{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "4b720c28-2cc8-4563-80ab-9836f180ffe3",
"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": "7306bdf2-eb05-4be2-9e39-0dcda402664e",
"metadata": {
"tags": []
},
"source": [
"# Stetige Zufallsvariablen und ihre Wahrscheinlichkeitsverteilungen"
]
},
{
"cell_type": "markdown",
"id": "b81c05fa-0e5e-4106-8ec9-6dd9e49794b1",
"metadata": {},
"source": [
"Eine Zufallsvariable, deren Werte nicht abzählbar sind, nennt man eine **stetige Zufallsvariable**. D.h. eine kontinuierliche Zufallsvariable kann jeden Wert annehmen (z.B. reelle Zahlenwerte), der in einem oder mehreren Intervallen enthalten ist. Da die Anzahl der in einem Intervall enthaltenen Werte unendlich ist, ist auch die mögliche Anzahl der Werte, die eine kontinuierliche Zufallsvariable annehmen kann, unendlich ({cite:p}`fahrmeirstatistik` s.251)."
]
},
{
"cell_type": "markdown",
"id": "bf2f830c-f41b-4ad7-bc01-4d7ed8ca360e",
"metadata": {},
"source": [
"Es gibt viel mehr kontinuierliche Wahrscheinlichkeitsverteilungen, als wir hier besprechen können. Beachten Sie jedoch, dass in Python mittlerweile eine große Anzahl verschiedener diskreter und kontinuierlicher Wahrscheinlichkeitsverteilungen implementiert sind, siehe hier."
]
},
{
"cell_type": "markdown",
"id": "e139064d-fd49-41cf-8b10-e5c4bfd28196",
"metadata": {},
"source": [
" In Python sind Wahrscheinlichkeitsfunktionen durch allgemeine Methoden wie `rvs`, `pdf`, `cdf` und `ppf` zugänglich. `rvs` ist das allgemeine Syntax für Zufallsvariablengeneratoren wie `uniform.rvs()` für die Gleichverteilung oder `norm.rvs()` für die Normalverteilung. `pdf` ist Methode für die Wahrscheinlichkeitsdichtefunktion wie `uniform.pdf` und `norm.pdf()`. Das `cdf` ist der Syntax für die kumulative Dichtefunktion wie `uniform.cdf()` und `norm.cdf()`. Das `ppf` ist der allgemeine Syntax für die Quantilfunktion, wie `uniform.ppf()` und `norm.ppf()`. Behalten Sie das im Hinterkopf, wenn wir die Kapazitäten in Python weiter erforschen."
]
},
{
"cell_type": "markdown",
"id": "99683689-d16b-40bf-8bfc-245d2b2e4d59",
"metadata": {},
"source": [
"## Wahrscheinlichkeitsdichtefunktionen"
]
},
{
"cell_type": "markdown",
"id": "6a3c81cf-5eda-4517-9185-a12a6f21e67a",
"metadata": {},
"source": [
"Die Form der Verteilung einer Zufallsvariablen kann durch eine glatte Kurve veranschaulicht werden. Solche Kurven, die die Verteilung von kontinuierlichen Variablen darstellen, werden **Wahrscheinlichkeitsdichtefunktionen (PDF)** oder einfach **Dichtefunktionen** genannt. Wahrscheinlichkeitsdichtefunktionen haben drei Haupteigenschaften ({cite:p}`Papula2011` s.327):"
]
},
{
"cell_type": "markdown",
"id": "44b2c1e9-ed12-4cde-b9dd-374e7832d359",
"metadata": {},
"source": [
"1) Eine PDF wird immer auf oder über der horizontalen Achse gezeichnet\n",
"\n",
"2) Die Gesamtfläche zwischen einer PDF und der horizontalen Achse ist gleich $1$ und somit liegt jeder Wert in jedem Teilintervall der PDF im Bereich von $0$ bis $1$\n",
"\n",
"3) Alle möglichen Beobachtungen der Variablen, die innerhalb eines bestimmten Bereichs liegen, entsprechen der entsprechenden Fläche unter der Dichtefunktion und können als prozentueller Anteil ausgedrückt werden."
