{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a8cafc13",
   "metadata": {},
   "source": [
    "# Erkennen und Filtern von Ausreißern\n",
    "\n",
    "Das Filtern oder Transformieren von Ausreißern ist weitgehend eine Frage der Anwendung von Array-Operationen. Betrachtet einen DataFrame mit einigen normal verteilten Daten:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3036ad5f",
   "metadata": {
    "execution": {
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     "iopub.status.idle": "2026-05-22T13:29:06.665764Z",
     "shell.execute_reply": "2026-05-22T13:29:06.665467Z",
     "shell.execute_reply.started": "2026-05-22T13:29:06.434864Z"
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   "outputs": [
    {
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       "</style>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-0.010284</td>\n",
       "      <td>-0.018033</td>\n",
       "      <td>0.012603</td>\n",
       "      <td>-0.015950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.006980</td>\n",
       "      <td>1.015495</td>\n",
       "      <td>0.989181</td>\n",
       "      <td>1.032210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-3.175732</td>\n",
       "      <td>-3.720231</td>\n",
       "      <td>-3.093263</td>\n",
       "      <td>-2.889419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.647827</td>\n",
       "      <td>-0.683638</td>\n",
       "      <td>-0.644732</td>\n",
       "      <td>-0.747090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-0.030960</td>\n",
       "      <td>-0.011795</td>\n",
       "      <td>0.033418</td>\n",
       "      <td>-0.023026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.665872</td>\n",
       "      <td>0.677355</td>\n",
       "      <td>0.656409</td>\n",
       "      <td>0.692767</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.310321</td>\n",
       "      <td>3.484527</td>\n",
       "      <td>3.275656</td>\n",
       "      <td>3.527782</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0            1            2            3\n",
       "count  1000.000000  1000.000000  1000.000000  1000.000000\n",
       "mean     -0.010284    -0.018033     0.012603    -0.015950\n",
       "std       1.006980     1.015495     0.989181     1.032210\n",
       "min      -3.175732    -3.720231    -3.093263    -2.889419\n",
       "25%      -0.647827    -0.683638    -0.644732    -0.747090\n",
       "50%      -0.030960    -0.011795     0.033418    -0.023026\n",
       "75%       0.665872     0.677355     0.656409     0.692767\n",
       "max       3.310321     3.484527     3.275656     3.527782"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "rng = np.random.default_rng()\n",
    "df = pd.DataFrame(rng.normal(size=(1000, 4)))\n",
    "\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66bbe4f3",
   "metadata": {},
   "source": [
    "Angenommen, ihr wollt in einer der Spalten Werte finden, deren absoluter Wert größer als 3 oder kleiner als -3 ist:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7706abfa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-22T13:29:06.666312Z",
     "iopub.status.busy": "2026-05-22T13:29:06.666191Z",
     "iopub.status.idle": "2026-05-22T13:29:06.668931Z",
     "shell.execute_reply": "2026-05-22T13:29:06.668635Z",
     "shell.execute_reply.started": "2026-05-22T13:29:06.666304Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "254   -3.238330\n",
       "422    3.484527\n",
       "464   -3.437452\n",
       "476   -3.019482\n",
       "499   -3.094016\n",
       "621   -3.720231\n",
       "674    3.145420\n",
       "Name: 1, dtype: float64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col = df[1]\n",
    "\n",
    "col[col.abs() > 3]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71ecdd17",
   "metadata": {},
   "source": [
    "Um alle Zeilen auszuwählen, in denen Wert größer 3 oder kleiner -3 in einer der Spalten ist, könnt ihr [pandas.DataFrame.any](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.any.html) auf einen booleschen DataFrame anwenden, wobei mit `any(axis=1)` üüberprüft wird, ob ein Wert in einer Zeile wahr ist:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "337e4285",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-22T13:29:06.669416Z",
     "iopub.status.busy": "2026-05-22T13:29:06.669337Z",
     "iopub.status.idle": "2026-05-22T13:29:06.673368Z",
     "shell.execute_reply": "2026-05-22T13:29:06.673181Z",
     "shell.execute_reply.started": "2026-05-22T13:29:06.669409Z"
    }
   },
   "outputs": [
    {
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       "      <th>68</th>\n",
       "      <td>-0.913320</td>\n",
       "      <td>0.675847</td>\n",
       "      <td>-0.237511</td>\n",
       "      <td>3.070655</td>\n",
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       "      <th>197</th>\n",
       "      <td>1.227823</td>\n",
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       "      <td>0.875736</td>\n",
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       "      <th>254</th>\n",
       "      <td>0.562163</td>\n",
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       "      <td>-0.808823</td>\n",
       "      <td>-0.130129</td>\n",
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       "      <th>319</th>\n",
       "      <td>0.011201</td>\n",
       "      <td>0.110650</td>\n",
       "      <td>-1.336874</td>\n",
       "      <td>3.000621</td>\n",
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       "    <tr>\n",
       "      <th>370</th>\n",
       "      <td>0.998057</td>\n",
       "      <td>1.127185</td>\n",
       "      <td>-0.648043</td>\n",
       "      <td>3.117027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>404</th>\n",
       "      <td>-0.340538</td>\n",
       "      <td>-2.698506</td>\n",
       "      <td>-3.093263</td>\n",
       "      <td>-0.399621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>409</th>\n",
       "      <td>3.310321</td>\n",
