{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-01-09T23:29:26.707212Z",
     "start_time": "2024-01-09T23:29:26.670908300Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "   Age  Attrition     BusinessTravel  DailyRate            Department  \\\n0   21        0.0      Travel_Rarely        391  Research_Development   \n1   19        1.0      Travel_Rarely        528                 Sales   \n2   18        1.0      Travel_Rarely        230  Research_Development   \n3   18        0.0      Travel_Rarely        812                 Sales   \n4   18        1.0  Travel_Frequently       1306                 Sales   \n\n   DistanceFromHome      Education EducationField EnvironmentSatisfaction  \\\n0                15        College  Life_Sciences                    High   \n1                22  Below_College      Marketing               Very_High   \n2                 3       Bachelor  Life_Sciences                    High   \n3                10       Bachelor        Medical               Very_High   \n4                 5       Bachelor      Marketing                  Medium   \n\n   Gender  ...  PerformanceRating RelationshipSatisfaction  StockOptionLevel  \\\n0    Male  ...          Excellent                Very_High                 0   \n1    Male  ...          Excellent                Very_High                 0   \n2    Male  ...          Excellent                     High                 0   \n3  Female  ...          Excellent                      Low                 0   \n4    Male  ...          Excellent                Very_High                 0   \n\n  TotalWorkingYears TrainingTimesLastYear WorkLifeBalance  YearsAtCompany  \\\n0                 0                     6          Better               0   \n1                 0                     2            Good               0   \n2                 0                     2          Better               0   \n3                 0                     2          Better               0   \n4                 0                     3          Better               0   \n\n   YearsInCurrentRole  YearsSinceLastPromotion YearsWithCurrManager  \n0                   0                        0                    0  \n1                   0                        0                    0  \n2                   0                        0                    0  \n3                   0                        0                    0  \n4                   0                        0                    0  \n\n[5 rows x 31 columns]",
      "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>Attrition</th>\n      <th>BusinessTravel</th>\n      <th>DailyRate</th>\n      <th>Department</th>\n      <th>DistanceFromHome</th>\n      <th>Education</th>\n      <th>EducationField</th>\n      <th>EnvironmentSatisfaction</th>\n      <th>Gender</th>\n      <th>...</th>\n      <th>PerformanceRating</th>\n      <th>RelationshipSatisfaction</th>\n      <th>StockOptionLevel</th>\n      <th>TotalWorkingYears</th>\n      <th>TrainingTimesLastYear</th>\n      <th>WorkLifeBalance</th>\n      <th>YearsAtCompany</th>\n      <th>YearsInCurrentRole</th>\n      <th>YearsSinceLastPromotion</th>\n      <th>YearsWithCurrManager</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>21</td>\n      <td>0.0</td>\n      <td>Travel_Rarely</td>\n      <td>391</td>\n      <td>Research_Development</td>\n      <td>15</td>\n      <td>College</td>\n      <td>Life_Sciences</td>\n      <td>High</td>\n      <td>Male</td>\n      <td>...</td>\n      <td>Excellent</td>\n      <td>Very_High</td>\n      <td>0</td>\n      <td>0</td>\n      <td>6</td>\n      <td>Better</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>19</td>\n      <td>1.0</td>\n      <td>Travel_Rarely</td>\n      <td>528</td>\n      <td>Sales</td>\n      <td>22</td>\n      <td>Below_College</td>\n      <td>Marketing</td>\n      <td>Very_High</td>\n      <td>Male</td>\n      <td>...</td>\n      <td>Excellent</td>\n      <td>Very_High</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>Good</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>18</td>\n      <td>1.0</td>\n      <td>Travel_Rarely</td>\n      <td>230</td>\n      <td>Research_Development</td>\n      <td>3</td>\n      <td>Bachelor</td>\n      <td>Life_Sciences</td>\n      <td>High</td>\n      <td>Male</td>\n      <td>...</td>\n      <td>Excellent</td>\n      <td>High</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>Better</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>18</td>\n      <td>0.0</td>\n      <td>Travel_Rarely</td>\n      <td>812</td>\n      <td>Sales</td>\n      <td>10</td>\n      <td>Bachelor</td>\n      <td>Medical</td>\n      <td>Very_High</td>\n      <td>Female</td>\n      <td>...</td>\n      <td>Excellent</td>\n      <td>Low</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>Better</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>18</td>\n      <td>1.0</td>\n      <td>Travel_Frequently</td>\n      <td>1306</td>\n      <td>Sales</td>\n      <td>5</td>\n      <td>Bachelor</td>\n      <td>Marketing</td>\n      <td>Medium</td>\n      <td>Male</td>\n      <td>...</td>\n      <td>Excellent</td>\n      <td>Very_High</td>\n      <td>0</td>\n      <td>0</td>\n      <td>3</td>\n      <td>Better</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n  </tbody>\n</table>\n<p>5 rows × 31 columns</p>\n</div>"
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random as rd\n",
    "import seaborn as sns\n",
    "rd.seed(42)\n",
    "df = pd.read_feather(\"../datasets/attrition.feather\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1470, 31)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Axes: >"