]
},
{
"cell_type": "markdown",
"id": "eef56241-1591-49aa-8379-9c97dc7648cb",
"metadata": {},
"source": [
"Die Fläche unter der Kurve wird durch das Integral des Wertes $x$ von $-\\infty$ bis $+\\infty$ berechnet und in der Regel auf den Wert $1$ normiert. "
]
},
{
"cell_type": "markdown",
"id": "b5553bf9-f14c-4713-9c98-ac3ded976b48",
"metadata": {
"tags": []
},
"source": [
"$$ \\int_{-\\infty}^{+\\infty} f(x)dx = 1 $$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "679bbe47-d43d-4bd9-9f6a-e11897e2cf32",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"Text(2, 0.4, '$\\\\int_{-\\\\infty}^\\\\infty f(x)dx=1$')"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from scipy.stats import f\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"v1 = 20\n",
"v2 = 20\n",
"x = np.linspace(0, 3, 1000)\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"ax.plot(x, f.pdf(x, v1, v2), color=\"k\")\n",
"# ax.fill_between(x, f.pdf(x), where=x <= z, color=\"r\", alpha=0.5)\n",
"ax.fill_between(x, f.pdf(x, dfn=v1, dfd=v2), color=\"r\", alpha=0.8)\n",
"ax.axhline(0, color=\"k\")\n",
"ax.axes.axis(\"off\")\n",
"\n",
"ax.text(\n",
" 2,\n",
" 0.7,\n",
" s=\"Die Fläche unter der Kurve\\nbeträgt 1 oder 100%\",\n",
" horizontalalignment=\"center\",\n",
" size=20,\n",
")\n",
"\n",
"ax.text(\n",
" 2,\n",
" 0.4,\n",
" s=r\"$\\int_{-\\infty}^\\infty f(x)dx=1$\",\n",
" horizontalalignment=\"center\",\n",
" size=24,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "bbf54b26-0096-463e-acf3-a646bead8834",
"metadata": {},
"source": [
"Die Wahrscheinlichkeit, dass eine stetige Zufallsvariable $x$ einen Wert innerhalb eines bestimmten Intervalls annimmt, ist durch die Fläche unter der Kurve zwischen den beiden Grenzen des Intervalls gegeben. Die farbige Fläche unter der Kurve für das Intervall $]-\\infty \\ $,$ \\ a]$ (linkes Feld) und für das Intervall $[a \\ $,$ \\ +\\infty[$ (rechtes Feld) ist in der folgenden Abbildung dargestellt."
]
},
{
"cell_type": "markdown",
"id": "2859529f-a44c-4578-aa07-54afbc71a10d",
"metadata": {},
"source": [
"Die Wahrscheinlichkeit, dass $x$ in das Intervall $]-\\infty \\ $,$ \\ a]$ fällt, ist"
]
},
{
"cell_type": "markdown",
"id": "2470a24a-f899-4608-80b2-c467aa7f76de",
"metadata": {},
"source": [
"$$P(X \\le a) = \\int_{-\\infty}^{a}f(x)dx$$"
]
},
{
"cell_type": "markdown",
"id": "ffcef509-0115-4232-901b-6f02b4813e45",
"metadata": {},
"source": [
"und die Wahrscheinlichkeit, dass $x$ in das Intervall $[a \\ $,$ \\ \\infty[$ fällt, ist"
]
},
{
"cell_type": "markdown",
"id": "57c1e672-0858-4a38-be88-8b4187a1e687",
"metadata": {},
"source": [
"$$P(X \\ge a) = 1 - P(X \\le a) = \\int_{a}^{\\infty}f(x)dx$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "30e699e7-6db5-49d1-a953-06149b25ee9d",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"Text(2.5, 0.45, '$P(X \\\\geq a) = \\\\int_a^\\\\infty f(x)dx$')"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from scipy.stats import f\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"a = 0.5\n",
"v1 = 20\n",
"v2 = 20\n",
"x = np.linspace(0, 3, 1000)\n",
"fig, ax = plt.subplots(figsize=(16, 8), ncols=2)\n",
"\n",
"\n",
"for _ax in ax:\n",
" _ax.plot(x, f.pdf(x, v1, v2), color=\"k\")\n",
" _ax.axhline(0, color=\"k\")\n",
" _ax.axes.axis(\"off\")\n",
" _ax.text(\n",
" 2.5,\n",
" 0.7,\n",
" s=\"Die Fläche unter der Kurve\\nliegt zwischen 0 und 1\",\n",
" horizontalalignment=\"center\",\n",
" size=18,\n",
" )\n",
"\n",
"\n",
"ax[0].fill_between(x, f.pdf(x, dfn=v1, dfd=v2), where=x <= a, color=\"r\", alpha=0.8)\n",
"ax[0].text(\n",
" 2.5,\n",
" 0.45,\n",
" s=r\"$P(X \\leq a) = \\int_{-\\infty}^a f(x)dx$\",\n",
" horizontalalignment=\"center\",\n",
" size=24,\n",
")\n",
"\n",
"\n",
