D7gYj0BJKopyoxSPWXnOC70rNxYp3nvm7oZ6uOKQmYjfP/9TxVPeIhpqb6bC2e3Zm0Pn8G3haRa1T1xTr2i8e5OJdWF4hIO5zG8cALax5OY2mgs6iFqpYDC0TkYZyqho443zTr2n6ssYWdiHQE/oBTx9/UAxKHArEEXNxFpC3ON+xlQfs2tCpoNvBrccZdVPd8muy+X3Bjf7D3gJ+JSDtVPeiWXQYU41STeVV9FzkIWALffHH4JfCqqlbfjTS4mstt/3oNGACcWF81aoCm+mwtniWTVkZV3xGRPwPPicipOH+YRTjVMtVJ4JCq7heRRcA9InIA5wJ2F071QvuAU74F3CjOQMh3cb6Vf2tgnoiMBB4C/o1T/90JuBPIUdU9HrYHfwavsYVajIhU99hqB4zFqWpLAqaoaqXXE4nIyThVSae77Sc1GYXTSP9LEanE+fv9MU7j+SYRGaWqOQBuddXuWs5Tkyfdc80Skd+5n+cPwIeq+nlAnNfiVEX2U9UtbvET7rFvisgfcDos3Ac8XN2l1u2l9hFwqqp+XEsM2Tj//n9wP18Vzv+DBJx2PI7xs4HTgeIc4Hagi4h0Cdi2VFVLj/WzGZffA13s4c8DuBCn2mAPTpVAAU732qkB+/THucAdxmmA/jk1D+i7G6cB/SDwEv+9Qxjubu+K0y6zEadabDtOj6teHrc/B2QFvWe9sdVyXB83tvPq+N0c9Rlr2UfdRxXOt+osnHaf7g09J3CKe65T6tjnYZwL7r3u7zofuAWnZ9Nu4OxG/p/oD8xxf6d73d9fp6B9rnfj7BNUPhRYgPONvRCnLStw0OY57nF1DooEhuF0BS4BdrmfrUcT/H/fHPDvFfzo05jPZg/nIe4vyxgT4URkAbBVVa/3O5aGEpFfA5NV9VS/YzGhYQ3wxjQfo3DuTJqjE3HurEwLZW0mxjQDAWNJmmUyUdUmn1rGRBar5jLGGNNoVs1ljDGm0VptNVdycrL26dPH7zCMMaZZWbx4cZGqpgSXt9pk0qdPH7KywrZ4nzHGtAgisqWmcqvmMsYY02iWTIwxxjSaJRNjjDGNZsnEGGNMo1kyMcYY02hhTyYiMkVE1opIrojcVcP2O0RklYgsE5H5ItI7YNt1IrLefVwXUD5WRJa75/yrBE8za4wxJqTCmkxEJBp4DJiKMxPnFSIyNGi3pUCmqo4EXsdZh7p6hbR7gfHAOOBed+lWgMdx1v4e4D6mYIwxJmzCPc5kHJCrqhsBRGQGzjKr1etyo6ofBey/ELjafX42ME9V97jHzgOmiMjHQHtVXeiWvwBcwNFLmxpTr4rKKhZv2cuW3UfYebCEjklxpHdK5Pg+nWkT32qHZRlTr3D/daThrHtRLQ/nTqM2N/LfpFDTsWnuI6+G8qOIyC046z/Qq1evhsRtWridB0p44pONzMzJp+hQ2VHbE2OjOXtYN249uR9DeoRz/S1jmoeI/aolIlcDmcDJTXVOVX0SZ0U5MjMzbYZLQ2WV8tyXm3lk3jpKKyo5Y0g3po9OZWiPDnRtH8/eI2Vs2HmYd5cXMntZAbOWFXLtCb356VmDaGt3KsZ8I9x/DflAz4DX6W7Zt4jIGcAvgJNVtTTg2FOCjv3YLU+v75zGBDtYUs7tM7JZsGYnkwem8Otpw8hIbvOtfXp0SKRHh0QmDkjmzimDeHDuWp77cjOfry/in9cdT68uST5Fb0xkCXdvrkXAABHJEJE44HJgZuAOInIc8A9gmqruDNg0FzhLRDq5De9nAXNVtRA4ICIT3F5c1wLvhOPDmOZr+/4SLn78Sz5Zt4v7pw/j+e8ef1QiCdYxKY4HLhzBSzeOZ+fBUqY/9jmLt+wNU8TGRLawJhNVrQBuw0kMq4FXVXWliNwvItPc3R4E2gKviUi2iMx0j92Ds/byIvdxf3VjPPAD4GkgF9iANb6bOuw+VMpVTy+kYF8Jz393HNee0IeG9CY/qX8yb//wJDokxnL9M1+zIn9/CKM1pnlotYtjZWZmqs0a3PocKCnniicXkrvzEC/cMI7xfbsc87ny9xVz6eNfUlJRxau3nkD/rm2bMFJjIpOILFbVzOByGwFvWo2qKuWOf2ezdvtBnrhmbKMSCUBax0RevnkCUQI3v5DFgZLyJorUmObHkolpNR7/ZAMfrt7JL88dwqmDujbJOTOS2/D3q8aydc8R/vfVHFrrnb4xlkxMq/BlbhEPfbCW6aNTue7EPk167nEZnfm/c4bwwaodPPXZxiY9tzHNhSUT0+IdLCnnZ68vIyO5Df/vohENamz36oaT+jBlWHcemruOdTsONvn5jYl0lkxMi/e7OWso3F/MQ5eOIikuNEOrRITfXjictgkx/O9rOVRUVoXkfYyJVJZMTIv22fpd/Ovrrdw8uS9jenWq/4BGSG4bz2+mD2dZ3n7+8alVd5nWxZKJabHKKqq4952VZCS34SdnDAzLe547sgdTh3fnbwvWk7f3SFje05hIYMnEtFjPfLGJjUWHuff8oSTERoftfX95nrOqwu/mrA7bexrjN0smpkXavr+Ev85fzxlDunFKE3UD9iqtYyI/PKU/c5Zv54vcorC+tzF+sWRiWqSHPlhLRZVyz3nBa6+Fx82T+9KrcxK/mb2Kyiobe2JaPksmpsVZt+Mgby7J47oTevs2q29CbDQ/O3sQa7YfZGaOTWJtWj5LJqbFeWjuWtrExfCDU/r7Gse5I3owLLU9f/rAWSvFmJbMkolpUZZs3csHq3Zwy+S+dGoT52ssUVHCz6cMJm9vMa/8Z6uvsRgTapZMTIvyyLx1dGkTxw0TM/wOBYDJA5IZn9GZv3+8gZJyuzsxLZclE9NiZG/bx2fri7h5cl/aRMiSuiLC7WcMYNfBUl7N2uZ3OMaETNiTiYhMEZG1IpIrInfVsH2yiCwRkQoRuSSg/FR3sazqR4mIXOBue05ENgVsGx3Oz2Qiw9/mr6djUixXT+jtdyjfckLfLmT27sQTH2+grMKmWTEtU1iTiYhEA48BU4GhwBUiEtx3cytwPfBKYKGqfqSqo1V1NHAacAT4IGCXn1VvV9XsUH0GE5lW5O9n/pqd3HBSBm0j5K6kmojwo9MHULC/hDeW5PkdjjEhEe47k3FArqpuVNUyYAYwPXAHVd2sqsuAur7CXQK8p6o2X4UBnLVK2sXHNPn08k1l8oBkRqV34IlPNti4E9MihTuZpAGBFcd5bllDXQ78K6jsARFZJiKPiEh8TQeJyC0ikiUiWbt27TqGtzWRaNueI7y3vJArJ/SiQ2Ks3+HUSES49eR+bNl9hHmrtvsdjjFNrtk1wItID2AEMDeg+G5gMHA80Bm4s6ZjVfVJVc1U1cyUlJSQx2rC45kvNhElwvUReldS7exh3enZOZGnPtvkdyjGNLlwJ5N8oGfA63S3rCG+A7ylqt8suK2qheooBZ7FqU4zrcD+I+X8e9E2po1KpUeHRL/DqVN0lHDTxL4s3rKXxVv2+B2OMU0q3MlkETBARDJEJA6numpmA89xBUFVXO7dCuIsoXcBsKIJYjXNwCtfb+VIWSU3TerrdyieXJqZTofEWJ761O5OTMsS1mSiqhXAbThVVKuBV1V1pYjcLyLTAETkeBHJAy4F/iEiK6uPF5E+OHc2nwSd+mURWQ4sB5KB34b6sxj/VVRW8eJXmzmxXxeGprb3OxxPkuJiuGJcLz5YtZ2CfcV+h2NMkwl7H0pVnQPMCSq7J+D5Ipzqr5qO3UwNDfaqelrTRmmagw9X76Bgfwn3ThvmdygNctX4Xvzj0w3M+Hord5w1yO9wjGkSnu5MRKRLqAMxpqGe+3IzaR0TOWNIN79DaZCenZM4dVBX/rVomw1iNC2G12quAhF5VUSmikiz6wFmWp412w+wcOMerjmhN9FR4nc4DXbNhN7sOljKB9ZN2LQQXhPDrUBXYDawTUR+JyLhWVTbmBq8+NUW4mOiuCyzZ/07R6DJA1Po2TmRlxZu8TsUY5qEp2Siqs+p6inAAOCfwJXAahH5QkRuFJG2IYzRmG85XFrBO9kFnDuyh+/TzB+r6CjhynG9WbhxD+t3HPQ7HGMarUFVVu40KPeoah/gTKASeBLY7k62OCYEMRrzLe8uK+RQaQVXjOvldyiN8p3MdOKio+zuxLQIDW7/EJEkEbkeuAeYCKwCHgGGAItE5GdNGqExQWYs2kq/lDZk9u7kdyiN0qVtPOeO7MGbS/I5XFrhdzjGNIrnZOJODf8ssB34C7AWmKCqI1T1V6o6Hmdak6OmlTemqazbcZAlW/dx+fG9cMaoNm9XT+jFQbfazpjmzGvX4A3AR0B/4MdAD1W9VVW/Dtp1PtC8vy6aiPavr7cSGy1cNOZY5geNPGN6dWJIj/a8uHALqjabsGm+vN6ZvA4MVdVJbmN8jVO/q+piVbWuwyYkSsoreWtpPmcN606XtjVODN3siAhXjuvJ6sIDrCw44Hc4xhwzrxf+lUBRTRtEpLOIXNt0IRlTs7krt7PvSDmXH988uwPXZtqoNOJionh9sS2cZZovr8nkWaBfLdsy3O3GhNSMr7eR3imRk/ol+x1Kk+qQFMtZQ7vxdnY+pRWVfodjzDHxmkzqaunsAtj9uQmpzUWH+Wrjbi7L7ElUMxzxXp9LM3uy70g5C1bv9DsUY45JrRM9ish0vr2k7q9EJHh5wgRgEs7U8saEzL+zthElzkW3JZrYP5nu7RN4bXEeU0f08DscYxqsrlmDu+KsaFitH9A9aJ8y4ANsyncTQpVVyptL8jhlUFe6d0jwO5yQiI5yeqg98ckGdh4ooWv7lvk5TctVazWXqj6lqser6vE464dcXP064HGSqt6oqrbSjwmZLzcUseNAKRePqXFlghbjkrHpVCm8tbShi48a4z+vc3OdqqqrQx2MMTV5c0k+7RJiOH1IV79DCam+KW0Z27sTry3OszEnptmpq83kB8BrqrrLfV4XVdXHvbyhiEzBGUEfDTytqr8P2j4Z+DMwErhcVV8P2FaJs5oiwFZVrV6dMQOYgdMZYDFwjaqWeYnHRLbDpRW8v2I7FxyXSkJstN/hhNylY9O5683l5OTtZ3TPjn6HY4xndbWZPApkAbvc53VRoN5kIiLRwGM4k0Tm4czlNVNVVwXsthW4HvjfGk5RrKqjayj/A/CIqs4QkSeAG73EYyLf+yu2U1xeyUUtvIqr2rkje3DfrJW8lrXNkolpVupqM4mqni7FfV7Xw+tXxnFArjv7cBnO3URgjzFUdbOqLgM8LUEnzgRNp+GM0gd4HrjAYzwmwr21NJ+enROb/aSOXrVLiGXq8B7MzCmgpNzGnJjmI9xTn6QB2wJe51HDmu51SBCRLBFZKCLVCaMLsE9Vq6ddrfWcInKLe3zWrl3BvZxNpCncX8wXG4q48Lj0FjGpo1cXjUnjYEkFH62xMSem+fA60eMkd9xJ9etkEXlFRLJF5E8iEhu6EL+lt6pm4izO9WcRqW1Ufo1U9UlVzVTVzJSUlNBEaJrMO9kFqMJFx7WMSR29OrFfMint4nk723p1mebD653JH4HhAa//ApwOLMRp3/i1x/PkA4GjztLdMk9UNd/9uRH4GDgO2A10FJHq9p8GndNEJlVnbMmYXh3pk9zG73DCKjpKOH9kKh+t2cX+I+V+h2OMJ16TySCcXlKISBJwIXC7qn4P+DlwmcfzLAIGiEiGiMQBlwMzvRwoIp1EJN59ngycBKxSpw/lR8Al7q7XAe94jMdEqJUFB1i341CraXgPdsFxqZRVVvHeikK/QzHGE6/JJA4ocZ+fhNML7F339TrA0/wPbrvGbcBcYDXwqqquFJH7RaS6m+/xIpIHXAr8Q0RWuocPAbJEJAcnefw+oBfYncAdIpKL04byT4+fy0SoN5fkExcdxXkjW+fUIiPSOtA3uY0NYDTNRl1dgwOtAabgVC1dBXylqgfdbanAHq9vqKpzgDlBZfcEPF+EU1UVfNyXfHt6l8BtG3F6ipkWoLJKmZlTwKmDU+iYFOd3OL4QES44Lo2H562jYF8xqR0T/Q7JmDp5vTO5H/iJO9HjlUDgQMMpwNKmDsy0Xgs37qboUCnTR7euhvdg00enAjAzx5b0NZHP63QqM3Gqmb4HDFfV9wI2fwU8EILYTCs1K6eANnHRnDa4ZU+fUp/eXdpwXK+OvG1VXaYZ8DzOxB1o+Iaqrgsqf1JVFzZ9aKY1Kquo4r0V2zlrWPdWMX1KfS4Yncaa7QdZs92WDDKRzWubCSKSAEzGac8Inh/b89xcxtTl89xd7C8u5/xRrbPhPdi5I3tw/+xVvL20gLumtvc7HGNq5SmZiMhE4A2gtpF+nubmMqY+s3IK6ZAYy8T+NqgUILltPJMGJDMzO5+fnz2oRa4yaVoGr9VcfwU24gwSjG/E3FzG1Kq4rJIPVm5n6vDuxMWEe6afyHXB6DQK9peQtWWv36EYU6uGDFq8T1VzVNWG5JqQ+GjtTg6XVTJtVKrfoUSUM4d2IyE2ipk51hBvIpfXZLKMo5fsNaZJzcopILltPOP7dvE7lIjSJj6G04d0Y87y7ZRXeppM25iw85pMvo8zzuTkUAZjWq+DJeUsWLOT80b2INraBY4yfVQqew6X8UVukd+hGFMjr8lkHjAAWCAixSKyM/gRwhhNKzBv1Q5KK6qsF1ctTh6UQvuEGBvAaCKW167Bj+H02DImJGblFJDWMZHjeraORbAaKj4mminDuzNn+XZKyittDI6JOJ6SiareF+I4TCu293AZn60v4sZJGdb1tQ7TRqXxalYeH63ZydQRdgdnIkuD+l+608BPEpErRaSTW5YgItaP0xyz91dup6JKOX+k9eKqywn9upDcNt6qukxE8rrSYoyI/BFnSdxPgBeBDHfzG8C9oQnPtAazcgrom9yGYak2wrsu0VHCeSN7MH/NTg6WWA99E1m83lE8ANyMsxZJXyCwLuId4Pwmjsu0EjsPlPDVxt2cNyq1Va3zfqzOH5VKWUUVc1fu8DsUY77FazK5FrhLVZ8FtgVt24CTYIxpsHeXF6IK06wXlydjenUkvVOiVXWZiOM1mXTESRo1iQM8dy0RkSkislZEckXkrhq2TxaRJSJSISKXBJSPFpGvRGSliCwTkcsCtj0nIptEJNt9jPYaj/HXrJwChvRoT/+u7fwOpVkQEc4flcoXuUXsPlTqdzjGfMNrMlkBTK9l21RgiZeTiEg0TjfjqcBQ4AoRGRq021bgeuCVoPIjwLWqOgxnQa4/i0jHgO0/U9XR7iPbSzzGX9v2HGHJ1n02tqSBpo1KpbJKmbPc