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(df.shape)\n",
    "df[\"Age\"].hist()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:35.462202600Z",
     "start_time": "2024-01-09T18:17:35.288372100Z"
    }
   },
   "id": "6bc0db10e43f819"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Simple sampling"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "a1c5e970018f62d9"
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "outputs": [
    {
     "data": {
      "text/plain": "<Axes: >"
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_simple_samp = df.sample(n=70, random_state=42)\n",
    "df_simple_samp[\"Age\"].hist()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:35.583059900Z",
     "start_time": "2024-01-09T18:17:35.419232300Z"
    }
   },
   "id": "15798369a2dca49e"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Systematic sampling\n",
    "Systematic sampling has a problem: if the data has been sorted, or there is some sort of pattern or meaning behind the row order, then the resulting sample may not be representative of the whole population. The problem can be solved by shuffling the rows, but then systematic sampling is equivalent to simple random sampling."
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "c4414501ea754011"
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "outputs": [
    {
     "data": {
      "text/plain": "<Axes: >"
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_size = 70\n",
    "pop_size = len(df)\n",
    "interval = pop_size // sample_size\n",
    "df_sys_samp = df.iloc[::interval]\n",
    "df_sys_samp[\"Age\"].hist()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:35.828413100Z",
     "start_time": "2024-01-09T18:17:35.578496200Z"
    }
   },
   "id": "f9d422e5ed6431b3"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Proportional stratified sampling\n",
    "\n",
    "* Split the population into subgroups\n",
    "* Use simple random sampling on every subgroup\n",
    "\n",
    "The proportions of each category or subgroup will be similar between the population and sampling data."
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "75658aae51baf9e8"
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "outputs": [
    {
     "data": {
      "text/plain": "<Axes: >"
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_strat_samp = df.groupby(\"Department\", observed=False).sample(frac=0.1, random_state=42)\n",
    "df_strat_samp[\"Age\"].hist()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:35.995234500Z",
     "start_time": "2024-01-09T18:17:35.823517300Z"
    }
   },
   "id": "359d88c37f86ab5a"
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "outputs": [
    {
     "data": {
      "text/plain": "Department\nResearch_Development    0.653741\nSales                   0.303401\nHuman_Resources         0.042857\nName: proportion, dtype: float64"
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Department\"].value_counts(normalize=True)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:35.997690300Z",
     "start_time": "2024-01-09T18:17:35.988534100Z"
    }
   },
   "id": "bdb40c09cedb8939"
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "outputs": [
    {
     "data": {
      "text/plain": "Department\nResearch_Development    0.653061\nSales                   0.306122\nHuman_Resources         0.040816\nName: proportion, dtype: float64"
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_strat_samp[\"Department\"].value_counts(normalize=True)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:36.008678100Z",
     "start_time": "2024-01-09T18:17:35.997690300Z"
    }
   },
   "id": "5a04b4bfebc60408"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Equal counts stratified sampling\n",
    "The sampling will extract n rows of each category"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "a8e08efe798af0d5"
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [
    {
     "data": {
      "text/plain": "<Axes: >"
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_eq_strat_samp = df.groupby(\"Department\", observed=False).sample(n=15, random_state=42)\n",
    "df_eq_strat_samp[\"Age\"].hist()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:36.195207100Z",
     "start_time": "2024-01-09T18:17:36.007290100Z"
    }
   },
   "id": "8fabd3002b70ea61"
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "outputs": [
    {
     "data": {
      "text/plain": "Department\nResearch_Development    0.653741\nSales                   0.303401\nHuman_Resources         0.042857\nName: proportion, dtype: float64"
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Department\"].value_counts(normalize=True)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:36.196275400Z",
     "start_time": "2024-01-09T18:17:36.189687100Z"
    }
   },
   "id": "4faaeaee6597546d"
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "outputs": [
    {
     "data": {
      "text/plain": "Department\nHuman_Resources         0.333333\nResearch_Development    0.333333\nSales                   0.333333\nName: proportion, dtype: float64"
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_eq_strat_samp[\"Department\"].value_counts(normalize=True)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:36.207147600Z",
     "start_time": "2024-01-09T18:17:36.196275400Z"
    }
   },
   "id": "f8d7b48586a49856"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Weighted random sampling\n",
    "Specify weights to adjust the relative probability of a row being sampled."
