Added mre MAT-203 stuff
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,winsdominoes,Fons-iMac-2.local,19.11.2024 23:03,file:///Users/winsdominoes/Library/Application%20Support/LibreOffice/4;
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@ -4,7 +4,19 @@
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"ename": "ModuleNotFoundError",
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"evalue": "No module named 'numpy'",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
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"Cell \u001b[0;32mIn[1], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;66;03m#Numerical Python\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m 4\u001b[0m \u001b[38;5;66;03m# To plot\u001b[39;00m\n\u001b[1;32m 5\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n",
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"\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'numpy'"
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]
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}
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],
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"source": [
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"#Numerical Python\n",
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"import numpy as np\n",
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@ -810,7 +822,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.4"
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"version": "3.13.0"
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}
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},
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"nbformat": 4,
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@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 21,
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"execution_count": 278,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -22,7 +22,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"execution_count": 279,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -32,7 +32,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"execution_count": 280,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -49,7 +49,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"execution_count": 281,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -59,7 +59,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"execution_count": 282,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -70,7 +70,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"execution_count": 283,
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"metadata": {},
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"outputs": [
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{
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@ -79,7 +79,7 @@
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"['Iceland', 'India', 'Indonesia', 'Iraq', 'Ireland', 'Israel', 'Italy']"
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]
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},
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"execution_count": 26,
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"execution_count": 283,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -92,7 +92,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"execution_count": 284,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -106,7 +106,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"execution_count": 285,
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"metadata": {},
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"outputs": [
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{
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@ -283,7 +283,7 @@
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"max 0.590000 0.948000 0.843000 0.516000 "
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]
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},
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"execution_count": 28,
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"execution_count": 285,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -294,7 +294,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 29,
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"execution_count": 286,
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"metadata": {},
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"outputs": [
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{
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@ -571,7 +571,7 @@
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"[121 rows x 13 columns]"
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]
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},
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"execution_count": 29,
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"execution_count": 286,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -582,7 +582,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 40,
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"execution_count": 287,
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"metadata": {},
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"outputs": [
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{
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@ -623,18 +623,18 @@
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>13</th>\n",
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" <th>0</th>\n",
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" <td>Afghanistan</td>\n",
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" <td>2022</td>\n",
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" <td>1.281</td>\n",
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" <td>2023</td>\n",
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" <td>1.446</td>\n",
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" <td>NaN</td>\n",
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" <td>0.228</td>\n",
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" <td>54.875</td>\n",
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" <td>0.368</td>\n",
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" <td>55.2</td>\n",
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" <td>0.228</td>\n",
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" <td>NaN</td>\n",
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" <td>0.733</td>\n",
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" <td>0.206</td>\n",
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" <td>0.576</td>\n",
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" <td>0.738</td>\n",
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" <td>0.261</td>\n",
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" <td>0.46</td>\n",
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" <td>Southern Asia</td>\n",
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" <td>Asia</td>\n",
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" </tr>\n",
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@ -643,31 +643,31 @@
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"</div>"
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],
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"text/plain": [
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" Country name year Life Ladder Log GDP per capita Social support \\\n",
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"13 Afghanistan 2022 1.281 NaN 0.228 \n",
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" Country name year Life Ladder Log GDP per capita Social support \\\n",
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"0 Afghanistan 2023 1.446 NaN 0.368 \n",
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"\n",
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" Healthy life expectancy at birth Freedom to make life choices \\\n",
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"13 54.875 0.368 \n",
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" Healthy life expectancy at birth Freedom to make life choices Generosity \\\n",
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"0 55.2 0.228 NaN \n",
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"\n",
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" Generosity Perceptions of corruption Positive affect Negative affect \\\n",
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"13 NaN 0.733 0.206 0.576 \n",
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" Perceptions of corruption Positive affect Negative affect Subregion \\\n",
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"0 0.738 0.261 0.46 Southern Asia \n",
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"\n",
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" Subregion Continent \n",
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"13 Southern Asia Asia "
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" Continent \n",
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"0 Asia "
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]
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},
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"execution_count": 40,
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"execution_count": 287,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"Dat.loc[Dat[\"Life Ladder\"] == Dat[\"Life Ladder\"].min()]"