1oc3kcPrOJPfAm+ISCLwGs6Yk9EiciFwKzDN43nGAbnuMruIyAycJFW9ljuqutnd9q15IwLXUVHVAnegZAqwz+N7mwgze5lzMbReXA0zuHs7BnRty8ycAq45oY/f4RgDeF9p8R2c5XrPAN7DaYB/GucO4hpVnevx/dL4dptLnlvWICIyDqd6LbDq7QG3+usREYmv5bhbRCRLRLJ27drV0Lc1TWxWTgGje3akZ+ckv0NpVkSE6aNTWbR5L/n7iv0OxxigYSstvqqqfYDBwEScaqpeqvpqiGKrkYj0wOma/F1Vrb57uduN63igM3BnTce6q0JmqmpmSoqtl+Gn3J2HWFV4gPNthuBjUv17m20N8SZCNHiwoaquU9UvVXWNqjZ0ipV8oGfA63S3zBMRaQ+8C/wicKlgVS1URynwLE51molgs5cVIALnjbT2kmPRu0sbRvXsaL26TMSotc1ERO5pyIlU9X4Puy0CBohIBk4SuRyn+qxeIhIHvAW8oKqvB23roaqF4gxUuACnw4CJUKrKrJwCxmd0plv74BWgjVfTRqXym9mr2LDrEP1S2vodjmnl6mqA/1HQ60SgunL7EFD9v/eI+6g3mahqhYjcBszF6U78jKquFJH7gSxVnSkix+MkjU7A+SLya7cH13dw1qDvIiLXu6e83u259bKIpOC05WQD36svFuOfVYUH2LDrMDdMzKh/Z1Or80b24LfvrmJmdgE/OXOg3+GYVq7WZKKq3zQqiMgJwMvAL4G3VLXY7dl1EfAb4Cqvb6iqc4A5QWX3BDxfhFP9FXzcS8BLtZzzNK/vb/w3K6eQmChh6nCr4mqMbu0TmJDRhVk5BfzPGQNsBgHjq4asAf87VX1FVYsBVLVYVV8Gfo8zdsSYelVXcU0ckEznNnF+h9PsTRudysaiw6zIP+B3KKaV85pMhgO1tfTlA0OaJhzT0i3dto/8fcU2tqSJTB3endhosfXhje+8JpN1wB3B4zdEJAG4A1jb1IGZlmlmdgFxMVGcOayb36G0CB2T4pg8IIXZywqpqrL164x/vI6A/xFOO0eeiMwDdgJdgTNxGuWnhiY805JUVinvLi/k1EEptE+I9TucFmPa6FTmr9nJos17GN+3i9/hmFbK6wj4T3HWgH8W6AGc7f58FhjgbjemTv/ZuJtdB0ttoGITO2NINxJio2zMifGV1zsTVLUQ+HkIYzEt3KxlBbSJi+b0wVbF1ZTaxMdwxpBuzFleyH3ThhEbbQufmvCz/3UmLMoqqpizfDtnDu1GYpznFQuMR9NHp7H3SDmf5xb5HYpppSyZmLD4bP0u9heXWxVXiEwemEz7hBhmZVtVl/GHJRMTFrNyCuiQGMukATbBZijEx0QzdXgP5q7cTkl5pd/hmFbIkokJueKySj5YtYNzRnQnLsb+y4XKtNGpHC6rZMGanX6HYlohT3/Z7gqJxhyT+Wt2cKSs0gYqhtiEvl1IaRfPTKvqMj7w+jUxX0T+KCI20t002KycArq2i7cxECEWHSWcO6IHC9bu5EBJud/hmFbGazJ5ArgEWCEi/3FXLGwfwrhMC3GgpJyP1u7i3JE9iI6yiQhDbdroVMoqqpi7YrvfoZhWxuugxftUtS/OiPe1wMNAoYi8LCJnhDJA07zNXSHfrMYAACAASURBVLGdsooq68UVJsf17EjPzok2gNGEXYNaQ1V1gapeC3THmWJlEDBXRDaLyH0iYlcM8y2zlhXSs3Mix/Xs6HcorYKIcP7IVL7csJuiQ6V+h2NakWPtWpOJs1DVYGAv8BlwE5ArIlc3UWymmdt9qJQvcos4f2SqrbURRtNGp1JZpcxZXuh3KKYV8ZxMRKS3iNwrIhuA+Thzc90ApKrqNUBv4B/Ag/WcZ4qIrBWRXBG5q4btk0VkiYhUiMglQduuE5H17uO6gPKxIrLcPedfxa5cEWHO8kIqq5Rpo+2GNZwGd2/PwG5trVeXCSuvXYM/AjbgJI8Xgb6qeraqvqqqZQCqWgm8AtQ68ZLbxfgxnFmGhwJXiMjQoN22Ate75wo8tjNwLzAeGAfcKyKd3M2PAzfjTEY5AJji5XOZ0JqVU8iArm0Z1K2d36G0OtNHp5G1ZS/5+4r9DsW0El7vTHYC5wB93Mb4LbXslw3UtbD3OCBXVTe6SWgGMD1wB1XdrKrLgKqgY88G5qnqHlXdC8wDpohID6C9qi5UVQVeAC7w+LlMiBTsK+brzXuYNsqquPxQPaZnljXEmzDxmkweA750L9bfIiJtRWQygKqW15FoANKAbQGv89wyL2o7Ns19Xu853S7NWSKStWvXLo9va47F7GXORcx6cfmjV5ckRvfsaFVdJmy8JpOPcKqlajLI3R7xVPVJVc1U1cyUFJsjKpRm5RQyMr0DfZLb+B1KqzVtVCqrCg+Qu/OQ36GYVsBrMqmrnqItcMTjefKBngGv092yxhyb7z4/lnOaENi46xDL8/czze5KfHXeyB5ECTbmxIRFrYtjuVVXpwQU3SQiwQ3bCcC5wHKP77cIGCAiGTgX/MuBKz0eOxf4XUCj+1nA3aq6R0QOiMgE4D/AtcDfPJ7ThMDbS/MRsSouv3Vtn8CEvl2YlVPAT84YYG1XJqTqWmlxPM7ARAAFLgUqgvYpA9YAP/PyZqpaISK34SSGaOAZVV0pIvcDWao6U0SOB94COgHni8ivVXWYmzR+g5OQAO5X1T3u8x8AzwGJwHvuw/hAVXkrO5+T+iXTrX2C3+G0etNGpXLXm8tZnr+fkek2cNSEjtTQpn70TiKbgAtVNTv0IYVHZmamZmVl+R1Gi5O1eQ+XPPEVf7p0FBePTa//ABNS+4+Uk/nAPK47oQ+/PK+2Zk9jvBORxaqaGVzudW6ujJaUSEzovLU0n4TYKM4e3t3vUAzQISmWkwemMHtZIVVV9X9xNOZY1dVmcg7wuaoecJ/XSVXnNGlkptkprahk9rJCzh7WnbbxddWgmnA6f1QqH67eydeb9zDBlgEwIVLXX/xsYALwtftcqb1Xl+K0gZhW7OO1zjrvFxzndeiQCYczh3YjMTaamTkFlkxMyNSVTDKAwoDnxtTprSX5JLeNY1L/ZL9DMQGS4mI4Y2g33lteyK+nDSM22pZONk2v1mQSOJK9nlHtxrD/SDkL1uzkqgm9iLGLVcSZPiqVWTkFfL6+iFMHd/U7HNMC1dVmktSQE6mq14GLpgV6d3khZZVVXHSc9eCKRJMHptAhMZaZOQWWTExI1FXNdQinLcQrazNpxd5emk//rm0ZnmarOUeiuJgopg7vzqycAorLKkmMsz9X07TqSiY30LBkYlqpbXuO8PXmPfzs7EE2yjqCTRuVyoxF25i/ZgfnjbTZCUzTqqvN5LkwxmGasTeW5CEC020RrIg2vm8XurdP4I3FeZZMTJOzllLTKFVVyuuL8zipXzLpnRrUzGbCLDpKuHhsGp+s28WOAyV+h2NamFqTiYh8Xb0Koogscl/X+ghfyCaSLNy4m7y9xVyaaQ3vzcElY3tSpc7dpDFNqa42k5VAccBzaz8xR3k1axvtEmI4e5hNn9IcZCS3YVyfzryelcf3T+5nbVymydTVZvLdgOfXhyUa06wcKCnnvRXbuTQznYRY6x3UXFySmc7PX1/G4i17yezT2e9wTAvR4DYTcaSIfaVp9WblFFBaUcWlY3vWv7OJGOeO6EFSXDSvZVlVl2k6npOJiJwjIl8CJcB2oEREvhSRc0MWnYlor2XlMahbO0amd/A7FNMAbeJjOG9kD2YvK+BIWfASRcYcG0/JRERuBWbhDGS8HWehrNvd1zPd7Z6IyBQRWSsiuSJyVw3b40Xk3+72/4hIH7f8KhHJDnhUichod9vH7jmrt9kQ3xBbt+Mg2dv2cWlmutW7N0OXZvbkcFklc5Zv9zsU00J4vTP5P+AfqnqWqj6hqm+6P88CngJ+4eUkIhINPAZMBYYCV1T3GAtwI7BXVfsDjwB/AFDVl1V1tKqOBq4BNgWtsXJV9XZV3enxc5lj9FrWNmKixGYIbqYye3ciI7kNr2Zt8zsU00J4TSZdcJbSrckbgNdWvHFArqpuVNUyYAYwPWif6cDz7vPXgdNraJ+5wj3W+KC8soq3luZz2uCuJLeN9zsccwxEhEvGpvP1pj1sLjrsdzimBfCaTD4CTq5l28nApx7PkwYEfhXKc8tq3EdVK4D9OMks0GXAv4LKnnWruH5lnQNCa8GanRQdKuM7mdbw3pxdPCadKIHXFtvdiWm8umYNDqx++ivwtIh0Ad4GdgJdgQtxqqxuCmWQQXGNB46o6oqA4qtUNV9E2uHcKV0DvFDDsbcAtwD06tUrHOG2SC//Zyvd2sdzyqAUv0MxjdC9QwKnDe7KvxflcfvpA4mLsQkxzLGr63/PCmC5+3gf6AncCrwHZLk/b3HL3/f4fvnu/tXS3bIa9xGRGKADsDtg++UE3ZWoar778yDwCk512lFU9UlVzVTVzJQUuxAei627j/Dpul1cfrytW9ISXDW+N0WHSpm3aoffoZhmrq4R8KeG4P0WAQNEJAMnaVwOXBm0z0zgOuAr4BJggaoqgIhEAd8BJlXv7CacjqpaJCKxwHnAhyGI3QAvf72F6CjhinF2Z9cSTB6YQlrHRF5auIVzR/bwOxzTjNU1Av6Tpn4zVa0QkduAuTjrnzyjqitF5H4gS1VnAv8EXhSRXGAPTsKpNhnYpqobA8rigbluIonGSSRPNXXsBkorKnktK4/TB3ele4cEv8MxTSA6SrhyfC8enLuW3J2H6N+1rd8hmWaqrjuTGrl3B0ddSbyutKiqc4A5QWX3BDwvwRnHUtOxHwMTgsoOA2O9vLdpnPdXbGfP4TKumtDb71BME/pOZk8embeOf329lV+dF9xT3xhvvA5aFBG5071bKAcO1vAwLdzLC7fSq3MSk/on+x2KaUIp7eI5e3h3Xl+cR0l5pd/hmGbKawvqj4G7cKqgBHgAuB9YB2zG7SFlWq51Ow7y9eY9XDm+F1FR1vO6pbl6fG/2F5cze1mh36GYZsprMrkZuBf4o/v6bVX9NTAMWAMMCEFsJoK8vHALcdFRXDrW1i1piSb07UzflDa8tHCL36GYZsprMskAslW1EqeaqyOAqlYBf8fpfWVaqCNlFby5JJ+pI7rTxUa8t0giwlXje5O9bR8r8vf7HY5phrwmk91AdTePrcBxAds6AYlNGZSJLO9kF3CwtIKrreG9RbtkTDrxMVF2d2KOiddk8gVwvPv8FeA+EXlARO4FHgbmhyI44z9V5ZnPNzGkR3sye3fyOxwTQh2SYrnwuDTeWprPnsNlfodjmhmvyeQ+4DP3+e+AZ4Drcaah/wj4flMHZiLDp+uLWL/zEDdNzLCp5luBGyZmUFpRxct2d2IayFMyUdW1qrrAfV6qqrerapqqdlbVy2zK95br6c82ktIunvNHpfodigmDgd3aMXlgCs9/tYXSCusmbLw7lmV700XkeBGxhSxauHU7DvLZ+iKuO6G3TQLYitw0MYOiQ6XMyrFuwsa7hizb+30R2QZsAf4DbBWRPBH5QciiM7565vNNxMdEceV4a3hvTSYNSGZgt7b88/NNuNPiGVMvryPg7wEexZkp+Fwg0/35HvBXd7tpQYoOlfLm0nwuHptO5zZxfodjwkhEuHFiBqsLD/DVht31H2AM3u9Mfgj8TlVvUdX3VXWJ+/Nm4PfudtOCvLxwK2UVVdxwUobfoRgfTB+dRpc2cfzz801+h2KaCa/JJJHaV1P8hBomfjTNV0l5JS8u3Mypg1JsFtlWKiE2mqsn9Gb+mp1s2HXI73BMM+A1mbwNXFTLtouB2U0TjokEM7MLKDpUxk2T+vodivHR1ROcjhfP2N2J8aCuZXvPCXj5HvBHEenD0cv2DgN+HroQTThVVimPf7KBoT3ac2K/Ln6HY3yU0i6ei8ek8driPH58+gC6tbcKCFO7utYzmQ0ozizB1dKAs2vY9yWCltI1zdPsZQVsKjrM41eNsUGKhu+f3J9Xs/L4xycbued8W+vE1K6uaq4MoK/7s76H5/oQEZkiImtFJFdE7qphe7yI/Nvd/h/3bggR6SMixSKS7T6eCDhmrIgsd4/5q9hV8JhUVSmPLshlYLe2nD2su9/hmAjQq0sSF4xO45Wvt1B0qNTvcEwEqzWZqOqWhjy8vJmIRAOPAVOBocAVIhL8dedGYK+q9gceAf4QsG2Dqo52H98LKH8cZ5r8Ae5jipd4zLe9v3I763ce4rbTBtiaJeYbPzy1H2UVVTz12cb6dzatVkMGLcaIyGUi8jcRedn9+R0RacjSv+OAXFXdqKplwAxgetA+04Hn3eevA6fXdachIj2A9qq6UJ0RVi8AFzQgJoMzoePfFuTSN6UN547o4Xc4JoL0TWnLeSNTefGrLey1CSBNLbwOWuwKZOG0i5yLU611Lk4yWCQiKR7fLw3YFvA6zy2rcR9VrQD2A9UtwRkislREPhGRSQH759VzzurPcYuIZIlI1q5duzyG3Dp8uHonqwsP8MNT+hNtdyUmyG2n9edIWSXPfGE9u0zNvN6ZPIxzQZ+gqn1V9QRV7QuMd8sfDlWAAQqBXqp6HHAH8IqItG/ICVT1SVXNVNXMlBSv+a/lc+5K1tOrcxLTR9uEjuZoA7u1Y+rw7jz3xWb2F5f7HY6JQF6TyTnAnar6dWChqi4C7sa5S/EiH+gZ8DrdLatxH7cKrQOw252teLf7vouBDcBAd//AtWRrOqepwyfrdrEsbz8/OKUfMdE2oaOp2W2n9edgaQXPf7nZ71BMBPJ65YgHDtay7SDgdfKmRcAAEckQkTjgcmBm0D4z+e8ywJcAC1RVRSTFbcBHRPriNLRvVNVC4ICITHDbVq4F3vEYT6tXVaU8PG8daR0TuWiMre9uajcstQNnDOnGU59ttLYTcxSvyWQhcKeItAksdF/f6W6vl9sGchswF1gNvKqqK0XkfhGZ5u72T6CLiOTiVGdVdx+eDCwTkWychvnvqeoed9sPgKeBXJw7lvc8fq5Wb/byQpbl7eenZw20aeZNvX529iAOl1bw2Ee5fodiIox4mWJaREbjrKiowAfADpwR8GfjDGo8RVVzQhhnk8vMzNSsrCy/w/BVaUUlZzz8CW3jY3n3RxOtO7Dx5M7Xl/HW0nzm//RkenZO8jscE2YislhVM4PLva60mI1TrfQkkAKciZNMngAGNLdEYhwvLdzKtj3F3D11sCUS49lPzhxIVBQ89MFav0MxEaTeMSIiEoszPmSTqh41Yt00T/uLy3l0wXomDUhm8