       "      <td>1.442338</td>\n",
       "      <td>0.362357</td>\n",
       "      <td>-1.605350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>422</th>\n",
       "      <td>0.175541</td>\n",
       "      <td>3.484527</td>\n",
       "      <td>0.432583</td>\n",
       "      <td>-1.932812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>442</th>\n",
       "      <td>3.288727</td>\n",
       "      <td>1.135310</td>\n",
       "      <td>-0.368762</td>\n",
       "      <td>1.578203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>464</th>\n",
       "      <td>1.496301</td>\n",
       "      <td>-3.437452</td>\n",
       "      <td>1.050452</td>\n",
       "      <td>0.070361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>470</th>\n",
       "      <td>-0.187702</td>\n",
       "      <td>0.400744</td>\n",
       "      <td>3.081391</td>\n",
       "      <td>-0.937770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>1.191677</td>\n",
       "      <td>-3.019482</td>\n",
       "      <td>-0.025482</td>\n",
       "      <td>1.082824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>0.553608</td>\n",
       "      <td>-3.094016</td>\n",
       "      <td>-0.101979</td>\n",
       "      <td>0.225328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>621</th>\n",
       "      <td>1.266543</td>\n",
       "      <td>-3.720231</td>\n",
       "      <td>-0.364275</td>\n",
       "      <td>1.231816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>661</th>\n",
       "      <td>-1.055270</td>\n",
       "      <td>-0.486829</td>\n",
       "      <td>0.617043</td>\n",
       "      <td>3.527782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>674</th>\n",
       "      <td>1.035528</td>\n",
       "      <td>3.145420</td>\n",
       "      <td>1.298255</td>\n",
       "      <td>1.106587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>901</th>\n",
       "      <td>-3.175732</td>\n",
       "      <td>0.553589</td>\n",
       "      <td>-0.767643</td>\n",
       "      <td>0.718555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>946</th>\n",
       "      <td>3.252568</td>\n",
       "      <td>-0.487513</td>\n",
       "      <td>-0.107456</td>\n",
       "      <td>1.845214</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            0         1         2         3\n",
       "68  -0.913320  0.675847 -0.237511  3.070655\n",
       "197  1.227823 -0.551239  3.275656  0.875736\n",
       "254  0.562163 -3.238330 -0.808823 -0.130129\n",
       "319  0.011201  0.110650 -1.336874  3.000621\n",
       "370  0.998057  1.127185 -0.648043  3.117027\n",
       "404 -0.340538 -2.698506 -3.093263 -0.399621\n",
       "409  3.310321  1.442338  0.362357 -1.605350\n",
       "422  0.175541  3.484527  0.432583 -1.932812\n",
       "442  3.288727  1.135310 -0.368762  1.578203\n",
       "464  1.496301 -3.437452  1.050452  0.070361\n",
       "470 -0.187702  0.400744  3.081391 -0.937770\n",
       "476  1.191677 -3.019482 -0.025482  1.082824\n",
       "499  0.553608 -3.094016 -0.101979  0.225328\n",
       "621  1.266543 -3.720231 -0.364275  1.231816\n",
       "661 -1.055270 -0.486829  0.617043  3.527782\n",
       "674  1.035528  3.145420  1.298255  1.106587\n",
       "901 -3.175732  0.553589 -0.767643  0.718555\n",
       "946  3.252568 -0.487513 -0.107456  1.845214"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[(df.abs() > 3).any(axis=1)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a6c3d55",
   "metadata": {},
   "source": [
    "Auf dieser Grundlage können die Werte begrenzt werden auf ein Intervall zwischen `-3` und `3`. Hierfür verwenden wir die Anweisung `np.sign(df)`,  die Werte `1` und `-1` erzeugt, je nachdem, ob die Werte in `df` positiv oder negativ sind:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a0d7f3e6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-22T13:29:06.673706Z",
     "iopub.status.busy": "2026-05-22T13:29:06.673629Z",
     "iopub.status.idle": "2026-05-22T13:29:06.680715Z",
     "shell.execute_reply": "2026-05-22T13:29:06.680386Z",
     "shell.execute_reply.started": "2026-05-22T13:29:06.673699Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "      <th>count</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-0.010960</td>\n",
       "      <td>-0.017153</td>\n",
       "      <td>0.012340</td>\n",
       "      <td>-0.016666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.003767</td>\n",
       "      <td>1.008652</td>\n",
       "      <td>0.987770</td>\n",
       "      <td>1.029968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-3.000000</td>\n",
       "      <td>-3.000000</td>\n",
       "      <td>-3.000000</td>\n",
       "      <td>-2.889419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.647827</td>\n",
       "      <td>-0.683638</td>\n",
       "      <td>-0.644732</td>\n",
       "      <td>-0.747090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-0.030960</td>\n",
       "      <td>-0.011795</td>\n",
       "      <td>0.033418</td>\n",
       "      <td>-0.023026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.665872</td>\n",
       "      <td>0.677355</td>\n",
       "      <td>0.656409</td>\n",
       "      <td>0.692767</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0            1            2            3\n",
       "count  1000.000000  1000.000000  1000.000000  1000.000000\n",
       "mean     -0.010960    -0.017153     0.012340    -0.016666\n",
       "std       1.003767     1.008652     0.987770     1.029968\n",
       "min      -3.000000    -3.000000    -3.000000    -2.889419\n",
       "25%      -0.647827    -0.683638    -0.644732    -0.747090\n",
       "50%      -0.030960    -0.011795     0.033418    -0.023026\n",
       "75%       0.665872     0.677355     0.656409     0.692767\n",
       "max       3.000000     3.000000     3.000000     3.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df.abs() > 3] = np.sign(df) * 3\n",
    "\n",
    "df.describe()"
   ]
  }
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