{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dfc79856-df74-4da1-a2c9-08828ef371ba",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "---------------------------------\n",
      "Working on the host: Joachims-MacBook-Pro.local\n",
      "\n",
      "---------------------------------\n",
      "Python version: 3.10.2 | packaged by conda-forge | (main, Feb  1 2022, 19:30:18) [Clang 11.1.0 ]\n",
      "\n",
      "---------------------------------\n",
      "Python interpreter: /opt/miniconda3/envs/srh/bin/python\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# Load the \"autoreload\" extension\n",
    "%load_ext autoreload\n",
    "# always reload modules\n",
    "%autoreload 2\n",
    "# black formatter for jupyter notebooks\n",
    "#%load_ext nb_black\n",
    "# black formatter for jupyter lab\n",
    "%load_ext lab_black\n",
    "\n",
    "%run ../../src/notebook_env.py"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "355d32e2-4068-4454-a167-a5260f752949",
   "metadata": {},
   "source": [
    "# Die kontinuierliche gleichmäßige Verteilung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "53e172b5-78b9-444d-ab61-3ea06043aa7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import uniform"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe0fa3c1-7eab-4ac4-83b6-f9de97cb71f2",
   "metadata": {},
   "source": [
    "Die <a href=\"https://de.wikipedia.org/wiki/Stetige_Gleichverteilung\">Gleichverteilung</a> ist die einfachste Wahrscheinlichkeitsverteilung, aber sie spielt eine wichtige Rolle in der Statistik, da sie bei der Modellierung von Zufallsvariablen sehr nützlich ist. Die Gleichverteilung ist eine kontinuierliche Wahrscheinlichkeitsverteilung und befasst sich mit Ereignissen, deren Auftreten gleich wahrscheinlich ist. Die kontinuierliche Zufallsvariable $X$ gilt als gleichmäßig verteilt oder hat eine rechteckige Verteilung auf dem Intervall $[a \\ $,$ \\ b]$. Wir schreiben $X \\sim U(a \\ $,$ \\ b)$, wenn seine Wahrscheinlichkeitsdichtefunktion gleich $f(x)=\\frac{1}{b-a},x \\in [a \\ $,$ \\ b]$ und ansonsten gleich $0$ ist ({cite:t}`Papula2011` s.331)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00673c73-c0ff-4af4-bc79-c79922a65e8a",
   "metadata": {
    "tags": []
   },
   "source": [
    "$$f(x) =\n",
    "\\begin{cases}\n",
    "\\frac{1}{b-a},  & \\text{wenn   $a \\le x \\le b$} \\\\[2ex]\n",
    "0, & \\text{wenn   $x < a$   oder   $x > b$}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2257b982-47c4-413d-b22d-2e189bddc9ff",
   "metadata": {},
   "source": [
    "Die folgende Abbildung zeigt eine kontinuierliche Gleichverteilung $X \\sim U(-2 \\ $,$ \\ 0,8)$, also eine Verteilung, bei der alle Werte von $x$ innerhalb des Intervalls $[-2 \\ $,$ \\ 0,8] $ gleich $ \\frac{1}{b-a}(=\\frac{1}{0,8-(-2)}\\approx 0,36)$ sind, während alle anderen Werte von $x$ gleich $0$ sind."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "abc4c050-21cb-4872-9fe0-f922a9bee9c3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Wahrscheinlichkeitsdichte')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4.2, 4.2, num=1000)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, uniform.pdf(x, -2, 2 + 0.8), linewidth=4)\n",
    "ax.set_title(r\"$X \\sim U(-2, 0.8)$\")\n",
    "ax.set_ylabel(\"Wahrscheinlichkeitsdichte\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a9e5aff-4802-4617-906b-4328b12fdfd2",
   "metadata": {},
   "source": [
    "Der Mittelwert und der Median sind gegeben durch "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6908b6cd-340f-4904-a227-6421c9c82398",
   "metadata": {},
   "source": [
    "$$\\mu = \\frac{a+b}{2}\\text{.}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f3ad392-b568-4cec-876b-19f33cb97c72",
   "metadata": {},
   "source": [