kDr2Wa8694hgRsnZvDYRxu4aWJfRqR38DskEwG83JlUAguAwSGOxYTRE59sYF9xOXdOsX9W03C3ntyPzm3i+N2c1bYaowE8JBNVrQLWAzZZUwtRsK+YZz7fxIWj0xieZt8qTcO1T4jlx6f156uNu/l4nQ0ANt57c/0CuEdERoQyGBMeD32wFgXuOGug36GYZuzK8b3p3SWJ/zdnNeWVVX6HY3zmNZn8Emeke7aIbBWRRSLydeAjhDGaJpS1eQ9vLsnnpokZpHeynjjm2MXFRPGLc4awbschnrVpVlo9r5M0rgRWhDIQE3oVlVX86p2VpHZI4LbT+vsdjmkBzhrWnTOGdOORees5d2QqaR0T/Q7J+MRTMlHV60MchwmDlxZuYXXhAf5+1RiS4hoy2bMxtbtv2lDOfPhT7pu5kqeuPWr4gWkl6qzmEpFEEblYRH4qIleKSLdwBWaaVuH+Yh76YB2TBiQzdbj1pTBNJ71TEj85cwDzVu3gg5Xb/Q7H+KTWZOLOf7USeA14EGdp3rUiclaYYjNNRFX51dsrqaiq4rcXDLfleE2T++5JGQzu3o77Zq7kcGmF3+EYH9R1Z/JHoAqYBCQBw4ClwD/CEJdpQu+t2M6Hq3fwkzMG0rtLm/oPMKaBYqOjeODC4RTsL+Ev89f7HY7xQV3J5ATgl6r6haqWqOpq4Fagl7u6oWkGdh8q5Z53VjAstT03TszwOxzTgo3t3ZkrxvXin59vInvbPr/DMWFWVzLpAQQv+rwBZ2JHq3RvBlSVX7y1ggPFFfzpO6NsrRITcnefM5ju7RO449Vsissq/Q7HhFF9VxebJ6EZezs7n/dXbueOswYyuHuDFqU05pi0T4jlwUtGsnHXYf7w/hq/wzFhVF//0LkiUlNr2vzgclXt2nRhmcbauvsI97y9krG9O3HzpL5+h2NakRP7J3P9iX147svNnDwohVMH2aWhNagrmfw6bFGYJlVWUcWPZixFBP582WiibXp5E2Z3TR3Mwo27+emrObx3+yS6tU/wOyQTYrUmE1UNSTIRkSnAX4Bo4GlV/X3Q9njgBWAssBu4TFU3i8iZwO9xlgguA36mqgvcYz7GaeMpdk9zlqruDEX8zcFDH6wlZ9s+Hr9qjC1eZHyREBvNo1cex/l/+4L/mZHNSzeNty81LVxYW2TdNdwfA6YCQ4ErRGRo0G43AntVtT/wCPAHt7wIOF9VR+CsEf9i0HFXqepo99FqE8l7ywt58tONXD2hF1NHWKc745/+Xdtx//RhfLVxty2k1QqEu3vPOCBXVTeqahkwA5getM904Hn3+evA6SIiqrpUVQvc8pVAonsXY1zrdxzkf1/L4bheHfnVecE52pjwuzSzJ1eO78XjH2/gveWFfodjQijcySQN2BbwOs8tq3EfVa0A9uPMWBzoYmCJqpYGlD0rItki8iupZYi3iNwiIlkikrVrV8tag2Hv4TJueXExiXExPHH1WOJjov0OyRgA7j1/KMf16shPX8thVcEBv8MxIdLsBh6IyDCcqq9bA4qvcqu/JrmPa2o6VlWfVNVMVc1MSWk5S9WWVlRy60uLyd9bzBNXj7HGThNR4mOieeLqsbRPiOXG5xex40CJ3yGZEAh3MskHega8TnfLatxHRGKADjgN8YhIOvAWcK2qbqg+QFXz3Z8HgVdwqtNahaoq5a43lvP1pj08eOlIMvt09jskY47SrX0Cz1x/PAeKy7nhuUUcsvm7WpxwJ5NFwAARyRCROOByYGbQPjNxGtgBLgEWqKqKSEfgXeAuVf2iemcRiRGRZPd5LHAerWTtFVXlt++u5q2l+fzvWQOZPjq4xtCYyDE0tT2PXjmGNdsPcssLWZSU2wj5liSsycRtA7kNmAusBl5V1ZUicr+ITHN3+yfQRURygTuAu9zy24D+OMsHZ7uPrkA8zuDKZUA2zp3NU+H7VP756/xcnvliE989qQ8/PNUWuzKR79TBXXnwkpF8uWE3P/7XUipsud8WQ1Rb54wpmZmZmpWV5XcYx+yxj3J5cO5aLhqTxkOXjCLK+vCbZuS5LzZx36xVnDuiB3++fDSxNm9csyEii1X1qFXQbLm9ZkZV+duCXB6et44LRqfyx4tHWiIxzc71J2VQUeVU01ap8pfLjyMuxhJKc2bJpBmpcv/4nvliExeNSePBS0bZqGLTbN00qS8iwm9mr+LQ84t4/OqxtI23S1JzZV8FmonSikp+8mo2z3yxietP7MNDlkhMC3DjxAz+eLHThnLlUwvZdbC0/oNMRLJk0gzsOljKFU8u5J3sAn529iDuPX+oVW2ZFuM7x/fkyWvGsm7HQaY/+jkrC/b7HZI5BpZMItySrXuZ/ujnrCo8wN+vGsMPT+1va7ibFuf0Id14/XsnosAlj3/FO9nBw89MpLNkEqGqqpSnP9vId574iqgo4fXvncg5NnGjacGGp3XgndtOYnhae26fkc3dby63sSjNiLV2RaDC/cX8/PVlfLa+iDOHduOhS0bRISnW77CMCbmu7RL4180T+NO8dTz+8Qa+2lDEHy4eyfi+wdPzmUhjdyYRpKKyiue/3MxZj3zK4i17+e0Fw3nymrGWSEyrEhMdxZ1TBvPKzeOpUrjsyYX86u0VNgVLhLM7kwixcONu7pu5kjXbDzKxfzIPXDic3l3a+B2WMb45sV8y7//PJP70wTqe+WIT81fv4BfnDuWcEd2t3TAC2Qh4n20uOsyf5q1jVk4BaR0T+dV5Qzh7mP2xGBNoyda93P3GctbuOMjI9A78/OzBTByQ7HdYrVJtI+AtmfhkzfYDPPbRBt5dVkBsdBS3ntyP75/cj8Q4W4fEmJpUVilvLc3nkXnryN9XzMT+yfzotP6My+hsX77CyJJJED+SSVWV8sWGIp7/cgsfrt5Bm7horj6hNzdOzKBrO1uDxBgvSsorefk/W3nso1z2HC5jSI/2fPfEPkwbnUpCrH0ZCzVLJkHCmUy27TnCa4vzeGNxHvn7iumUFMv1J2Zw3Ym96ZgUF5YYjGlpissqeTs7n+e/3Mya7QfplBTLRWPSOX9UKqPSO9jdSohYMgkSymSiqqzbcYgPV+9g3qodZG/bhwhMGpDCdzLTOWNIN/sGZUwTUVUWbtzDC19tZv7qnZRVVtGzcyLnjkhlyvDujEjrYFMPNSFLJkGaMpmoKnl7i1m0eQ+LNu/l89xdbNtTDMCo9A6cObQbF45JJ61jYpO8nzGmZvuLy5m3agezcgr4PLeIyiqlQ2IsJ/brwsQByUzo24WMLm1sOqJGsGQS5FiTiaqSv6+Y1YUHWV14gFUFB8jJ20fhfmdd63YJMYzP6MzpQ7px+uCudLX12I3xxd7DZXyWW8Tn63fx+foiCgL+Rkeld2RkegdGpHVgQLe29O7SxtZU8ShikomITAH+AkQDT6vq74O2xwMvAGNx1n6/TFU3u9vuBm4EKoEfq+pcL+esybEmk2uf+ZpP1+365nWfLkkMS+vAuD6dOb5PZwZ1b2e31MZEGFVlY9FhFm/eS3bePpbl7WNN4UEqqpzrX0yU0Ce5DRnJbUjrmEhqxwR6dEgk1X3etV2C/V27IiKZiEg0sA44E8jDWRP+ClVdFbDPD4CRqvo9EbkcuFBVLxORocC/gHFAKvAhMNA9rM5z1uRYk8nMnAL2F5cztEd7BndvRxtbf8GYZqmkvJL1Ow6Ru+sguTsPsX7HITbvPkzhvhIOBo22jxLokBhLp6Q4OiZV/3Set4mLJik+hqS4aBJjo0mKiyEpPpok93lcTBQx0UJctPMzNjqK2KgoYmOEmKgoYqOlWXUWiJSVFscBuaq60Q1qBjAdCLzwTwfuc5+/Djwqzm96OjBDVUuBTe4a8ePc/eo7Z5OZNio1FKc1xoRZQmw0I9I7MCK9w1HbDpSUU7ivhIL9xRTsK2b7/hL2Hilj75Fy9h0po3B/CasLD7CvuJwjZY2fjDImSoiKEqIEokQQ3J8CUVGBr92ygP1EhKgoEJzjxS0HqH5S/bo6aT1z3fH06pLU6Li/9Rma9Gz1SwO2BbzOA8bXto+qVojIfqCLW74w6Ng093l95wRARG4BbgHo1avXsX0CY0yL1z4hlvbdYxnUvV29+1ZVKSUVlRwpq+RIaSVHyis4UlZJcVklh0srKK9UKqqqKKuooqJKKa+scsoqq755Xl5ZRaUqKFSpUuX+VHWq6KoUFPenW16933/3URRwa+6ornX6pu4poBIqFEskt6o6GlV9EngSnGoun8MxxrQAUVHiVG3FxUBbv6PxT7i7L+QDPQNep7tlNe4jIjFAB5yG+NqO9XJOY4wxIRTuZLIIGCAiGSISB1wOzAzaZyZwnfv8EmCBOvdrM4HLRSReRDKAAcDXHs9pjDEmhMJazeW2gdwGzMXpxvuMqq4UkfuBLFWdCfwTeNFtYN+Dkxxw93sVp2G9AvihqlYC1HTOcH4uY4xp7WzQojHGGM9q6xpsQz6NMcY0miUTY4wxjWbJxBhjTKNZMjHGGNNorbYBXkR2AVuO8fBkoKgJwwkFi7FpRHqMkR4fWIxNJVJi7K2qKcGFrTaZNIaIZNXUmyGSWIxNI9JjjPT4wGJsKpEeo1VzGWOMaTRLJsYYYxrNksmxedLvADywGJtGpMcY6fGBxdhUIjpGazMxxhjTaHZnYowxptEsmRhjjGk0SyYNJCJTRGStiOSKyF1+xxNIRHqKyEciskpEVorI7X7HVBsRiRaRpSIy2+9YaiIiHUXkdRFZIyKrReQEv2MKJiI/cf+dV4jIv0QkIQJiekZEdorIioCyziIyT0TWuz87RWCMD7r/1stE5C0R6RhpMQZs+6mIqIgk+xFbbSyZNICIRAOPAVOBocAVIjLU36i+pQL4qaoOBSYAP4yw+ALdDqz2O4g6/AV4X1UHA6OIsFhFJA34MZCpqsNxll+43N+oAHgOmBJUdhcwX1UHAPPd1356jqNjnAcMV9WRwDrg7nAHFeQ5jo4REekJnAVsDXdA9bFk0jDjgFxV3aiqZcAMYLrPMX1DVQtVdYn7/CDOBTDN36iOJiLpwLnA037HUhMR6QBMxllbB1UtU9V9/kZVoxgg0V2RNAko8DkeVPVTnHWIAk0HnnefPw9cENaggtQUo6p+oKoV7suFOCu2+qaW3yPAI8DP+daK7pHBkknDpAHbAl7nEYEXawAR6QMcB/zH30hq9GecP4gqvwOpRQawC3jWrYp7WkTa+B1UIFXNBx7C+YZaCOxX1Q/8japW3VS10H2+HejmZzAe3AC853cQwURkOpCvqjl+x1ITSyYtkIi0Bd4A/kdVD/gdTyAROQ/YB53BYgAAAwZJREFUqaqL/Y6lDjHAGOBxVT0OOIz/VTPf4rY7TMdJfKlAGxG52t+o6ucuwR1x36qricgvcKqLX/Y7lkAikgT8H3CP37HUxpJJw+QDPQNep7tlEUNEYnESycuq+qbf8dTgJGCaiPz/9u4exM4iDMPw/TQqgq1ECBgRSaGFKIKYzigElZQ2smwkpNNa7EUCgpWFKWzEH5AguNiIoGChhRBMggoqKnoKf1oRxOK1mFE26yobppgJ3Bcsu3zVw+5+PN/MOWfe72nbhA8meW1upH/ZAJuq+ntVd55WLit5CPiuqn6tqj+Bt4EHJmf6Lz8nuQWgf/9lcp59JTkFPAY8Uet9AO922oPDxX7vHAYuJDk0NdUulsnV+RS4I8ltSa6jveC5MznTP5KEts//ZVW9ODvPfqrq2ao6XFVHaL+/D6pqqSfqqvoJ+DHJ0X7pOPDFxEj7+QG4P8mN/e9+nMXeJLDLDrDdf94G3pmYZV9JTtC2Xk9W1e+z8+xVVZer6uaqOtLvnQ1wT/9fXYJlchX6C3RPAe/Rbty3qurzuamucAzYoj3tf9a/Hpkd6hr1NPB6kkvA3cDzk/Ncoa+azgMXgMu0e3n6cRtJ3gQ+AY4m2SQ5DZwFHk7yNW1FdXbBjC8BNwHv9/vm5QUzLs3jVCRJw1yZSJKGWSaSpGGWiSRpmGUiSRpmmUiShlkmkqRhlokkaZhlIkkaZplIk/VBXJskr+65vpPkq37In7Q0y0SarM9KOQ1s9WPGSfIkbebL9opnRUl7eZyKtIgk52iDo04AHwLnquqZuamkg7FMpEX0OTSXaPNJvgHurao/5qaSDsZtLmkRVfUb8C5wPfCKRaJriSsTaRFJ7gM+ph0pfytw50rzKqT/Y5lIC0hyA202ybfA48BF2pCzk1ODSQfkNpe0hueAQ8CZ/u6tU8CjfZSstDxXJtJkSY4BHwFbVfXGrusvAGeAu6pqMyufdBCWiSRpmNtckqRhlokkaZhlIkkaZplIkoZZJpKkYZaJJGmYZSJJGmaZSJKG/QVzPHZgzQztKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u=6 # mean\n",
    "s=2 # standard deviation\n",
    "x=np.arange(0,15,0.1)\n",
    "y=(1/(np.sqrt(2*np.pi*s*s)))*np.exp(-(((x-u)**2)/(2*s*s)))\n",
    "plt.plot(x,y,'-')\n",
    "plt.title('Gaussian PDF: $\\mu$=%.1f, $\\sigma$=%.1f' % (u,s),fontsize=15)\n",
    "plt.xlabel('x',fontsize=15)\n",
    "plt.ylabel('Probability density',fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examples:\n",
    "    * Measures of size of living tissue (length, height, skin area, weight);\n",
    "    * The length of inert appendages (hair, claws, nails, teeth) of biological specimens, in the direction of growth; presumably the thickness of tree bark also falls under this category;\n",
    "    * Certain physiological measurements, such as blood pressure of adult humans.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.5 Central Limit Theorem\n",
    "\n",