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "1cfc1ca86ba620d3"
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "outputs": [
    {
     "data": {
      "text/plain": "<Axes: >"
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_weight = df\n",
    "condition = df_weight[\"Department\"] == \"Sales\"\n",
    "df_weight[\"weight\"] = np.where(condition, 2, 1) # weight 2 if match - 1 don't match => 2 times the chance of beign picked\n",
    "df_weight = df.sample(frac=0.1, weights=\"weight\", random_state=42)\n",
    "df_weight[\"Age\"].hist()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:36.407116800Z",
     "start_time": "2024-01-09T18:17:36.203767500Z"
    }
   },
   "id": "ba3b8a14c558df8c"
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "outputs": [
    {
     "data": {
      "text/plain": "Department\nResearch_Development    0.653741\nSales                   0.303401\nHuman_Resources         0.042857\nName: proportion, dtype: float64"
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.value_counts(\"Department\", normalize=True)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:36.420165900Z",
     "start_time": "2024-01-09T18:17:36.402905900Z"
    }
   },
   "id": "10f01d89bbf6b641"
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "outputs": [
    {
     "data": {
      "text/plain": "Department\nResearch_Development    0.537415\nSales                   0.435374\nHuman_Resources         0.027211\nName: proportion, dtype: float64"
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_weight.value_counts(\"Department\", normalize=True)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T18:17:36.421218600Z",
     "start_time": "2024-01-09T18:17:36.410843Z"
    }
   },
   "id": "bf432e27e6cb2952"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Cluster sampling\n",
    "* Use simple random sampling to pick some subgroups\n",
    "* Use simple random sampling on only those subgroups"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "2db075dd5cba8831"
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\b061995\\AppData\\Local\\Temp\\ipykernel_21152\\4183575958.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  df_filtered[\"JobRole\"] = df_filtered[\"JobRole\"].cat.remove_unused_categories()\n",
      "C:\\Users\\b061995\\AppData\\Local\\Temp\\ipykernel_21152\\4183575958.py:6: FutureWarning: The default of observed=False is deprecated and will be changed to True in a future version of pandas. Pass observed=False to retain current behavior or observed=True to adopt the future default and silence this warning.\n",
      "  df_clust_samp = df_filtered.groupby(\"JobRole\").sample(n=10, random_state=42)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Axes: >"
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "job_roles = list(df[\"JobRole\"].unique())\n",
    "job_roles_samp = rd.sample(job_roles, k=4)\n",
    "condition = df[\"JobRole\"].isin(job_roles_samp)\n",
    "df_filtered = df[condition]\n",
    "df_filtered[\"JobRole\"] = df_filtered[\"JobRole\"].cat.remove_unused_categories()\n",
    "df_clust_samp = df_filtered.groupby(\"JobRole\").sample(n=10, random_state=42)\n",
    "df_clust_samp[\"Age\"].hist()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T19:08:30.584141Z",
     "start_time": "2024-01-09T19:08:30.403512700Z"
    }
   },
   "id": "b59f600b56c026db"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Relative error\n",
    "\n",
    "$$\n",
    "RE=100*\\frac{|\\text{population mean} - \\text{sample mean}|}{\\text{population mean}}\n",
    "$$"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "3e951798a9ae4a13"
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.05063291139242\n"
     ]
    }
   ],
   "source": [
    "attrition_srs100 = df.sample(n=100, random_state=42)\n",
    "mean_attrition_srs100 = attrition_srs100[\"Attrition\"].mean()\n",
    "rel_error_pct100 = 100 * abs(df[\"Attrition\"].mean() - mean_attrition_srs100) / df[\"Attrition\"].mean()\n",
    "print(rel_error_pct100)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T22:10:26.772175100Z",
     "start_time": "2024-01-09T22:10:26.764408100Z"
    }
   },
   "id": "9cc55bcb181b6fb4"
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {
    "collapsed": false
   },
   "id": "3c1dfca1fd820eb7"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Bootstrapping\n",
