From 805e5732938bdf7c98bd507099f8f2d11fd9bfe7 Mon Sep 17 00:00:00 2001 From: YannAhlgrim Date: Fri, 4 Apr 2025 12:46:01 +0200 Subject: [PATCH] Remove example notebook from the Zufallszahlenlabor directory --- .../0_zufallszahlenlabor/1_beispiel.ipynb | 0 .../0_zufallszahlenlabor/main.ipynb | 262 ++++++++++++++++++ 2 files changed, 262 insertions(+) delete mode 100644 1_data_science/0_zufallszahlenlabor/1_beispiel.ipynb create mode 100644 1_data_science/0_zufallszahlenlabor/main.ipynb diff --git a/1_data_science/0_zufallszahlenlabor/1_beispiel.ipynb b/1_data_science/0_zufallszahlenlabor/1_beispiel.ipynb deleted file mode 100644 index e69de29..0000000 diff --git a/1_data_science/0_zufallszahlenlabor/main.ipynb b/1_data_science/0_zufallszahlenlabor/main.ipynb new file mode 100644 index 0000000..bc85d2a --- /dev/null +++ b/1_data_science/0_zufallszahlenlabor/main.ipynb @@ -0,0 +1,262 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Zufallszahlenlabor" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Beispiel: Poisson-Verteilung" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lage- und Streuungsmaße:\n", + "Mittlere Tore Heim: 1.80, Standardabweichung: 1.34\n", + "Mittlere Tore Auswärts: 1.30, Standardabweichung: 1.14\n", + "Mittlere Tordifferenz: 0.50, Standardabweichung: 1.76\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "np.random.seed(11)\n", + "\n", + "# gegebenen Parameter\n", + "anzahl_fussballspiele = 1000000\n", + "tore_heim_avg = 1.8\n", + "tore_auswaerts_avg = 1.3\n", + "\n", + "# Erstellung einer Poison-Verteilung\n", + "# Simulation der geschossenen Tore\n", + "tore_heim = np.random.poisson(tore_heim_avg, anzahl_fussballspiele)\n", + "tore_auswaerts = np.random.poisson(tore_auswaerts_avg, anzahl_fussballspiele)\n", + "\n", + "# Berechnung der Tordifferenz\n", + "tordifferenz = tore_heim - tore_auswaerts\n", + "\n", + "# Plot der Verteilungen\n", + "fig, axes = plt.subplots(1, 3, figsize=(18, 5))\n", + "\n", + "# Verteilung der geschossenen Tore der Heimmannschaft\n", + "values, counts = np.unique(tore_heim, return_counts=True)\n", + "probs = counts / anzahl_fussballspiele\n", + "axes[0].bar(values, probs, alpha=0.7, color='blue', edgecolor='black')\n", + "axes[0].set_title('Verteilung der Tore (Heimmannschaft)')\n", + "axes[0].set_xlabel('Anzahl Tore')\n", + "axes[0].set_ylabel('Häufigkeit')\n", + "\n", + "# Verteilung der geschossenen Tore der Gastmannschaft\n", + "values, counts = np.unique(tore_auswaerts, return_counts=True)\n", + "probs = counts / anzahl_fussballspiele\n", + "axes[1].bar(values, probs, alpha=0.7, color='green', edgecolor='black')\n", + "axes[1].set_title('Verteilung der Tore (Gastmannschaft)')\n", + "axes[1].set_xlabel('Anzahl Tore')\n", + "axes[1].set_ylabel('Häufigkeit')\n", + "\n", + "# Verteilung der Tordifferenz\n", + "values, counts = np.unique(tordifferenz, return_counts=True)\n", + "probs = counts / anzahl_fussballspiele\n", + "axes[2].bar(values, probs, alpha=0.7, color='red', edgecolor='black')\n", + "axes[2].set_title('Verteilung der Tordifferenz')\n", + "axes[2].set_xlabel('Tordifferenz')\n", + "axes[2].set_ylabel('Häufigkeit')\n", + "\n", + "plt.tight_layout()\n", + "plt.show()\n", + "\n", + "# Lage- und Streuungsmaße\n", + "print(\"Lage- und Streuungsmaße:\")\n", + "print(f\"Mittlere