    "Die kumulative Dichtefunktion ist unten dargestellt und ergibt sich aus der Gleichung"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15de3f2d-f38e-4f1c-a6be-5cb6a519b519",
   "metadata": {},
   "source": [
    "$$F(x) =\n",
    "\\begin{cases}\n",
    "0,  & \\text{for $x < a$} \\\\[2ex]\n",
    "\\frac{x-a}{b-a},  & \\text{for $x \\in [a,b)$} \\\\[2ex]\n",
    "1, & \\text{for $x \\ge b$}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a1cf216f-b0f3-4fb1-b9e9-3b95957b8033",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Kummulierte Wahrscheinlichkeitsdichte')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4.2, 4.2, num=1000)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, uniform.cdf(x, -2, 2 + 0.8), linewidth=4)\n",
    "ax.set_title(r\"$X \\sim U(-2, 0.8)$\")\n",
    "ax.set_ylabel(\"Kummulierte Wahrscheinlichkeitsdichte\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d248bad5-cf8b-443d-a863-e536d82d6f1c",
   "metadata": {},
   "source": [
    "## Die kontinuierliche gleichmäßige Verteilung in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6ae92b4-75fb-498a-9d45-ed37f42a6fbe",
   "metadata": {},
   "source": [
    "Python ermöglicht den Zugriff auf die Gleichverteilung mit den Funktionen `uniform.pmf()`, `uniform.cdf()`, `uniform.ppf()` und `uniform.rvs()`. Wenden Sie die Funktion `dir()` auf diese Funktionen an, um weitere Informationen zu erhalten.\n",
    "\n",
    "Die Funktion `uniform.rvs()` erzeugt Zufallsabweichungen der Gleichverteilung und wird als `uniform.rvs(loc, loc+scale, size)` geschrieben. Wir können auf einfache Weise $n$ Zufallsstichproben innerhalb eines beliebigen Intervalls erzeugen indem wir die Zahlenwerte für minimalen ($a$) und maximalen Wert ($b$) in `random.uniform(a,b, size)` einsetzen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8ade9006-d807-48bb-bddf-286ac0198baa",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.49423725,  0.26276601,  0.99941659, -0.94404041, -0.41986593,\n",
       "        0.34363989,  0.12070883,  0.46646236, -0.41928963, -0.02032979,\n",
       "       -0.24322852, -0.81200601, -0.39657292, -0.08343389, -0.37569097,\n",
       "        0.37324126, -0.70646557,  0.44563635,  0.30023937, -0.51321266,\n",
       "        0.9091371 , -0.92235404, -0.74603909,  0.67451317, -0.2172681 ,\n",
       "        0.73934229, -0.05676821,  0.38577142, -0.4443734 ,  0.57194726,\n",
       "        0.99401505,  0.75209712, -0.96875976, -0.51015716,  0.23434428,\n",
       "        0.38969345, -0.36672054,  0.15041627, -0.92863787, -0.96947179])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_rvs = np.random.uniform(-1, 1, size=40)\n",
    "u_rvs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "713fa8e8-64d8-484a-b3c6-c9cced87d506",
   "metadata": {},
   "source": [
    "Wir können die Dichtefunktion für $X \\sim U(-2 \\ $,$ \\ 0,8)$ mit Hilfe der Funktion `uniform.rvs()` approximieren und die Ergebnisse als Histogramm darstellen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "386b161e-e4b3-49fe-b086-5f5a519ec3d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([506., 481., 550., 501., 511., 454., 485., 473., 523., 485., 494.,\n",
       "        495., 489., 511., 518., 505., 481., 492., 529., 517.]),\n",
       " array([-1.99968443, -1.85972763, -1.71977082, -1.57981402, -1.43985722,\n",
       "        -1.29990041, -1.15994361, -1.0199868 , -0.88003   , -0.7400732 ,\n",
       "        -0.60011639, -0.46015959, -0.32020278, -0.18024598, -0.04028918,\n",
       "         0.09966763,  0.23962443,  0.37958124,  0.51953804,  0.65949484,\n",
       "         0.79945165]),\n",
       " <BarContainer object of 20 artists>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Erzeuge gleichverteilte werte\n",
    "u_rvs = np.random.uniform(-2, 0.8, size=10000)\n",
    "\n",
    "# Plotte Histogramm\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlim(-3, 3)\n",