    "The normal distribution is also important, because it is involved in the Central Limit Theorem:\n",
    "\n",
    "> Take the mean of $n$ random samples from ANY arbitrary distribution with a $well$ $defined$ standard deviation $\\sigma$ and mean $\\mu$. As $n$ gets bigger the **distribution of the sample mean** will always converge to a Gaussian (normal) distribution with mean $\\mu$ and standard deviation $\\frac{\\sigma}{\\sqrt{n}}$.\n",
    "\n",
    "Colloquially speaking, the theorem states the distribution of an average tends to be normal, even when the distribution from which the average is computed is decidedly non-normal. This explains the ubiquity of the Gaussian distribution in science and statistics. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Uniform Distribution\n",
    "\n",
    "The uniform distribution is obviously non-normal.  Let's call it the $parent$ $distribution$.\n",
    "\n",
    "To compute an average, two samples are drawn ($n=2$), at random, from the parent distribution and averaged. Then another sample of two is drawn and another value of the average computed.  This process is repeated, over and over, and averages of two are computed.  \n",
    "\n",
    "Repeatedly taking more elements ($n = 3,4...$) from the parent distribution, and computing the averages, produces a normal probability density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  import sys\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 4, sharey=True, squeeze=True, figsize=(14, 5))\n",
    "x = np.linspace(0, 1, 100)\n",
    "for i in range(4):\n",
    "    f = np.mean(np.random.random((10000, i+1)), 1)\n",
    "    m, s = np.mean(f), np.std(f, ddof=1)\n",
    "    fn = (1/(s*np.sqrt(2*np.pi)))*np.exp(-(x-m)**2/(2*s**2))  # normal pdf            \n",
    "    ax[i].hist(f, 40, normed=True, color=[0, 0.2, .8, .6]) \n",
    "    ax[i].set_title('n=%d' %(i+1))\n",
    "    ax[i].plot(x, fn, color=[1, 0, 0, .6], linewidth=5)\n",
    "plt.suptitle('Demonstration of the central limit theorem for a uniform distribution', y=1.05)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.6 Kernel density estimates\n",
    "\n",
    "In some instances, we may not be interested in the parameters of a particular distribution of data, but just a **continous representation** of the data at hand. In this case, we can estimate the distribution non-parametrically (i.e. making no assumptions about the form of the underlying distribution) using kernel density estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa31b037358>]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats.distributions import norm\n",
    "\n",
    "# Some random data\n",
    "y = np.random.random(15) * 10\n",
    "x = np.linspace(0, 10, 100)\n",
    "\n",
    "x1 = np.random.normal(-1, 2, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 3, 10)\n",
    "y = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n",
    "x = np.linspace(min(y), max(y), 100)\n",
    "\n",
    "\n",
    "# Smoothing parameter\n",
    "s = 0.4\n",
    "\n",
    "# Calculate the kernels\n",
    "kernels = np.transpose([norm.pdf(x, yi, s) for yi in y])\n",
    "\n",
    "plt.plot(x, kernels, 'k:')\n",
    "plt.plot(x, kernels.sum(1), 'r')\n",
    "plt.plot(y, np.zeros(len(y)), 'go', ms=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa3187f94a8>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW0AAAD4CAYAAAAn3bdmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nO3dd3gU1foH8O9JARJCk6r0jhTpoYnSQRCUooKUawPBiFxEsF7LFQVFgZ+oKAgIgiiioNKkI6iACb0ECNXQS0IKqTvf3x8nOzchbZPsZnaT9/M8+yybzJ55s8y8e+a0USQhhBDCM3hZHYAQQgjHSdIWQggPIklbCCE8iCRtIYTwIJK0hRDCg/i4otBy5cqxRo0arihaCCEKpJCQkGsky2e3nUuSdo0aNRAcHOyKooUQokBSSp11ZDtpHhFCCA8iSVsIITyIJG0hhPAgkrSFEMKDSNIWQggPIklbCCE8iCRtIYTwIJ6dtENCgC++AE6etDoSIYTIFy6ZXJMvEhOBQYOAM2f067p1gTFjgPHjLQ1LCCFcyXNr2l99pRP2V18Bs2YB5coBL74IhIZaHZkQQriMZybtW7eAyZOBjh2Bp54Cnn8eWLkSKFoU+OQTq6MTQgiX8cyk/dlnwMWLwHvvAUrpn1WoAAwbBixcCNy4YW18QgjhIp6XtKOigKlTgV69dE07tXHjdC187lxrYhNCCBfzvKQ9Y4auSU+enP53TZoAXbsCn34KJCXlf2xCCOFinpe0v/0W6NEDaNky49//+99AeDjw00/5G5cQQuQDz0raFy8Cx4/rpJ2Z3r2BOnV0jVwIIQoYz0ra27bp5/vvz3wbLy9g1Chg1y5d4xZCiALEs5L21q1AyZJAs2ZZb2eviW/a5PKQhBAiP3lW0t62Dbj3XsAnm4mcTZroyTaStIUQBYznJO1Ll/Rsx06dst/Wywvo0kUnbdLloQkhRH7xnKT9++/6Oav27NS6dgUuXNAdl0IIUUB4TtLetg0ICABatHBs+y5d9LM0kQghChDPSdpbtzrWnm1XuzZQrZokbSFEgeIZSfvKFeDIEcebRgC9JknXrsCWLYDN5rrYhBAiH3lG0ra3ZzvSCZla165ARASwb5/TQxJCCCt4RtLetg0oXjzzqeuZkXZtIUQB4xlJe8cOoF07wNc3Z++7806gYUNg82bXxCWEEPnM/ZN2crJuz3Z01MjtunQBtm/XtycTQggP5/5J+8QJnXAbN87d+++7T6+xfeCAc+MSQggLuH/SPnRIP+c2aQcG6ue//3ZOPEIIYSHPSNpeXkCDBrl7f7VqQPnywO7dzo1LCCEs4BlJu04dwM8vd+9XSte2JWkLIQoAz0jauW0asWvdGjh6FIiOdk5MQghhEfdO2nFxQFhY3pN2YKBe7S8kxDlxCSGERdw7aYeGAobhnJo2IE0kQgiP51DSVkqNV0odVkodUkotVUoVc3VgAPI+csSuXDmgZk0ZQSKE8HjZJm2lVGUALwBoRbIxAG8Ag10dGACdtIsU0R2ReSWdkUKIAsDR5hEfAH5KKR8A/gAuuC6kVA4d0kP9cjp9PSOBgcC5c/oOOEII4aGyTdokzwP4CMA5ABcB3CS5/vbtlFKjlFLBSqngq1evOie6gwfz3jRiZ2/XliYSIYQHc6R5pAyAhwDUBHAXgOJKqWG3b0dyDslWJFuVL18+75HdvAn884/zknaLFnqSjiRtIYQHc6R5pBuA0ySvkkwC8BOA9q4NC8Dhw/q5SRPnlFe8ONCokbRrCyE8miNJ+xyAtkopf6WUAtAVwFHXhgXnjRxJLTBQ17TlDu1CCA/lSJv2LgDLAewBcDDlPXNcHJdO2gEBeu0QZwkMBG7cAE6dcl6ZQgiRjxwaPULyLZINSDYmOZxkgqsDw6FDujnDy4nzf+x3vtmzx3llCiFEPnLfGZGHD+u7zjhT48Z6+KBMZxdCeCj3TNpRUfoO7PXqObfcokV14paathDCQ7ln0j55Uj/Xrev8slu00ElbOiOFEB7IPZP2iRP62RnT12/XogVw/bqeHSmEEB7GPZN2WJh+rl3b+WVLZ6QQwoO5b9K+80495M/Z7rkH8PaWpC2E8EjumbRPnHBN0wigb1t2992StIUQHsk9k3ZYmOuSNqCbSEJCpDNSCOFx3C9px8To5VNdMXLErkUL4PJl4OJF1+1DCCFcwP2Str0T0pU17RYt9LM0kQghPIz7Jm1X1rSbNQOUkpmRQgiP435J2z5G2xXD/ewCAoD69aWmLYTwOO6XtMPCgIoVgRIlXLsf+8xIIYTwIO6ZtF3ZNGLXogUQHq7XOBFCCA/hfknblWO0U7PPjJR2bSGEB3GvpB0bq4fh5VdNWym5Z6QQwqO4V9K2r+6XHzXtkiV1Z2RwsOv3JYQQTuJeSduVq/tlpHVruWekEMKjuFfSzo+JNam1aqVnX164kD/7E0KIPHK/pF2hgm66yA+tW+tnadcWQngI90raJ07kTyekXbNmeplWadcWQngI90rarl7d73Z+fvqekVLTFkJ4CPdJ2jabrmW3apW/+23dWte0pTNSCOEB3Cdpe3sDW7YAzz+fv/tt1Qq4cQM4fTp/9yuEELngPknbKtIZKYTwIJK0GzcGihaVzkghhEeQpF2kCNC0qdS0hRAeQZI2oJtIQkIAw7A6EiGEyJIkbUB3RsbEAMeOWR2JEEJkSZI2AAQG6uedO62NQwghsiFJGwAaNADKlAH++MPqSIQQIkuStAHAywvo0AHYscPqSIQQIkuStO06dNBt2levWh2JEEJkyqGkrZQqrZRarpQKVUodVUq1c3Vg+e7ee/Xzn39aG4cQQmTB0Zr2/wFYR7IBgKYAjrouJIu0aqXHbEu7thDCjflkt4FSqhSA+wA8AQAkEwEkujYsCxQrpm/2K+3aQgg35khNuyaAqwAWKKX2KqW+UkoVv30jpdQopVSwUir4qqe2C997r55kEx9vdSRCCJEhR5K2D4AWAGaTbA4gFsArt29Ecg7JViRblS9f3slh5pMOHYDERFmHRAjhthxJ2uEAwknuSnm9HDqJFzzt2+tnaSIRQripbJM2yUsA/lFK1U/5UVcAR1walVXKlwfq15fOSCGE28q2IzLFWABLlFJFAJwC8KTrQrJYhw7AihV68SgvGcYuhHAvDmUlkvtS2qvvIfkwyQhXB2aZe+8FIiKA0FCrIxFCiHSkKnk7+ySbrVstDUMIITIiSft2deoA1asDGzZYHYkQQqQjSft2SgE9egCbNwNJSVZHI4QQaUjSzkjPnkBUFLBrV/bbCiFEPpKknZEuXfTIkfXrrY5ECCHSkKSdkTJlgDZtgN9+szoSIYRIQ5J2Znr00Hdov3HD6kiEEMIkSTszPXsCJLBpk9WRCCGESZJ2Zlq3BkqVkiYSIYRbkaSdGR8foFs33RlJWh2NEEIAkKSdtR49gH/+kSntQgi3IUk7Kz176ue1a62NQwghUkjSzkr16kCzZsCPP1odiRBCAJCknb1Bg/Qd2s+ftzoSIYSQpJ2tQYP0808/WRuHEEJAknb26tcHGjcGli+3OhIhhJCk7ZBBg4Dt24GLF62ORAhRyEnSdsSgQXqs9ooVVkcihCjkJGk7omFDoEEDaSIRQlhOkrYjlNK17W3bgCtXrI5GCFGISdJ21KBB+g7tMopECGEhSdqOuuce3USyeLHVkQghCjFJ2o5SCnjiCeCPP4Djx62ORghRSEnSzonhw/VtyBYutDoSIUQhJUk7J+66Sy8itXAhYLNZHY0QohCSpJ1TTz6p1yGRO9oIISwgSTun+vbVN/79+murIxFCFEKStHOqWDHg8cf17MjISKujEUIUMpK0c+OJJ4D4eOC776yORAhRyEjSzo2WLYEmTYCvvrI6EiFEISNJOzeUAkaNAkJC9EMIIfKJJO3cGjYM8PMD5syxOhIhRCEiSTu3SpcGBg8Gvv0WiI62OhohRCHhcNJWSnkrpfYqpVa5MiCPMmoUEBMDLF1qdSRCiLwyDCA0FLh50+pIspSTmvY4AEddFYhHatNGLyT15ZdWRyKEyI34eODzz4GHHwbKlwfuvls/9+oFfPGFWyZwh5K2UqoKgD4AZLhEakoBzz4L7NkDBAdbHY0QwlEk8OOP+gYnQUHAoUM6cc+dC4wbB4SFAWPGAB06AFevWh1tGo7WtGcCmATAyGwDpdQopVSwUir4qpv9kS41dCjg7y+1bSE8xfHjQJcueo18f39g/XqdpOfNA555Bpg2DThxAli3Djh5EujeHbhxw+qoTdkmbaXUgwCukMxybBvJOSRbkWxVvnx5pwXo9kqV0h2SS5cCUVFWRyOEyIzNBnz0EdC0KbBvH/DZZ/q5e/f02yqlF4f7+Wfg6FH9bzdpKnGkpt0BQD+l1BkA3wHoopSSOwGk9uyzQGysHkkihHA/u3cD7dsDEycCPXoAhw8Dzz0H+Phk/b4ePXQzyv79emlmN5Bt0ib5KskqJGsAGAxgM8lhLo/Mk7RuDTRrpptISKujEULYnT2r1wpq0wY4c0ZXrFau1MssO+rBB4HJk4FffwU2bnRZqI6ScdrOYO+Q3LcP+Ptvq6MRonBLSgJWrwYeewyoV08v7vb667rdesgQfb7m1AsvADVrAhMmWL6Wfo6SNsmtJB90VTAe7fHHgeLFpUNSiPx29ape337qVGDgQKByZV073rwZGD1adypOngyUKJH7fRQrBnzwAXDggOXLMiu64HK+VatWDC6MQ+BGjtSXXxcu6A5KIYRzJSfr9um1a4Ht23Xb9LVr//t97dq6KeSxx4AHHgB8fZ23bxK4917g1Cn9RRAQ4LyyASilQki2ym47aR5xpmefBW7dkju2C+FsN24AL70EVKigx06//z4QF6fHVk+froftXb+um0CWLAH69XNuwgZ0s8rHHwOXLgEffujcsnMShtS0naxlS92mtn9/7trOhBD/k5Cgh+ZNnqxvOvLYY0D//nqYXpky1sQ0aJBujjl/Xo/zdhKpaVtl1Cjg4EF9CSeEyL2rV4GOHXXnX5s2uiK0dCnw6KPWJWwAGDtWf4F8/70lu5ek7WxDhuhv37lzrY5ECM91+rRuBjl4EFi+XLdhN2lidVTafffpNUq++MKS3UvSdraSJXXi/u47mSEpRG7s368nwly7ppshBg60OqK0lNKjUnbv1usO5TNJ2q4wcqSeISlLtgqRMxcu6BX2fHyAHTt08nZHI0boK+rZs/N915K0XSEwUF/KSROJEI5LTNSdfNHRujmkYUOrI8pc6dL6ivrbb/N9TRJJ2q6Q+h6SFlw+CeGRxo0D/voLWLAAaNzY6miyN3q0HuL7zTf5ultJ2q4ydKieRSW1bSGyN3++7th7+WXgkUesjsYxrVrpRz7fJ1aStquUKaOHJi1Zotu3hRAZO31aD6Pr1g147z2ro8mZf/1Lj3A5fDjfdilJ25VGjdLtcxaN5xTC7ZH6PPH21rVtb2+rI8qZQYMAL698PcclabtS+/Z6PGc+Xz4J4TEWLNDLnX74IVC1qtXR5FylSkCnTjpp59OyzJK0XcneIblrlx57KoT4nwsXgBdf1JNVRo2yOprcGzxY38Js37582Z0kbVcbPhwoWlQ6JIW43fPP67VFvvpKNzF4qgED9LjyfGoi8eBPykOULavbvb75Rg8PEkLocdgrVgBvvgnUrWt1NHlTtqxewOq77/KliUSSdn4YNUpPaV+2zOpIhLBeQoIek12vnm4eKQgGD9a3Ntu1y+W7kqSdHzp2BOrXl7vaCAEAM2bomwh88oluOiwIHnoIKFIkX5pIJGnnB/s9JHfuzLfOCiHcUng48O67Osn17Gl1NM5TqhTQu7e+mjYMl+5KknZ+eeIJwM9PL+guRGH10kv6xrgzZlgdifNNnKjPbxe3a0vSzi9lyuip7UuWABERVkcjRP7bulU3H7z8sr6zeUHTvr2+/ZmLJwhJ0s5PQUH6vnYW381ZiHyXlKSnqteoAbzyitXReDRJ2vmpWTP9bfz55y5v9xLCrXz+OXDokG4W8fOzOhqPJkk7vwUF6TtGb9hgdSRC5I/Ll/V47J49dQekyBNJ2vlt4ECgQgXpkBSFxyuv6GbBTz7RI6lEnkjSzm9Fi+rJNqtW6fUKhCjItmzRfTgTJujJNCLPJGlbIShID8SfPt3qSIRwnVu39P1S69QB/vMfq6MpMCRpW6FSJb14+tdf6/Y+IQqiN98ETp7Ui6X5+1sdTYEhSdsqEyboG5nOmmV1JEI43+7deqTIs8/q9aaF00jStkq9ekD//rpDMibG6miEcJ74eODpp4E77wQ++MDqaAocSdpWmjQJiIzU6wkLUVC88IIekz1njl6TQziVJG0rtWmj79oxfbpuKhHC0y1YoNuwX31VL6AknE6SttVeew345x+pbQvPt28f8NxzQJcuwH//a3U0BVa2SVspVVUptUUpdUQpdVgpNS4/Ais0evTQte133wViY62ORojcuXJFTxwrWxZYulTffku4hCM17WQAE0g2BNAWQJBSqqFrwypElALefx+4dAn49FOroxEi565c0bXrixeBH37QM36Fy2SbtEleJLkn5d/RAI4CqOzqwAqVDh2APn10T3tkpNXRCOE4e8I+dUrP8m3XzuqICrwctWkrpWoAaA4g3Y3QlFKjlFLBSqngq1evOie6wmTyZL3O9kcfWR2JEI45fRro3Fkn7NWrdfIWLudw0lZKBQD4EcC/SUbd/nuSc0i2ItmqfPnyzoyxcGjWTN8cdMYM4MIFq6MRInMksHAh0LSpvn3YmjU6eYt84VDSVkr5QifsJSR/cm1Ihdh77+lbMU2YYHUkQmTs3Dngscf07fOaNwcOHJAZj/nMkdEjCsA8AEdJygpHrlSrlh7f+t13wKZNVkcjxP8cOgSMGAHUrg2sWAFMmQJs3gxUr251ZIWOYjY3oVRK3QtgO4CDAOy3W3mN5JrM3tOqVSsGBwc7LchCJT4eaNxYD5nav18v5SpEfktOBoKDdVv16tXA3r160aeRI4EXXwSqVbM6wgJHKRVCslV222U7mJLkDgCycnl+KVZMLyLVu7eeKfnqq1ZHJAo6w9B3UwoOBv7+Wz/27NE3LvDy0qObpk0DnnxSj8MWlsq2pp0bUtN2ggEDgHXr9GVprVpWRyMKElIfVxs36tve/fEHEJUytsDPT7dVBwYCbdsC3bsDd9xhbbyFhNNq2sIi//d/upnkiSf03T+8va2OSHi6y5f1Gu5z5+p1rgGgfn1gyBCdpFu1Aho2lNmMbk7+d9xV1ao6cT/5JDBzpowoEbn3zz/A66/r6eXJyXrZhFde0UsoSNu0x5Gk7c7+9S/dU//660CvXkCjRlZHJDxJTAzw4Yd6wpZhAM8/r29K0KCB1ZGJPJBV/tyZUnpN4hIl9HCrpCSrIxKeIiQEuOcevRDZQw8Bx47piVuSsD2eJG13V7Ei8MUXujf/zTetjka4O1J/0bdvr5tCfv9dN4vIeOoCQ5K2Jxg4UI+PnToVWL/e6miEu0pK0rf5evZZvQ7I3r1Ax45WRyWcTJK2p5g5U7dpDx+ul3EVIrWEBD29fMECfUW2erWMqS6gJGl7Cn9/4PvvgehonbgNI/v3iMIhLk7fJHrFCuCTT4B33tGTYkSBJP+znqRRI31SbtyoF5cSIj4e6NtXT8SaMwcYO9bqiISLSdL2NE8/DQwdCrz1liwqVdgZhr7q2rRJT5oZOdLqiEQ+kKTtaZTSo0kaNAAefxw4f97qiIQVSGD8eGD5cj0Oe8QIqyMS+USSticKCAB+/FHfCHjwYBm/XRh9/LFuKvv3v/Wqe6LQkKTtqe6+W7dh7tihpySLwmPFCmDiROCRR3TyVrIIZ2HiVkl7586dqFatGr799tt0v9uwYQM6duyI7du3Izw8HJ06dcL48eNx5swZNG7cGDNmzMB//vMf9O3bF7GxsQCAKVOmIDg4GMePH8e///1vnDt3DgCwYMECPPLIIzByMQLDZrNh5MiRWLBgAQDgxo0bqFu3Lp5//nkAQFJSEiZPnowzZ87k8lNI68KFCxg3bhz27t0LAIiJicG6deuQlJSkm0eCgvQSrj/84JT9CTd34IBuxw4MBBYtAry8YLPZAABRUVHo3bs35s+fb26enJzscNEJCQnYunUr/vnnH7O8F198EQcOHMh1uKGhoYiPj08J/QCGDh2K3bt3Z7itYRjYuXOnGfPff/+NAQMG4K+//gIArFu3Do8//rh5HgPA5cuXzX9v3rwZo0ePRnR0tMPxpc4B3377LTp16oSbN28CAPr27YsaNWrocw1AZGRkupyRepXU999/HxEREQ7vO9dIOv3RsmVL5sbChQvp4+PD2bNnMyYmho0aNWL58uV57NgxBgQEEACnTJlCpRSVUvTx8WGVKlWolGL9+vUZEBDAYsWKsW3btvzmm2/Mn0+cOJEAuGTJEpLkww8/TAA8ePAgSXLatGmcMmUKk5KSMoxrzpw5/PTTT0mSiYmJ9PHxYbNmzUiSly5dIgA2bdqUJHn58mUC4DvvvJOrz4AkDx06xP3795vl+fv7m7Hv2LGDAPjdd9/pjRMSyLZtyeLFySNHcr1P4QGuXCGrVyfvuos8f56JiYl84IEH+Oqrr5IkDcNgYGAgly1bRpK8ePEia9WqxR07djhU/JEjR+jl5cUZM2aQJPfs2UM/Pz+uXr2aJHnt2jXzuHTEzp07CYBLly4lSW7fvp3Vq1fn2bNnzd8vW7aMhmGQJH/55RcC4MaNG0mS48ePJwD+/vvvJMlPPvmEFStW5M2bN0mS77//PpVSPHToEEly7ty5rFixIiMjI0mSy5cv55w5c5iYmJhhfL/88gtr1qzJa9eukSQ7d+5MAIyIiCBJ3n333fTx8WFycjJJsnXr1qxVq5YZ79KlS9miRQvGx8eTJKdOnWrmlNwAEEwH8qtbJW2S5geyb98++vj4EABDQkLYu3dvLlmyhDabjQ899BAnTZrEWrVqsVSpUpw5cyYB8OGHH+azzz5LAPTx8WGbNm04fPhw7tmzhw888ACLFy/OAwcO8PLly1yyZIm5r1atWrFHjx6ZxjRgwAC2b9/e3L5du3asUaMG4+Pjef36db7xxhs8d+4cSXLjxo0sUqQI16xZQ5Jcs2YN+/TpYx4Y2UlKSmKVKlXYq1cv82f2g4YkY2JiuGrVKvMLZuXKlfzj++/JChXI+vXJlANaFDAJCeR995HFijH5r7/MHwcFBZkVitudOXOGLVq04PHjxzMtduvWrfzwww/N1zt37kxzrCYnJ5vH2iuvvEIfHx+eP38+0/LOnj1rJl2bzcZZs2bx8uXLGW778ssvMyAgwPySuXXrFt977z1u2LCBJBkXF8f58+czLi6OpD4PK1SoYCbpzp07s3Tp0uaXwO0effRRtmzZMl3Stp9PBw8eZJcuXbhnzx6S5Ndff01/f38eSan8TJkyhWPGjDH/lrp167J58+ZmHli0aBF79uzJCxcuZPp55IRHJu0tW7awefPmvHbtGj/44AMC4Ntvv83u3bsTABs1asSgoCDzg1y0aBG7devGs2fPsm7dupwwYQINw+C7777LGjVqcNCgQRw+fDj379/PjRs3snTp0tyyZUuafSYlJbFu3bp84IEHaBgGw8PD+cYbb/C9997jxYsXSZKzZ88mAP6VcrKsXbuWn332GW02W7q/YciQIaxdu7b57Tt27Fg2a9bMfJ2Zs2fPmgfDn3/+6XCS79WrF5s1a0bbpk2ktzf58MNkBnEJDzd6NAnw5LvvskGDBjx27JhDb7MfUyQ5btw4fvnll2l+/9RTT7FBgwZMSEjItqzr16/z+++/N1/fzKCC0LNnT1atWjXT2m1qiYmJbNiwIdu3b0+bzcbt27ezSZMmbN26dZq4U++vbt26bNeuHW02Gw8fPswDBw6Yf6c9mdsZhsGoqCiS+gth4cKFfOqppzhq1CjzZ3feeSfbt29vvic6OjrDWMPCwtixY0cOGTKE06ZN47Jly6iUMq9CnMEjk/Zff/3F6tWr89ixY0xMTOTcuXOZnJzM4OBgdu3alQDYoEEDtm7d2jzIDMNgTEwMW7duTV9fX65atYp+fn6sXLkyZ86cSaUUu3fvztDQUHbs2JGnT59mREQEu3fvzr1795Iko6KizANw2rRp9Pf3Z7FixTht2jSS+j+ya9eu/OKLL7L9G/78809+/fXXJMnIyEiWLl2aI0aMIEkmJCRw/vz56Q7IgwcP0t/fP90J5YioqCizppH80Uf6v/Stt3JcjnBjs2fr/9eXX+a5c+fYtm3bHF+GJyQksFevXpw4cSKjo6PNCsmtW7fMxJYTu3fvZunSpfnbb7/RZrOZtfGTJ0/y5MmTWb735s2b5vb283HNmjUEwC+//DLTmjlJrl+/nvv27eOCBQvo5+fHffv2kdRNJ76+vpk233z++ecEwBEjRvCNN94wz8GWLVuycuXK2VaqNm/ezOrVq7N3796cNGkSx48fTx8fnyyvYnLKI5P2hAkTCIA7duzgpEmTWKFCBV6/fp2xsbE8ffo0V6xYwfvuu49169bl/v3707RBR0dHs1u3bvz111/ZpEkTPvnkkzQMg1OnTuWpU6dI0qy9Hjp0iBUrVuS2bdvS7D8+Pp69e/dmYGAgV65cyUcffZQRERFMSkpir169GBQUlKO/Z8eOHZwwYYLZRjZv3jwC4Pbt29NsZ7PZ+MYbb+T5MuvF8eO58o479H/rjz/mqSzhJn7/nYaPDy+1bEkj5XjPqBbqCHtTx7333suWLVuabb+5cfnyZQ4fPpxXrlzh4MGD+dRTTzkUl72vyn4u3bp1i506deIrr7zCmTNnpmkKJPW5MWHCBLMiZHfx4kW+9tpr5vYRERGcPn16hjHs37+foaGh3LFjB202G1988UXzivvGjRv8559/soz5+PHjvH79OhMSEsz97d27lyEhIebfMHLkyCybjRzhkUl71apVrFKlCsPCwvjwww+zaNGivHDhAvv06cO6desyISGB4eHhXLduHX18fDhixAjOnj2bCQkJjImJYa1atTh8+HBWqlSJDz/8MG02G4cOHcolS5bw3LlzDAgI4DvvvGN25s2ZM4ckGR4ezjNnzrBOnchtAeIAABlCSURBVDqcNGkS582bx6VLl7Js2bK86667ePLkScbHx+f4ZBk9ejTr1KnDqKgoJiYmcsCAAXzjjTdI6hPv448/5vXr13P1WWVk3bp1/O9rr5Ft2uiOyRx0Ggk3dPo0Wb48b1aqxFKA2dabVz///DOrVKnC7t27O6W8//znPxwyZEi6hJuZd999l5s2bSKpz4PnnnuOixcvNn8fGRnJsWPHMjY2lomJiezWrRvHjx+faXk3btzg7NmzzfPz/PnzfPXVV80vqbp16/Lee++lYRiMiIhgqVKl6Ofn51AlKS4ujlWrVmW/fv3Mny1btoxeXl5mB+lHH31Eb29vLlq0yKG/PzMembSTkpLMToz4+Hiz3e7jjz9mv379zP+UI0eOsGzZsnz99dcJwPywzp8/z+TkZK5evZrHjx/nhQsX6Ofnx3bt2jEsLIy+vr7mN/wvv/zC5ORkbtu2jUWLFuWyZcvYt29f8xvYZrOxdu3aLF++PGNiYnL19yQnJ5uXetHR0ezUqRM/++wzkroD0cvLi++9916uys7S+fNMqliRiZUqkeHhzi9fuF5EBHn33WTp0rQdPsyffvop1zVsUrfJrlu3zny9atUq/vnnn7ku78aNG+YV7E8//UQA/PnnnzPdfu/evQwLCzNfnzt3jpcuXcpw219//ZVFixY1E3t2FaapU6fS19eXR48eJambQgICAszXe/bs4fHjx80ynn76aZYqVSrbZpzU8aTuQ4iJieH7779vXun/8ssvbN++fa6amVLzyKQdFBRkjha5ePGi2as8adIktm7dOk3yjI+Pp81mY//+/dm1a9cML/UMw2Dv3r35Y0pTQUhIiNl5uG7dOtpsNm7dupWNGzdmeHg4V69ezXLlynHv3r1MSkpi+fLl2bBhQ3N/R3I5pM4wDL700kt85plnzP1//fXXZi3e2QzD4L+aNmW0lxeNe+6RESWeJiGByfffzyQvL0auXOmUIh988EFWqVLFHImR2rJly3jmzJkcldetWzfWq1ePiYmJNAyDv/32W6aJNSkpiXXq1OF9991HwzCYnJzMRo0ambXf2xmGwS5durBPnz40DCPbLyubzWb2T9nNnTuXs2fPJqlry127duXTTz9t/t7eUWqvfd9u48aNXL9+fdYfAvVVwcKFC/P0hWrnkUl74cKFrFChAs+ePcvnnnuOAQEBvHLlCg3DYGxsLEmdPJ988kkeOHCAhmGwY8eOBMCxY8emK+/8+fMsUaIEX375ZYaHh7N8+fKcMWMGV61aRQCcOHEiAwIC6OPjw+3bt/PUqVNs06YNt27dSlJ3ENoP5jFjxrBMmTIOj+pIzTAMvv7663z22Wf5+OOPc8GCBSxXrhynT59ubpPb2nxmQkNDGTprFunjQ3brpoeMCfdnGOS//kUCfKZIEf70009OKfbatWsZVjoiIyNZtmxZPvHEEzkqLyQkJE3N3e7MmTMcPXp0uo69PXv2pPli2LRpE4ODgzMtf86cOZw3bx43bNjADh068OrVqw7FtWHDBgYFBbF///5s164dFy9ezB49erB58+YMCAhI18n5wQcfsEaNGml+bhgG27ZtyzZt2mSbjN955x36+vryxIkTDsWXFY9M2iTNmsCcOXNYo0aNdJdQZ8+eZeXKlc0JAOHh4XzggQd448aNDMsLDQ1lcnIyQ0ND6eXlxVGjRvHo0aOsUKECN2zYwHnz5pkjOuw9zOXKlUtTIzEMg+PHj+dbeRyVERERwRYtWvDdd9/l888/b/5HT5s2jfXr13f4wMyRr78mAV7t1o3MZPKQcBOGQePFF/Vp+fbbmTYfOOrvv//m2LFjMxyamtqhQ4ccqjScPn2a33zzTZbbLFq0iGXKlOGRI0e4du1as9+I1HMvVqxYkel7r1+/bo4GsVu9ejUDAwMd7vt58803ec899/DKlSs8e/YsZ8yYwU6dOnHfvn0ZdlQGBwfzhRdeSPcZXblyxaEKWlJSEnfu3OlQbNnxyKR98OBBDh06lHFxcfzzzz85cOBA3rp1iyTNmjZJ9uvXj02bNk03FvTChQsMDAxM03ZmFxkZyaZNm3L79u1cuXIlv/jiC9psNv76668EwK+++opr165l5cqV0x1YERERrFmzJidMmEBSt8+tzMFl682bN81Yo6Ki2KhRIw4ePNj8/bRp0zhy5EiHO3JyIj4+nlPLldP/1Y8+SjowflZYwDAYHRREAjzdt6+ucefRhx9+mGHFJzPx8fEcPnw4d+3aleHvR44cybJly2ZaQbKzJ7v+/fuzefPm5rHfp08f1q5dO9Mx4f369eNdd91lnvN29oRqs9nMoYoZmT59Ojt37sxr167RMAy2a9eOVapUMfcfHx+fZSKeOXMmBwwYkOumjo0bN3Lu3Lm5ei/poUl70aJFLFeuXLp23mvXrrFhw4bmuOn169dz3rx56d7/4osvEkC64UGkHj9ap04d/vzzz6xYsSIB8L///S/fe+89AmCPHj24fft23n///YyIiOCxY8c4cuRIs8Z99epV8+Dp06cPa9asme3YTlIPB2rSpIk5oJ/U7W32TpYtW7aYXxqk/ob/+++/Hfm4HHbp0iXGv/8+CdAYMEASt7sxDPK110iAK+66i+t/+y1PxdkniBiGkW2CTe3s2bOsVasWFyxYcFt4OonFxcUxNDQ023Ls58XcuXPZoEEDc5TGjRs3Mp29SOpz1H5eZOSll17iXXfdlWniXbJkCQcPHmx+KTRs2NDsIyP1xLd69epl2K5P6mnrvr6+uWoCJfWQ3rw0c3pk0v7www/p5eWVbuKAzWbjwIEDs13PIy4uLs2wm9TJPzk52TyY7EN2ZsyYwevXr/Puu+9mtWrVePXqVXOSzZdffsk77riDp0+fTrOPiIgINmjQgK+99hpJmh0rWXn//fczHa71ww8/cObMmWZP9NChQ1mmTJkMZ5vlVdKHH5IAwxo0kM5Jd5GUxEuPPKJPxVGjaOTxauurr75i1apVGZ7LUUOpr2gvXbrExYsXs3v37g7NmCR1xalz585MSEjgli1beM8993DgwIGZNtFs2LCBb7/9tkNlHzx4kFOmTEnzs5iYmDRXBps3bzbX6Vm8eDGHDx9u/u6PP/7g559/nub9iYmJ5mdlH05sFY9M2tHR0Vy4cKH5+ptvvuGVK1dIkn379nW4dkuS3377rTkWOzY2lt27d+fUqVNJ6kQJgI8//jjj4uLYs2dPbty4kb///jv9/Py4du1aTps2jQDMDk/7zCd7R6h9aOB///tf9uzZM90l3cKFC7OdtRYXF8dq1arxscceI6mbcHr27MlZs2aZ2zijV9ouPj6e8wIDafPy0sPJnDibS+TCjRuMbd+eBPhn+/ZOWX5g3759HDFiRKa1SUedPHmSpUuX5uDBg9m5c+cMR1hkZNGiRZwwYYJZkfn444/Zv39/Xrlyhd9++22643ns2LFs3LhxjmuoYWFhnDZtWrpKTmBgIP39/dPVlkNDQ/nrr7+ar0NCQvjll1/y0UcfZY0aNdJNX1+5ciVHjhzp8JeVM3hk0k7t7NmzLFq0qDmo/tq1a9nOXErthx9+YMmSJXn06FEahsHhw4ebtWP7kKN69epxw4YN9PLy4rBhw8xkvmDBAsbGxpqdLt988w19fHzMtUdSe+KJJ9i3b980B2NkZCQrVqzIkSNHZhvnmTNnzC+mP/74g9WrVzdnaq5atYr3339/njukUjMMg9yyhSxblokBATyeagSLyD9Je/aQ9eqRvr784+mn83RltWfPHn7yySdOi+3EiRNcvXo13377bZ48eTLbjsy1a9eaC6SR+ovDPuvXMAzabDZ+8MEH9PLy4uHDh3np0iWzEz4pKSnH45sNw+CkSZN4xx13MDg4mMuXLze/VH788Uc2a9Ys3ZXGY489xjvvvNOs9I0YMYLVq1fnxo0b06ynYjd58mQGBgamq4y5kscmbfuKWwkJCaxZs6ZZC82piIgIPvfccwwPD2dycrLZjm2/lFq/fj0XLFjAxMRE1q9f35ypOHPmTB48eJA2m429e/fmmjVruH//fpYsWdJcHMZ+CZmQkMB69eqxf//+NAyD33//PV944QVGRUXxxIkTOe5YHDBgAFu0aGGeJOPHj2fz5s0dvrrICePUKYYWK0YCNIYMIZ34xSCyEBfHM8OHMxFg8h13kCmz6vIiKCiIVatWzfPkDrtu3bqxZs2aaZaJGD9+fLqmCVI3XbZo0YKdO3c2x1Q3adKEgYGBaSoyycnJ/P3332mz2dioUSM2bdo02y+DjNjnZjzzzDM8ffo04+PjWaFCBdavXz9Nh+XtYmNjGRwczMTERA4dOpRBQUHmypxJSUlcvXp1uqsA+3kXGxvLmTNnOrQIVl54VNLetIls1IgEDPPRqBE5fvwv3LZtG8PCyMcf10OO9c3xMn4olfq1QSCabduG8NNPDxP4jEBUmn0UL06OHJnIHj3GcNasWUxMTGSJEiVYqVIlnjhxgl5eXgwMDOTp06fZp08fbtsWzmeeSaRSuhxfX9LHx0hTJhDF4cOjmMEAlmxt2LDBnDEZFRXFsmXLsl+/8RwzhixRwiBgo79/EseMYa7Kv92Nixd5bexYskgRGqVLc/eIEUxw8DJY5JDNxvgfftDL5wJcf+edPJ7LGYlJSUlcuHChOeMvIiKCu3dfTzlO9HlQogQdPk5sNht//PFHXr16lWFh5NChkQwIsJnljBqVxAceeJ6TJk0iqTvXp0+fbjYpnDp1ivPnzzdrpYcPHzabJ8LCdBz+/klUymCJEmTnzkeoVB1z2G5q9u3tf0fx4jo3FC9umPG0bLmLzzzzvy+Q6tW7EPiUxYolZPq3p/4CateuHQHwjz/+IEl+/PFKAp+mxKj3Wbdu6nxjEIhnr17XMvw8b485J599ah6TtN95J+tEPGwYWbRo1ttk/UhOSei2DH/v7U36+xtcvVp/yw4bNoxlypRheHg4v/vuO3bt2pVnz57lmDG/UKlbKUk66316eRn09yd7956V6yFAO3bsoJdXHxYpkkhf37Tl+/rqmJcvj82+IEeEhvKfevVIgEmlSpFvvkkji6FVIgfi4sh583iueHH9n1erFpnL0SH2mmB0dDRLlSrFF154gSS5Zg3p789MjhP9+6zKO3bsGJVSfPLJZVmW8+uv+spx/vz5BMDJkyeT1Dc3AJCmPyp1XN7ettvKM1ikSCKXLtWzmPft28eVK1fy11+TM9y/Tpqpz69kAjF8++1dXLOG9POz0ds7+bbzOpn+/gbXrNHt05UqVTKbGaOjozlt2jTabDauWUMWLZqUUmbm+7Q/ihYlR4/+2RyhltvPPiNOTdoAegE4BiAMwCvZbe9o0t60KS/J2LmPIkUSGRamm026d+/OpKQkzpo1iwDYrduz9PaOy0W5sWzUSC80YxgG586da67XkJ1du67R1zchm/Jj+OefeibXrVu38tRpadhsPPjZZ2TfviRAm1I8cMcdNKZNIw8fljW6c+LCBR557TXuq1NHV9sAXqlcmb89+WSOJjjdvhZ26gWeDh8+TJvNxrAwnRyyOk78/dPX+p5++mmOHj3afL106W76+2ddIfHxiWdYmK5QlC5dmhMnTiSpb/Qxbty4NFPDH3vsNRYpkuhQXKNHj2aJEs2y3X/6czaJfn7Z/+0ffbSCvXv3Tnfu6c8uZ/sESKXi2KfPC7n+7DPjtKQNwBvASQC1ABQBsB9Aw6ze42jS1k0i2T1y/qHm7pHAUaMSGRYWxg4dOjAoKIjbtm1j+fLlWaLEIvr4ZFxTz/o/N4m1a6/lu+++y23bthEAe/fuzcjISJ47d47dunXjqlWrSOoJOLt37zbby8eMyajGkT7m557TJ3azZs1YsWJF87NdvHhxugXrHR5REBrKv7p3Z7h9Ug7AW97ePFGpkg7sgw+4/9VXeXrRIvLQIfL8ecZdv06jgCd2w2ajERdHXrnC6JAQHl6wgPHff09+8gnDhwzh7goVaKtY0fzMLnh5MfZf/9K1k9u+UO1LM9jbX0+dOsWlS5ear6dPn84qVaqYr7/88ku+9NJL6dpVHTlOfH3JNm3+TpP0J06cyJdeesl8/cgjV9LViNM/EmlfnXjgwIEcN24cSXLUqFEsUaKEOWhg2rRpLFFiUQa117QPHx8bg4J000XlyiupVFIOzy/jtibRjP52g/7+8zlkyBDzb33rrbe4fv16B8+xjB42PvjgGY4Zw2yvvH19SUdXdHY0aSu9beaUUu0AvE2yZ8rrV1PuLTkls/e0atWKwcHBWZary8p2k3x2E0BpAECLFi2wZ8+elJ9HAiiV5zJTU0oh9Wfv5eV1201DbwIomevynaUagC4AmgNoAaARgDJZbB+f8khK9TBSPXjbwy6zozDrozNrmR1e6rZ/3/7wSnn4APBNeRQF4IfM74QdD+AEgD0AQgD8lfKcl/gd4+ixmd1x4qxyclteXs4xR/dxu7ye13Do/SVLAjdvZrsZlFIhJFtlt51P9kWhMoB/Ur0OB9Amgx2OAjAKAKpVq+ZAse4oAAAwceJETJkyBf7+/khMTARQIk9l+vv7o1y5cuZdpH18fFC6dGlcu3YNAODt7Y0SJUogMjISgD2BBzhcvre3N4oUKYK4uDjz/V5eXuZdrb29vWEYhvkl4e3tbd7BO7vX5wB84+2Nr1P9vrSXF+4yDFSBPhXuUAolSfhBJzZ/peBNmgnPWymAhDdSkmLKazsvpE1u9i80e3JVmfzekddM2Z+Ren9KwXbb9jYShP5iQcrrJADJAAylcItEHHRyjvXywjXDQCSAywDOe3vjYqrPx8fHJ81d0LP7vG//ws7Za0ePzQDzbwVgfj7/Kytn5WQfW07Ly8s55tg+bj8v8npeZ14tSCsmJg+7yYAjSdshJOcAmAPomrazys1PJUt64+bN/4WekJCQ8nMgOjovZcbm4n2O7VOXn5z9hqJAytlxkvlp6axyclteXs4xR/eR/ud5O69Jx94f4Gj9y0GZXe2ldh5A1VSvq6T8LM8aNXJGKc7h6wsMH57x74YN0793ZpnZcWSfeSlfFAzOOk6cfbzltLzcnGNKZd/E6orzWildpmXnaHaN3tC18VMAauJ/HZGNsnqPJ44eyaqX15Fe4pyWmR1n90yLgslZx4mzj7eclpebc6xYMTo0esTZ53WxYvq9bjt6RJeF3gCOQ48ieT277d1pnLaXV9rn2x96nHb24ykzG4+ZlzKz48wxoKLgctZx4uzjLaflOXqOpX5/XmPOyXkN6FyUuky3Haed00duZkQ2bpz2j27cWP+c1N9Uw4bldEYkGRCgh9ts2qSfAwIy/n1Oag9BQWTJknpfRYqkjymnZeZkn15e+tmZ5YuCwVnHibOPt5yWd/v2AQE6FwQEZP7+vMac0T5TloVJk4SHDcu4TGd9Zo4m7WyH/OWGo0P+hBBCaI