Tore Heim: {np.mean(tore_heim):.2f}, Standardabweichung: {np.std(tore_heim):.2f}\")\n", + "print(f\"Mittlere Tore Auswärts: {np.mean(tore_auswaerts):.2f}, Standardabweichung: {np.std(tore_auswaerts):.2f}\")\n", + "print(f\"Mittlere Tordifferenz: {np.mean(tordifferenz):.2f}, Standardabweichung: {np.std(tordifferenz):.2f}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Beispiel: Geometrische Verteilung" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lage- und Streuungsmaße:\n", + "Mittlere Tage seit letztem Fehler: 125.04\n", + "Standardabweichung: 124.51\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "np.random.seed(22)\n", + "\n", + "# Parameter für die geometrische Verteilung\n", + "durchschnitt_tage = 125\n", + "anzahl_maschinen = 1000000\n", + "\n", + "# Simulation der Tage seit letztem Fehler\n", + "tage_seit_letztem_fehler = np.random.geometric(1/durchschnitt_tage, anzahl_maschinen)\n", + "\n", + "# Plot der Verteilung\n", + "values, counts = np.unique(tage_seit_letztem_fehler, return_counts=True)\n", + "probs = counts / anzahl_maschinen\n", + "\n", + "plt.bar(values, probs, alpha=0.7, color='purple', edgecolor='black')\n", + "plt.title('Verteilung der Tage seit letztem Fehler')\n", + "plt.xlabel('Tage seit letztem Fehler')\n", + "plt.ylabel('Häufigkeit')\n", + "plt.show()\n", + "\n", + "# Lage- und Streuungsmaße\n", + "print(\"Lage- und Streuungsmaße:\")\n", + "print(f\"Mittlere Tage seit letztem Fehler: {np.mean(tage_seit_letztem_fehler):.2f}\")\n", + "print(f\"Standardabweichung: {np.std(tage_seit_letztem_fehler):.2f}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Beispiel: Binomialverteilung" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "n = 10000, p = 0.08333333333333333, size = 1000000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lage- und Streuungsmaße:\n", + "Mittlere Anzahl Kunden: 833.35\n", + "Standardabweichung: 27.63\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "np.random.seed(33)\n", + "\n", + "# Parameter für die Binomialverteilung\n", + "anzahl_tage = 1_000_000\n", + "anzahl_kunden_pro_tag = 10_000\n", + "laden_oeffnungszeiten = 12 # Stunden\n", + "zeit_kunden_einkaufen = 1 # Stunde\n", + "p = zeit_kunden_einkaufen / laden_oeffnungszeiten # Wahrscheinlichkeit, dass ein Kunde im Laden ist\n", + "\n", + "# Simulation der Anzahl der Kunden, die in einer Stunde einkaufen\n", + "print(f\"n = {anzahl_kunden_pro_tag}, p = {p}, size = {anzahl_tage}\")\n", + "anzahl_kunden = np.random.binomial(anzahl_kunden_pro_tag, p, anzahl_tage)\n", + "\n", + "# Plot der Verteilung\n", + "values, counts = np.unique(anzahl_kunden, return_counts=True)\n", + "probs = counts / anzahl_tage\n", + "\n", + "plt.bar(values, probs, alpha=0.7, color='orange')\n", + "plt.title('Verteilung der Anzahl der Kunden im Laden')\n", + "plt.xlabel('Anzahl Kunden pro Stunde')\n", + "plt.ylabel('Häufigkeit')\n", + "plt.show()\n", + "\n", + "\n", + "# Lage- und Streuungsmaße\n", + "print(\"Lage- und Streuungsmaße:\")\n", + "print(f\"Mittlere Anzahl Kunden: {np.mean(anzahl_kunden):.2f}\")\n", + "print(f\"Standardabweichung: {np.std(anzahl_kunden):.2f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "hft_ml", + "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": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}