    "ax.set_title(\"Histogramm für rand.uniform\")\n",
    "ax.set_ylabel(\"Wahrscheinlichkeitsdichte\")\n",
    "ax.hist(u_rvs, bins=20, edgecolor=\"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c30c306-eec7-4db4-a2f0-a5f649b7f3f9",
   "metadata": {},
   "source": [
    "Außerdem stellen wir sowohl das Dichtehistogramm von oben als auch die gleichmäßige Wahrscheinlichkeitsverteilung für das Intervall $[-2 \\ $,$ \\ 0,8]$ dar, indem wir die Funktion `uniform.pdf()` anwenden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d46da55a-987f-4bae-b9a7-ef50abc1a134",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16baa98d0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Erzeuge x-werte\n",
    "x = np.linspace(-2.2, 1, num=1000)\n",
    "\n",
    "# Erzeuge gleichverteilte werte\n",
    "u_rvs = uniform.rvs(loc=-2, scale=2 + 0.8, size=10000)\n",
    "\n",
    "# Plotte Histogramm und uniforme pdf\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title(\"Histogramm für rand.uniform\")\n",
    "ax.set_ylabel(\"Wahrscheinlichkeitsdichte\")\n",
    "ax.hist(u_rvs, bins=20, edgecolor=\"k\", density=True)\n",
    "ax.plot(x, uniform.pdf(x, -2, 2 + max(u_rvs)), linewidth=4, alpha=0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "74914719-602a-4407-b34b-bdbdafc86100",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.7"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unif_mean = (-2 + 0.6) / 2\n",
    "unif_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "691f94f5-42d9-4b06-9131-7c55fa77e6ce",
   "metadata": {},
   "source": [
    "Die Abbildung zeigt, dass unsere $10.000$ Stichproben, die nach dem Zufallsprinzip aus einer Gleichverteilung gezogen wurden (Histogramm), sich der Gleichverteilung $X \\sim U(-2 \\ $,$ \\ 0,8)$ (Liniendiagramm).\n",
    "\n",
    "Außerdem können wir die Funktion `uniform.cdf()` verwenden, um die Fläche unter der Kurve für einen bestimmten Schwellenwert zu berechnen, oder wir können die Funktion `uniform.ppf()` verwenden, um einen Schwellenwert für eine bestimmte Wahrscheinlichkeit zurückzugeben."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05459222-722a-47db-9a79-f24d799f7816",
   "metadata": {},
   "source": [
    "### Übung"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01156691-e42f-4d7a-bfe8-98e20436742f",
   "metadata": {},
   "source": [
    "Betrachten wir die gleichmäßige Wahrscheinlichkeitsverteilung, die durch $X \\sim U(-3 \\ $,$ \\ 5,5)$ gegeben ist."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8e916a6-25af-47d9-a3c2-9063ca632e3b",
   "metadata": {},
   "source": [
    "**Frage 1**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42b505f2-67dd-498f-b8f5-900d3a3e2606",
   "metadata": {},
   "source": [
    "Wie lautet der Mittelwert $\\mu$ für die gegebene Gleichverteilung."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5926c31b-6543-44d1-9997-5d0ccdc2e0bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.25"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unif_mean = (-3 + 5.5) / 2\n",
    "unif_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "379d5480-5209-4b3a-9348-39e3a8e68e6e",
   "metadata": {},
   "source": [
    "Der Mittelwert $\\mu$ für die durch $X \\sim U(-3 \\ $,$ \\ 5,5)$ gegebene gleichmäßige Wahrscheinlichkeitsverteilung beträgt $1,25$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb5d10b0-018c-4b09-89c4-1a09630a665f",
   "metadata": {},
   "source": [
    "**Frage 2**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6f20770-d9cf-4a18-963f-2c3ab99c16a8",
   "metadata": {},
   "source": [
    "Welcher Wert von $x$ entspricht dem Wert, der die gegebene Gleichverteilung in zwei gleiche Teile teilt, oder anders ausgedrückt: $P(X \\lt ?)=0,5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c42e8972-586f-4d36-88f4-42763616a242",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.25"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_50 = uniform.ppf(0.5, -3, 8.5)\n",