4O+XOkI1IIIYSbkKQthBAeRJK2EEJ4EJe0aSulrgI4m8Um5QBcc/qOPY98DvIZAPIZAPIZAEB9ktlO03TajMjUSJbP6vdKqWBHGtwLOvkc5DMA5DMA5DMA9GfgyHbSPCKEEB5EkrYQQngQq5L2HIv2627kc5DPAJDPAJDPAHDwM3BJR6QQQgjXkOYRIYTwIJK0hRDCg1iWtJVS05RSoUqpA0qpFUop190zy80opXoppY4ppcKUUq9YHU9+U0pVVUptUUodUUodVkqNszomqyilvJVSe5VSq6yOxSpKqdJKqeUp+eBoyi0OCxWl1PiUc+GQUmqpUqpYZttaWdPeAKAxyXugl3191cJY8o1SyhvAZwAeANAQwBClVENro8p3yQAmkGwIoC2AoEL4GdiNA3DU6iAs9n8A1pFsAKApCtnnoZSqDOAFAK1INoa+mfrgzLa3LGmTXE/Sfp+sndB3xCkMAgGEkTxFMhHAdwAesjimfEXyIsk9Kf+Ohj5JK1sbVf5TSlUB0AfAV1bHYhWlVCkA9wGYBwAkE0lGWhuVJXwA+CmlfAD4A7iQ2Ybu0qb9FIC1VgeRTzK6UXKhS1h2Sqka0Dd732VtJJaYCWASUu4nXEjVBHAVwIKUZqKvlFLFrQ4qP5E8D+Aj6PtoXwRwk+T6zLZ3adJWSm1MaaO5/fFQqm1eh75cXuLKWIT7UUoFAPgRwL9JRlkdT35SSj0I4ArJEKtjsZgPgBYAZpNsDiAWQKHq51FKlYG+2q4J4C4AxZVSwzLb3iVrj9iR7JbV75VSTwB4EEBXFp4B4y67UbInUUr5QifsJSR/sjoeC3QA0E8p1RtAMQAllVKLSWZ6shZQ4QDCSdqvtJajkCVtAN0AnCZ5FQCUUj8BaA9gcUYbWzl6pBf0pWE/kresisMCfwOoq5SqqZQqAt3h8IvFMeUrpZSCbsM8SnK61fFYgeSrJKuQrAF9DGwuhAkbJC8B+EcpVT/lR10BHLEwJCucA9BWKeWfcm50RRadsS6taWfjUwBFAWzQcWInydEWxpMvSCYrpZ4H8Bt0L/F8koctDiu/dQAwHMBBpdS+lJ+9RnKNhTEJ64wFsCSlEnMKwJMWx5OvSO5SSi0HsAe6qXgvspjSLtPYhRDCg7jL6BEhhBAOkKQthBAeRJK2EEJ4EEnaQgjhQSRpCyGEB5GkLYQQHkSSthBCeJD/B3NM83udm/ALAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import kde\n",
    "\n",
    "x1 = np.random.normal(-1, 0.5, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 1, 10)\n",
    "y = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n",
    "x = np.linspace(min(y), max(y), 100)\n",
    "\n",
    "s = 0.4 # Smoothing parameter\n",
    "\n",
    "kernels = np.transpose([norm.pdf(x, yi, s) for yi in y]) # Calculate the kernels\n",
    "density = kde.gaussian_kde(y)\n",
    "\n",
    "plt.plot(x, kernels, 'k:')\n",
    "plt.plot(x, kernels.sum(1), 'r')\n",
    "plt.plot(y, np.zeros(len(y)), 'bo', ms=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:2: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa3187af0f0>]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xgrid = np.linspace(x.min(), x.max(), 200)\n",
    "plt.hist(y, bins=28, normed=True)\n",
    "plt.plot(xgrid, density(xgrid), 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy implements a Gaussian KDE that automatically chooses an appropriate bandwidth. Let's create a bi-modal distribution of data that is not easily summarized by a parametric distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a bi-modal distribution with a mixture of Normals.\n",
    "x1 = np.random.normal(-1, 2, 15) # parameters: (loc=0.0, scale=1.0, size=None)\n",
    "x2 = np.random.normal(6, 3, 10)\n",
    "\n",
    "# Append by row\n",
    "x = np.r_[x1, x2] # r_ Translates slice objects to concatenation along the first axis.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:1: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([0.16036149, 0.10690766, 0.16036149, 0.05345383, 0.16036149,\n",
       "        0.05345383, 0.21381532, 0.10690766, 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.05345383, 0.05345383, 0.05345383,\n",
       "        0.        , 0.10690766, 0.05345383]),\n",
       " array([-3.44106666, -2.69275732, -1.94444799, -1.19613865, -0.44782932,\n",
       "         0.30048002,  1.04878936,  1.79709869,  2.54540803,  3.29371736,\n",
       "         4.0420267 ,  4.79033603,  5.53864537,  6.2869547 ,  7.03526404,\n",
       "         7.78357337,  8.53188271,  9.28019204, 10.02850138]),\n",
       " <a list of 18 Patch objects>)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins=18, normed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:3: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa31873c6a0>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "density = kde.gaussian_kde(x)\n",
    "xgrid = np.linspace(x.min(), x.max(), 200)\n",
    "plt.hist(x, bins=18, normed=True)\n",
    "plt.plot(xgrid, density(xgrid), 'r-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='black'>\n",
    "## 4 Estimation\n",
    "\n",
    "\n",
    "<font\\> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/sitthichok/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:2: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.normal(0.0, 1.0, 10000)\n",
    "a = plt.hist(x,50,normed='True')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**Definition:** *Estimation* is the process of inferring the parameters (e.g. mean) of a distribution from a statistic of samples drown from a population.\n",
    "\n",
    "For example: What is the estimated mean $\\hat{\\mu}$ of the following normal data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use our definition of empirical mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The empirical mean of the sample is  0.008406895592074463\n"
     ]
    }
   ],
   "source": [
    "print('The empirical mean of the sample is ', x.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Sample mean\n",
    "\n",
    "+ The process is called **estimation** and the statistic we used **estimator**.\n",
    "\n",
    "+ The median is also an estimator (more robust to outliers). \n",
    "\n",
    "+ \"Is median better than sample mean?\" is a question with at least two different answers. We can use two different objectives to answer this question: the minimization of error or the maximization to get the right answer. \n",
    "\n",
    "+ If there are no outliers, we can use the **sample mean** to minimize **mean squared error** (where $m$ is the number of times you play the estimation game, not the size of the sample!):\n",
    "\n",
    "$$ MSE = \\frac{1}{m} \\sum(\\hat{\\mu} - \\mu)^2$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  0.001005177709377845\n"
     ]
    }
   ],
   "source": [
    "NTs=200\n",
    "mu=0.0\n",
    "var=1.0\n",
    "err = 0.0\n",
    "NPs=1000\n",
    "for i in range(NTs):\n",
    "    x = np.random.normal(mu, var, NPs)\n",
    "    err += (x.mean()-mu)**2\n",
    "\n",
    "print('MSE: ', err/NTs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Variance\n",
    "\n",
    "We can also estimate the variance with:\n",
    "\n",
    "$$ \\hat{\\sigma}^2 = \\frac{1}{n} \\sum_i (x_i - \\mu)^2 $$\n",
    "\n",
    "This estimator works for large samples, but it is biased for small samples. We can use this one:\n",
    "\n",
    "$$ \\hat{\\sigma}^2_{n-1} = \\frac{1}{n-1} \\sum_i (x_i - \\mu)^2 $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Other concepts: Standard scores\n",
    "\n",
    "$$ z_i = \\frac{x_i - \\mu}{\\sigma}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This measure is dimensionless and its distribution has mean 0 and variance 1.\n",
    "\n",
    "It inherits the \"shape\" of $X$: if it is normally distributed, so is $Z$. If $X$ is skewed, so is $Z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 Covariance\n",
    "\n",
    "**Covariance** is a measure of the tendency of two variables to vary together. \n",
    "\n",
    "If we have two series $X$ and $Y$ with $X=\\{x_i\\}$ and $Y=\\{y_i\\}$, and they vary together, their deviations $x_i - \\mu_X$ and $y_i - \\mu_Y$ tend to have the same sign.\n",
    "\n",
    "If we multiply them together, the product is positive, when the deviations have the same sign, and negative, when they have the opposite sign. So adding up the products gives a measure of the tendency to vary together.\n",