"ax[1].fill_between(x, f.pdf(x, dfn=v1, dfd=v2), where=x >= a, color=\"r\", alpha=0.8)\n",
"ax[1].text(\n",
" 2.5,\n",
" 0.45,\n",
" s=r\"$P(X \\geq a) = \\int_a^\\infty f(x)dx$\",\n",
" horizontalalignment=\"center\",\n",
" size=24,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "4fccae92-f175-492b-b3c0-b6e22cad530e",
"metadata": {},
"source": [
"Die Wahrscheinlichkeit, dass eine kontinuierliche Zufallsvariable $x$ einen Wert innerhalb eines bestimmten Intervalls annimmt, ist durch die Fläche unter der Kurve zwischen den beiden Grenzen des Intervalls gegeben. Der Wert der farbige Fläche unter der Kurve von $a$ bis $b$ in der folgenden Abbildung gibt die Wahrscheinlichkeit an, dass $x$ in das Intervall $[a \\ $,$ \\ b]$ fällt."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "06083775-2dc3-41fe-b575-7d81cb93ff48",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"Text(2.2, 0.4, '$P(a\\\\leq x\\\\leq b) = \\\\int_a^b f(x)dx$')"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from scipy.stats import f\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"a=0.5\n",
"b=1.6\n",
"v1 = 20\n",
"v2 = 20\n",
"x = np.linspace(0, 3, 1000)\n",
"fig, ax = plt.subplots(figsize=(16,8))\n",
"ax.plot(x, f.pdf(x, v1, v2), color=\"k\")\n",
"ax.fill_between(x, f.pdf(x,dfn=v1, dfd=v2), where=(x >= a) & (x <= b), color=\"r\", alpha=0.8)\n",
"ax.axhline(0, color=\"k\")\n",
"ax.axes.axis(\"off\")\n",
"\n",
"ax.text(\n",
" 2,\n",
" 0.7,\n",
" s=\"Die Fläche unter der Kurve\\nentspricht der Wahrscheinlichkeit\\n$P(a\\leq x\\leq b)$\",\n",
" horizontalalignment=\"center\",\n",
" size=20,\n",
")\n",
"\n",
"ax.text(\n",
" 2.2,\n",
" 0.4,\n",
" s=r\"$P(a\\leq x\\leq b) = \\int_a^b f(x)dx$\",\n",
" horizontalalignment=\"center\",\n",
" size=24,\n",
")\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "8dca082a-2d8f-454d-ba2c-bc9805a6f791",
"metadata": {},
"source": [
"$ P(a \\le x \\le b) = \\int_{a}^{b}f(x)dx$\n",
"\n",
"$ = P(x \\le b) - P(x \\le a) $\n",
"\n",
"$ = \\int_{-\\infty}^{b}f(x)dx - \\int_{-\\infty}^{a}f(x)dx $"
]
},
{
"cell_type": "markdown",
"id": "9a7df957-42b3-4c21-b33a-7f9a1bd6fb0a",
"metadata": {},
"source": [
"Man beachte, dass das Intervall $a\\le x \\le b$ besagt, dass $x$ größer oder gleich $a$, aber kleiner oder gleich $b$ ist."
]
},
{
"cell_type": "markdown",
"id": "3e8b6f7e-2a41-4aba-87ba-c0538240b48a",
"metadata": {},
"source": [
"Bei einer kontinuierlichen Wahrscheinlichkeitsverteilung wird die Wahrscheinlichkeit immer für ein Intervall berechnet. **Die Wahrscheinlichkeit, dass eine kontinuierliche Zufallsvariable $x$ einen einzigen Wert annimmt, ist immer Null**. Das liegt daran, dass die Wahrscheinlichkeit, genau einen Wert aus einer unendlichen Anzahl von Werten $\\in \\mathbb R$ zu wählen, gleich Null ist. Im geometrischen Sinne bedeutet dies, dass die Fläche einer Linie, die einen einzigen Punkt darstellt, Null ist."
]
},
{
"cell_type": "markdown",
"id": "5b6ce335-1281-4d29-94ab-865d3bc4eb2c",
"metadata": {},
"source": [
"$$P(x) = 0$$"
]
},
{
"cell_type": "markdown",
"id": "ce1ecd8c-821b-47bf-b872-075c143c6075",
"metadata": {},
"source": [
"Daraus lässt sich ableiten, dass für eine stetige Zufallsvariable gilt"
]
},
{
"cell_type": "markdown",
"id": "77d198a5-5c25-43bb-9cb8-c3a98fbe7551",
"metadata": {},
"source": [
"$$P(a \\le x \\le b) = P(a < x < b)$$"
]
},
{
"cell_type": "markdown",
"id": "6b1b6af8-dd40-42a5-9cad-39d626c6fb0e",
"metadata": {},
"source": [
"Mit anderen Worten: Die Wahrscheinlichkeit, dass $x$ einen Wert im Intervall $a$ bis $b$ annimmt, ist gleich groß, unabhängig davon, ob die Werte $a$ und $b$ im Intervall enthalten sind oder nicht."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.10.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}