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"Dat2023.loc[Dat2023[\"Life Ladder\"] == Dat2023[\"Life Ladder\"].min()]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 43,
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"execution_count": 288,
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"metadata": {},
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"outputs": [
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{
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@ -708,18 +708,18 @@
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>497</th>\n",
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" <td>Denmark</td>\n",
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" <td>2005</td>\n",
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" <td>8.019</td>\n",
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" <td>10.849</td>\n",
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" <td>0.972</td>\n",
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" <td>68.3</td>\n",
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" <td>0.971</td>\n",
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" <td>NaN</td>\n",
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" <td>0.237</td>\n",
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" <td>0.777</td>\n",
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" <td>0.154</td>\n",
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" <th>35</th>\n",
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" <td>Finland</td>\n",
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" <td>2023</td>\n",
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" <td>7.699</td>\n",
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" <td>10.808</td>\n",
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" <td>0.947</td>\n",
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" <td>71.3</td>\n",
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" <td>0.943</td>\n",
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" <td>-0.001</td>\n",
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" <td>0.185</td>\n",
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" <td>0.717</td>\n",
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" <td>0.173</td>\n",
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" <td>Northern Europe</td>\n",
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" <td>Europe</td>\n",
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" </tr>\n",
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@ -728,47 +728,47 @@
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"</div>"
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],
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"text/plain": [
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" Country name year Life Ladder Log GDP per capita Social support \\\n",
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"497 Denmark 2005 8.019 10.849 0.972 \n",
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" Country name year Life Ladder Log GDP per capita Social support \\\n",
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"35 Finland 2023 7.699 10.808 0.947 \n",
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"\n",
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" Healthy life expectancy at birth Freedom to make life choices \\\n",
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"497 68.3 0.971 \n",
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" Healthy life expectancy at birth Freedom to make life choices \\\n",
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"35 71.3 0.943 \n",
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"\n",
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" Generosity Perceptions of corruption Positive affect Negative affect \\\n",
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"497 NaN 0.237 0.777 0.154 \n",
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" Generosity Perceptions of corruption Positive affect Negative affect \\\n",
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"35 -0.001 0.185 0.717 0.173 \n",
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"\n",
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" Subregion Continent \n",
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"497 Northern Europe Europe "
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" Subregion Continent \n",
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"35 Northern Europe Europe "
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]
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},
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"execution_count": 43,
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"execution_count": 288,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"Dat.loc[Dat[\"Life Ladder\"] == Dat[\"Life Ladder\"].max()]"
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"Dat2023.loc[Dat2023[\"Life Ladder\"] == Dat2023[\"Life Ladder\"].max()]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 48,
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"execution_count": 289,
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"metadata": {},
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"outputs": [],
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"source": [
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"avg_health = Dat[\"Healthy life expectancy at birth\"].median()"
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"avg_health = Dat2023[\"Healthy life expectancy at birth\"].median()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 50,
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"execution_count": 290,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"65.22\n"
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"66.3\n"
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]
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}
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],
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},
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{
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"cell_type": "code",
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"execution_count": 56,
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"execution_count": 291,
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"metadata": {},
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"outputs": [
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{
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"np.float64(0.231)"
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]
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},
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"execution_count": 56,
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"execution_count": 291,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -801,7 +801,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 57,
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"execution_count": 292,
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"metadata": {},
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"outputs": [
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{
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@ -810,7 +810,7 @@
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"array([4.6125, 5.42 , 6.3215])"
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]
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},
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"execution_count": 57,
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"execution_count": 292,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -822,34 +822,373 @@
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},
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{
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"cell_type": "code",
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"execution_count": 64,
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"execution_count": 293,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"5.42\n",
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"5.4660082404265635\n",
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"5.3416056329049155\n",
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"5.207292342092034\n",
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"5.446561471442401\n",
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"1.7089999999999996\n",
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"5.4660082404265635\n"
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"5.868\n",
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"5.601454545454545\n",
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"5.46003534802306\n",
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"5.277807689332831\n",
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"5.670474226804124\n",
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"5.738901639344262\n",
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"5.601454545454545\n"
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]
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}
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],
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"source": [
