ZHAWNotes/Notes/Semester 3/STS - Stochastik und Statistik/Diagrams.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Manuel\\AppData\\Local\\Temp\\ipykernel_21784\\915643508.py:9: MatplotlibDeprecationWarning: The 'use_line_collection' parameter of stem() was deprecated in Matplotlib 3.6 and will be removed two minor releases later. If any parameter follows 'use_line_collection', they should be passed as keyword, not positionally.\n",
      "  plt.stem(A,f, linefmt='red',markerfmt='ro', use_line_collection=True)\n"
     ]
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "A=np.arange(1,7,1) # Mögliche Ergebnisse\n",
    "h=np.array([4, 3, 4, 0, 6, 3])\n",
    "# Absolute Häufigkeiten\n",
    "f = h/20 # relative Häufigkeiten\n",
    "plt.figure(1)\n",
    "plt.subplot(2,2,1)\n",
    "plt.stem(A,f, linefmt='red',markerfmt='ro', use_line_collection=True)\n",
    "plt.ylabel('Relative Häufigkeit')\n",
    "plt.xlabel('Würfelergebnisse')\n",
    "plt.title('Relative Häufigkeitsfunktion')\n",
    "plt.subplot(2,2,3)\n",
    "plt.bar(A,f, 0.4,color=\"red\")\n",
    "plt.ylabel('Relative Häufigkeit')\n",
    "plt.xlabel('Würfelergebnisse')\n",
    "plt.title('Relative Häufigkeitsfunktion')\n",
    "plt.tight_layout()\n",
    "\n",
    "A=np.array([1, 2, 3, 4, 5]) # Anzahl der Flugreisen\n",
    "h=np.array([9, 8, 5, 7, 1]) # Absolute Häufigkeit\n",
    "n=np.sum(h) # Grösse der Stichprobe\n",
    "f=h/n # relative Häufigkeit\n",
    "H=np.cumsum(h) # absolute Summenhäufigkeit\n",
    "F=np.cumsum(f) # relative Summenhäufigkeit, kumulative Verteilungsfunktion (CDF)\n",
    "# Anpassung der Arrays, damit der Plot schöner wird\n",
    "A_p=np.concatenate((np.array([0]),A,np.array([6])),axis=0)\n",
    "h_p=np.concatenate((np.array([0]),h,np.array([0])),axis=0)\n",
    "H_p=np.concatenate((np.array([0]),H,np.array([n])),axis=0)\n",
    "f_p=h_p/n\n",
    "F_p=np.cumsum(f_p)\n",
    "\n",
    "plt.subplot(2,2,(2,4))\n",
    "plt.step(A_p, F_p,where='post', color='red')\n",
    "plt.title('Kumulative Verteilungsfunktion')\n",
    "plt.xlabel('Anzahl Flugreisen')\n",
    "plt.ylabel('Anteil')\n",
    "plt.xlim(0,6)\n",
    "plt.ylim(0,1)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.0014793333333333332)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Ausgaben für Transport\n",
    "#stetig metrisches Merkmal und Klassierung der Daten\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "K=np.array([0, 100, 200, 500, 800,\n",
    "1000, 2000]) # Klassengrenzen\n",
    "h=np.array([0, 35, 182, 317, 84, 132,0]) # absolute Klassenhäufigkeiten\n",
    "APDF=np.array([0, 35/100, 182/300, 317/300, 84/200, 132/1000, 0]) # absolute Säulenhöhen im Histogramm\n",
    "PDF=APDF/np.sum(h) # Säulenhöhen der PDF im Histogramm\n",
    "plt.figure(1)\n",
    "plt.step(K,PDF,color='red',where='post')\n",
    "plt.xlabel('Ausgaben in Franken')\n",
    "plt.ylabel('Häufigkeitsverteilung - PDF')\n",
    "plt.title('Jährliche Ausgaben - Histogramm')\n",
    "plt.xlim(left=0)\n",
    "plt.ylim(ymin=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'CDF der Stichprobe')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Quantile (aus CDF)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "X=np.array([4, 4, 0, 3, 5, 3, 1])\n",
    "Xnum,absH =np.unique(X, return_counts=True)\n",
    "relH=absH/np.size(X)\n",
    "kumrelH =np.cumsum(relH)\n",
    "plt.figure()\n",
    "plt.step(Xnum,kumrelH,where='post',color='red')\n",
    "plt.xlim(0, np.max(X)+1)\n",
    "plt.ylim(0, 1)\n",
    "plt.vlines(1,0,0.25,color='blue',linestyles='dashed',label='1.Quartil') #1.Quartil\n",
    "plt.hlines(0.25,0,1,color='blue',linestyles='dashed')\n",
    "plt.vlines(3,0,0.5,color='green',linestyles='dashed',label='2.Quartil') #Median\n",
    "plt.hlines(0.5,0,3,color='green',linestyles='dashed')\n",
    "plt.vlines(4,0,0.75,color='orange',linestyles='dashed',label='3.Quartil') #3.Quartil\n",
    "plt.hlines(0.75,0,4,color='orange',linestyles='dashed')\n",
    "plt.legend()\n",
    "plt.title('CDF der Stichprobe')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "ZHAWNotes-Ak5ZQvuq",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9 (tags/v3.10.9:1dd9be6, Dec  6 2022, 20:01:21) [MSC v.1934 64 bit (AMD64)]"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
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 },
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}