    "\n",
    "Covariance is the mean of the products:\n",
    "\n",
    "$$ Cov(X,Y) = \\frac{1}{n} \\sum_{i=1}^n (x_i - \\mu_X)*(y_i - \\mu_Y), $$\n",
    "\n",
    "where $n$ is the length of the two series.\n",
    "\n",
    "It is a measure that is difficult to interpret."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cov(X, X) = 18.89\n",
      "Var(X) = 18.89\n",
      "Cov(X, Y) = 0.18\n"
     ]
    }
   ],
   "source": [
    "def Cov(X, Y):\n",
    "    def _get_dvis(V):\n",
    "        return [v - np.mean(V) for v in V]\n",
    "    dxis = _get_dvis(X)\n",
    "    dyis = _get_dvis(Y)\n",
    "    return np.sum([x * y for x, y in zip(dxis, dyis)])/len(X)\n",
    "\n",
    "\n",
    "X = [5, -1, 3.3, 2.7, 12.2]\n",
    "X= np.array(X)\n",
    "Y = [10, 12, 8, 9, 11]\n",
    "\n",
    "print(\"Cov(X, X) = %.2f\" % Cov(X, X))\n",
    "print(\"Var(X) = %.2f\" % np.var(X))\n",
    "\n",
    "print(\"Cov(X, Y) = %.2f\" % Cov(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us create some examples of positive and negative correlations like those showing the relations of stock market with respect to the economic growth or the gasoline prices with respect to the world oil production:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "MAXN=100\n",
    "\n",
    "MAXN=40\n",
    "X=np.array([[1,9],[3, 2], [5,3],[5.5,4],[6,4],[6.5,4],[7,3.5],[7.5,3.8],[8,4],\n",
    "            [8.5,4],[9,4.5],[9.5,7],[10,9],[10.5,11],[11,11.5],[11.5,12],[12,12],[12.5,12],[13,10]])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='b',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('Economic growth(T)',fontsize=15)\n",
    "plt.ylabel('Stock market returns(T)',fontsize=15)\n",
    "plt.gcf().set_size_inches((20,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.array([[1,8],[2, 7], [3,6],[4,8],[5,8],[6,7],[7,7],[8,5],[9,5],[10,6],[11,4],[12,5],[13,3],[14,2],[15,2],[16,1]])\n",
    "plt.subplot(1,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='b',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('World Oil Production(T)',fontsize=15)\n",
    "plt.ylabel('Gasoline prices(T)',fontsize=15)\n",
    "plt.gcf().set_size_inches((20,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5 Pearson's Correlation\n",
    "\n",
    "Shell we take into account the variance? An alternative is to divide the deviations by $\\sigma$, which yields standard scores, and compute the product of standard scores:\n",
    "\n",
    "$$ p_i = \\frac{(x_i - \\mu_X)}{\\sigma_X} \\frac{(y_i - \\mu_Y)}{\\sigma_Y} $$\n",
    " \n",
    "The mean of these products is:\n",
    "\n",
    "$$ \\rho = \\frac{1}{n} \\sum p_i = \\frac{1}{n} \\sum  \\frac{(x_i - \\mu_X)}{\\sigma_X} \\frac{(y_i - \\mu_Y)}{\\sigma_Y}  $$\n",
    "\n",
    "Or we can rewrite $\\rho$ by factoring out $\\sigma_X$ and $\\sigma_Y$:\n",
    "\n",
    "$$ \\rho = \\frac{Cov(X,Y)}{\\sigma_X \\sigma_Y}$$\n",
    "\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr(X, X) = 2.00000\n",
      "Corr(X, Y) = 0.05958\n"
     ]
    }
   ],
   "source": [
    "def Corr(X, Y):\n",
    "    assert len(X) == len(Y)\n",
    "    return Cov(X, Y) / np.prod([np.std(V) for V in [X, Y]])\n",
    "\n",
    "print(\"Corr(X, X) = %.5f\" % Corr(X, X))\n",
    "\n",
    "Y=np.random.random(len(X))\n",
    "\n",
    "print(\"Corr(X, Y) = %.5f\" % Corr(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When $\\rho = 0$, we cannot say that there is no relationship between the variables!\n",
    "\n",
    "Pearson's coefficient only measures **linear** correlations!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.6 Spearman’s rank correlation\n",
    "\n",
    "Pearson’s correlation works well if the relationship between variables is linear and if the variables are roughly normal. But it is not robust in the presence of **outliers**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spearman’s rank correlation is an alternative that mitigates the effect of outliers and skewed distributions. To compute Spearman’s correlation, we have to compute the rank of each value, which is its index in the sorted sample. \n",
    "\n",
    "For example, in the sample {7, 1, 2, 5} the rank of the value 5 is 3, because it appears third if we sort the elements. \n",
    "\n",
    "Then, we compute the Pearson’s correlation, **but for the ranks**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ranks:  [4.0, 1.0, 2.0, 3.0]\n",
      "Pearson rank coefficient: 0.28\n",
      "[1.0, 2.0, 3.0, 4.0, 5.0]\n",
      "[2.0, 1.0, 3.0, 5.0, 4.0]\n",
      "Spearman rank coefficient: 0.80\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def list2rank(l):\n",
    "    #l is a list of numbers\n",
    "    # returns a list of 1-based index; mean when multiple instances\n",
    "    return [np.mean([i+1 for i, sorted_el in enumerate(sorted(l)) if sorted_el == el]) for el in l]\n",
    "\n",
    "l = [7, 1, 2, 5]\n",
    "print(\"ranks: \", list2rank(l))\n",
    "\n",
    "def spearmanRank(X, Y):\n",
    "    # X and Y are same-length lists\n",
    "    print(list2rank(X)) \n",
    "    print(list2rank(Y))\n",
    "    return Corr(list2rank(X), list2rank(Y))\n",
    "\n",
    "X = [10, 20, 30, 40, 1000]\n",
    "Y = [-70, -1000, -50, -10, -20]\n",
    "plt.plot(X,'ro')\n",
    "plt.plot(Y,'go')\n",
    "\n",
    "print(\"Pearson rank coefficient: %.2f\" % Corr(X, Y))\n",
    "print(\"Spearman rank coefficient: %.2f\" % spearmanRank(X, Y))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Obtain for the Anscombe's quartet [2] given in the figures bellow, the different estimators (mean, variance, covariance for each pair, Pearson's correlation and Spearman's rank correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.array([[10.0, 8.04, 10.0, 9.14, 10.0, 7.46, 8.0, 6.58],\n",
    "[8.0, 6.95, 8.0, 8.14, 8.0, 6.77, 8.0, 5.76],\n",
    "[13.0,7.58,13.0,8.74,13.0,12.74,8.0,7.71],\n",
    "[9.0,8.81,9.0,8.77,9.0,7.11,8.0,8.84],\n",
    "[11.0,8.33,11.0,9.26,11.0,7.81,8.0,8.47],\n",
    "[14.0,9.96,14.0,8.10,14.0,8.84,8.0,7.04],\n",
    "[6.0,7.24,6.0,6.13,6.0,6.08,8.0,5.25],\n",
    "[4.0,4.26,4.0,3.10,4.0,5.39,19.0,12.50],\n",
    "[12.0,10.84,12.0,9.13,12.0,8.15,8.0,5.56],\n",
    "[7.0,4.82,7.0,7.26,7.0,6.42,8.0,7.91],\n",
    "[5.0,5.68,5.0,4.74,5.0,5.73,8.0,6.89]])\n",
    "\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "plt.scatter(X[:,0],X[:,1],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "plt.scatter(X[:,2],X[:,3],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "plt.scatter(X[:,4],X[:,5],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "\n",
    "plt.subplot(2,2,4)\n",
    "plt.scatter(X[:,6],X[:,7],color='r',s=120, linewidths=2,zorder=10)\n",
    "plt.xlabel('x1',fontsize=15)\n",
    "plt.ylabel('y1',fontsize=15)\n",
    "plt.gcf().set_size_inches((10,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Main reference\n",
    "[1] *Think Stats: Probability and Statistics for Programmers*, by Allen B. Downey, published by O'Reilly Media.\n",
    "http://www.greenteapress.com/thinkstats/\n",
    "\n",
    "[2] Anscombe's quartet, https://en.wikipedia.org/wiki/Anscombe%27s_quartet"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}