    "p_50"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86bee041-008a-4d51-af3e-3f19442d0601",
   "metadata": {},
   "source": [
    "Das ist überhaupt keine Überraschung. Der Wert von $x$, der die Gleichverteilung in zwei gleiche Teile teilt, beträgt $1,25$ und ist somit gleich $\\mu$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f3af749-6b4c-4ddc-93c8-be6811e44eda",
   "metadata": {},
   "source": [
    "**Frage 3**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2c4cf45-62ab-4564-97fe-6cc96385efa0",
   "metadata": {},
   "source": [
    "Angenommen, die obige Verteilung beschreibt ein physikalisches Phänomen. Wie groß ist die Wahrscheinlichkeit, dass bei einer Messung des physikalischen Prozesses, der das Phänomen bestimmt, ein Wert $\\ge 4$ gemessen wird, oder anders ausgedrückt: $P(X \\ge 4)$. Aufgrund des Charakters einer Gleichverteilung ist die Messung eines beliebigen Wertes innerhalb des Intervalls $[-3 \\ $,$ \\ 5,5]$ gleich wahrscheinlich ist.\n",
    "\n",
    "Wir werden diese Frage auf zwei Arten lösen, numerisch und analytisch. Um die Frage numerisch zu lösen, müssen wir zunächst ein Experiment durchführen. Wir wiederholen unsere Messung eine große Anzahl von Malen und zählen dann, wie oft wir einen Wert $\\ge 4$ registriert haben\n",
    ". Dank der Leistungsfähigkeit von Python und dem integrierten Zufallszahlengenerator `uniform.rvs()` für gleichmäßig verteilte Daten) ist die Wiederholungsaufgabe sehr einfach, allerdings sollte man sich darüber im Klaren sein, dass in realen Anwendungen oft nur eine sehr begrenzte Anzahl von Messungen verfügbar ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ad11e250-6905-444d-94f3-c6673f70ec97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1701"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Erzeuge gleichverteilte Zufallsvariablen und Variable count\n",
    "u_rvs = uniform.rvs(-3, 8.5, size=10000)\n",
    "\n",
    "# Zähle Werte größer gleich 4\n",
    "count = sum(u_rvs >= 4)\n",
    "\n",
    "# Dividiere durch Gesamtanzahl der Werte\n",
    "count = count / len(u_rvs)\n",
    "count"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44ee1b35-7704-481c-9d64-380b0e070f5f",
   "metadata": {},
   "source": [
    "Die Ergebnisse zeigen, dass etwa $18 \\%$ der Messungen Werte $\\ge 4$ ergeben.\n",
    "\n",
    "Zweitens, um die Frage analytisch zu lösen, verwenden wir die kumulative Wahrscheinlichkeitsdichtefunktion, die in Python für gleichmäßige Verteilungen durch die Funktion `uniform.cdf()` implementiert ist. \n",
    "Wir interessieren uns also für die Fläche unter der Kurve bis zum Wert von $x=4$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "41a2b3ff-a151-4d74-894b-6bae693ff12e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.17647058823529416"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - uniform.cdf(4, -3, 8.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8823199-1340-4577-b775-d866fc0b5e9b",
   "metadata": {
    "tags": []
   },
   "source": [
    "Der analytische Ansatz ergibt ein Ergebnis von $0,1764706$ oder anders ausgedrückt, mit einer Wahrscheinlichkeit von $17,65 \\%$ erhalten wir Werte $\\ge 4$, also $P(X \\ge 4) \\approx 0,18$.\n",
    "\n",
    "Es ist offensichtlich, dass beide Ansätze sehr ähnliche Ergebnisse liefern. Es ist jedoch zu beachten, dass das Ergebnis des numerischen Ansatzes eine Annäherung an das analytische Ergebnis darstellt. Bedenken Sie, dass die Qualität einer solchen Annäherung sehr stark von der Anzahl der Zufallsvariablen abhängt, aus denen die Stichprobe besteht, in unserem Fall von der Anzahl der Messungen."
   ]
  }
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