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"ll = Dat[\"Life Ladder\"]\n",
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"ll = Dat2023[\"Life Ladder\"]\n",
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"\n",
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"Mean = ll.mean()\n",
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"\n",
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"print(ll.median())\n",
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"print(ll.mean())\n",
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"print(Mean)\n",
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"print(gmean(ll))\n",
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"print(hmean(ll))\n",
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"print(trim_mean(ll, 0.1))\n",
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"print(trim_mean(ll, 0.25))\n",
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"print(iqr(ll).mean())\n",
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"print(winsorize(ll).mean())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 294,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1.1545804575939485\n",
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"1.1593812286445444\n",
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"6.253\n",
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"1.8730000000000002\n",
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"0.8130000000000006\n",
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"0.9629526671675434\n"
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]
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}
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],
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"source": [
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"S2Biased = np.var(ll)\n",
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"S2Unbiased = np.var(ll, ddof=1)\n",
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"\n",
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"S1 = np.sqrt(S2Biased)\n",
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"S2 = np.sqrt(S2Unbiased)\n",
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"R = ll.max() - ll.min()\n",
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"IQR = iqr(ll)\n",
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"MAD = median_abs_deviation(ll)\n",
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"AAD = abs(ll-ll.mean()).mean()\n",
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"\n",
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"print(S1)\n",
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"print(S2)\n",
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"print(R)\n",
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"print(IQR)\n",
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"print(MAD)\n",
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"print(AAD)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 295,
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"metadata": {},
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"outputs": [],
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"source": [
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"def an(n):\n",
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" return np.sqrt((n-1)/2) * gamma((n-1)/2) / gamma(n/2)\n",
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"\n",
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"def c4(n):\n",
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" return 1/an(n)\n",
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"\n",
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"# d2 for n in 2,...,25\n",
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"d2 = {2:1.128, 3:1.693, 4:2.059, 5:2.326, 6:2.534, 7:2.704, 8:2.847, 9:2.970, 10:3.078, 11:3.173, 12:3.258, 13:3.336, 14:3.407, 15:3.472, 16:3.532, 17:3.588, 18:3.640, 19:3.689, 20:3.735, 21:3.778, 22:3.819, 23:3.858, 24:3.895, 25:3.931}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 296,
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"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"121\n",
|
||||
"0.9979188593597667\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"N = len(ll)\n",
|
||||
"\n",
|
||||
"print(N)\n",
|
||||
"print(c4(N))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 297,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"1.1617990959589308\n",
|
||||
"1.3884569776304965\n",
|
||||
"1.2053556036450552\n",
|
||||
"1.2068821913267496\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"\n",
|
||||
"\n",
|
||||
"sigma_1 = S2 / c4(N)\n",
|
||||
"#sigma_2 = R / d2[N]\n",
|
||||
"sigma_3 = IQR / (2 * norm.ppf(0.75))\n",
|
||||
"sigma_4 = MAD / norm.ppf(0.75)\n",
|
||||
"sigma_5 = AAD * np.sqrt(np.pi/2)\n",
|
||||
"\n",
|
||||
"print(sigma_1)\n",
|
||||
"#print(sigma_2)\n",
|
||||
"print(sigma_3)\n",
|
||||
"print(sigma_4)\n",
|
||||
"print(sigma_5)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 298,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"m2 = S2Biased\n",
|
||||
"m3 = ((ll-Mean)**3).mean()\n",
|
||||
"\n",
|
||||
"k2 = S2Unbiased\n",
|
||||
"k3 = N**2 / ((N-1)*(N-2))*m3"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 299,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"g1_byhand = m3 / m2**(3/2)\n",
|
||||
"g1 = skew(ll)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 300,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(np.float64(-0.6037), np.float64(-0.6037))"
|
||||
]
|
||||
},
|
||||
"execution_count": 300,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"g1_byhand.round(4), g1.round(4)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 301,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"G1_byhand = k3 / k2**(3/2)\n",
|
||||
"G1 = skew(ll, bias=False)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 302,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(np.float64(-0.6113), np.float64(-0.6113))"
|
||||
]
|
||||
},
|
||||
"execution_count": 302,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"G1_byhand.round(4), G1.round(4)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"m4 = ((ll-Mean)**4).mean()\n",
|
||||
"\n",
|
||||
"k4 = N**2*((N+1)*m4 - 3*(N-1)*m2**2) / ((N-1)*(N-2)*(N-3))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Coefficient of kurtosis based on central moments"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"g2_byhand = m4/m2**2\n",
|
||||
"g2 = kurtosis(ll, fisher=False)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(np.float64(4.8753), np.float64(4.8753))"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"g2_byhand.round(4), g2.round(4)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 303,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"ename": "NameError",
|
||||
"evalue": "name 'k4' is not defined",
|
||||
"output_type": "error",
|
||||
"traceback": [
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
|
||||
"Cell \u001b[0;32mIn[303], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m G2_byhand \u001b[38;5;241m=\u001b[39m \u001b[43mk4\u001b[49m\u001b[38;5;241m/\u001b[39mk2\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m3\u001b[39m\n\u001b[1;32m 2\u001b[0m G2 \u001b[38;5;241m=\u001b[39m kurtosis(ll, fisher\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m, bias\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m)\n",
|
||||
"\u001b[0;31mNameError\u001b[0m: name 'k4' is not defined"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"G2_byhand = k4/k2**2 + 3\n",
|
||||
"G2 = kurtosis(ll, fisher=False, bias=False)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(np.float64(7.2795), np.float64(7.2795))"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"G2_byhand.round(4), G2.round(4)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"ename": "NameError",
|
||||
"evalue": "name 'g2_byhand' is not defined",
|
||||
"output_type": "error",
|
||||
"traceback": [
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
|
||||
"Cell \u001b[0;32mIn[251], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m g2_excess_byhand \u001b[38;5;241m=\u001b[39m \u001b[43mg2_byhand\u001b[49m \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m3\u001b[39m\n\u001b[1;32m 2\u001b[0m g2_excess \u001b[38;5;241m=\u001b[39m kurtosis(ll)\n",
|
||||
"\u001b[0;31mNameError\u001b[0m: name 'g2_byhand' is not defined"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"g2_excess_byhand = g2_byhand - 3\n",
|
||||
"g2_excess = kurtosis(ll)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(np.float64(1.8753), np.float64(1.8753))"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"g2_excess_byhand.round(4), g2_excess.round(4)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"G2_excess_byhand = G2_byhand - 3\n",
|
||||
"G2_excess = kurtosis(ll, bias=False)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(np.float64(4.2795), np.float64(4.2795))"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"G2_excess_byhand.round(4), G2_excess.round(4)"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
|
|
@ -868,7 +1207,7 @@
|
|||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.12.6"
|
||||
"version": "3.13.0"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
Binary file not shown.
Loading…
Reference in New Issue