    "\n",
    "*Sampling*: going from a population to a smaller sample.\n",
    "\n",
    "*Bootstraping*: building up a theorical population from the sample.\n",
    "\n",
    "**Process:**\n",
    "\n",
    "1. Make a resample of the same size as the original sample.\n",
    "2. Calculate the statistic of interest for this bootstrap sample.\n",
    "3. Repeat steps 1 and 2 many times.\n",
    "\n",
    "**Bootstrap distribution mean:**\n",
    "\n",
    "* Usually close to the sample mean.\n",
    "* May not be a good estimate of the population mean. (here we use sampling distribution)\n",
    "* Bootstrapping cannot correct biases from sampling.\n",
    "\n",
    "**Standard error:** standard deviation of the statistic of interest.\n",
    "\n",
    "* standard error * sqrt(sample_size) => population standard deviation\n",
    "* Estimated standard error -> standard deviation of the bootstrap distribution for a sample statistic.\n",
    "* It can be a good estimate of the population std\n",
    "* Bootstrapping doesn't suffer that much from biases\n"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "df8c9191b9599079"
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "outputs": [
    {
     "data": {
      "text/plain": "<Axes: ylabel='Count'>"
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_resample = df.sample(frac=1, replace=True)\n",
    "means = []\n",
    "for i in range(1000):\n",
    "    means.append(np.mean(df.sample(frac=1, replace=True)[\"Age\"]))\n",
    "sns.histplot(means)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-09T23:29:37.068843300Z",
     "start_time": "2024-01-09T23:29:36.518302100Z"
    }
   },
   "id": "5a5f9704be95cd7c"
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Confidence "
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "d301591b3248bbb1"
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "outputs": [
    {
     "data": {
      "text/plain": "<Axes: xlabel='Age', ylabel='Count'>"
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(df[\"Age\"])"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-10T00:07:45.479965600Z",
     "start_time": "2024-01-10T00:07:45.326828900Z"
    }
   },
   "id": "bfe7a7d694218129"
  },
  {
   "cell_type": "markdown",
   "source": [
    "Ways to calculate:\n",
    "\n",
    "1. Mean plus or minus one standard deviation:"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "ca908d93de1725dd"
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[27.78843603467279, 46.05918301294626]\n"
     ]
    }
   ],
   "source": [
    "mean = np.mean(df[\"Age\"])\n",
    "c1 = mean - np.std(df[\"Age\"], ddof=1)\n",
    "c2 = mean + np.std(df[\"Age\"], ddof=1)\n",
    "print([c1, c2])"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-10T00:05:56.985439200Z",
     "start_time": "2024-01-10T00:05:56.976144100Z"
    }
   },
   "id": "ce7cabb03b505084"
  },
  {
   "cell_type": "markdown",
   "source": [
    "2. Quantile method for confidence intervals"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "b8b9d30bb876311"
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[21.0, 56.0]\n"
     ]
    }
   ],
   "source": [
    "q1 = np.quantile(df[\"Age\"], 0.025)\n",
    "q2 = np.quantile(df[\"Age\"], 0.975)\n",
    "print([q1, q2])"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-10T00:07:02.886095800Z",
     "start_time": "2024-01-10T00:07:02.876254600Z"
    }
   },
   "id": "8ad909dac3468ff"
  },
  {
   "cell_type": "markdown",
   "source": [
    "3. Inverse cumulative distribution function - Standard error method for confidence itnerval"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "f2c01ee8e89f647c"
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[19.018806499779515, 54.82881254783953]\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "point_estimate = np.mean(df[\"Age\"])\n",
    "std_error = np.std(df[\"Age\"], ddof=1) # here we should use the standard error (std(bootstrap_distribution))\n",
    "lower = norm.ppf(0.025, loc=point_estimate, scale=std_error)\n",
    "upper = norm.ppf(0.975, loc=point_estimate, scale=std_error)\n",
    "print([lower, upper])"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-01-10T00:12:11.673899Z",
     "start_time": "2024-01-10T00:12:11.668428Z"
    }
   },
   "id": "47c22c76acb0d459"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}