{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "39c05d8c-b420-495f-8cb0-a7a5ee1a94b2",
"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": "a1b76da9-face-4c9b-ab4a-af8a202b4928",
"metadata": {},
"source": [
"# Die Normalverteilung"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1a77d3d0-6c86-496e-a2d7-3c149e33b718",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"from scipy.stats import norm\n",
"import statsmodels.api as smi"
]
},
{
"cell_type": "markdown",
"id": "28934526-8b85-4276-898d-4bd89623a515",
"metadata": {},
"source": [
"Die Normalverteilung wird in der Wahrscheinlichkeitstheorie, der Statistik sowie in den Natur- und Sozialwissenschaften häufig verwendet. Sie wird auch **Gauß-Verteilung** genannt, weil Carl Friedrich Gauß $(1777-1855)$ einer der ersten war, der sie für die Analyse astronomischer Daten verwendete ({cite:t}`fahrmeirstatistik` s.83,s.271)."
]
},
{
"cell_type": "markdown",
"id": "5b36ea6c-3876-47d6-8a8f-b623b091aad5",
"metadata": {},
"source": [
"Die **Normalverteilung** oder die **Normalkurve** ist eine glockenförmige (symmetrische) Kurve. Ihr Mittelwert wird mit $\\mu$ und ihre Standardabweichung mit $\\sigma$ bezeichnet. Eine kontinuierliche Zufallsvariable $x$, die eine Normalverteilung aufweist, wird als **normale Zufallsvariable** bezeichnet."
]
},
{
"cell_type": "markdown",
"id": "57a52210-8019-4e70-895d-e3cd8e3fd0dd",
"metadata": {},
"source": [
"Die Notation für eine Normalverteilung lautet $X \\sim N( \\mu, \\sigma)$. Die Wahrscheinlichkeitsdichtefunktion (PDF) wird geschrieben als"
]
},
{
"cell_type": "markdown",
"id": "05236adf-ae40-4000-9192-087ff0addc05",
"metadata": {},
"source": [
"$$f(x) = \\frac{1}{\\sigma \\sqrt{2 \\pi}}e^{-\\frac{1}{2}\\left(\\frac{x-\\mu}{\\sigma}\\right)^2}$$"
]
},
{
"cell_type": "markdown",
"id": "df8bc937-a21e-4a27-b5fc-5608b6a6d92d",
"metadata": {},
"source": [
"wobei $e \\approx 2,71828$ und $\\pi \\approx 3,14159$. Die Wahrscheinlichkeitsdichtefunktion $f(x)$ gibt den vertikalen Abstand zwischen der horizontalen Achse und der Normalkurve im Punkt $x$ an."
]
},
{
"cell_type": "markdown",
"id": "fbd0e8fe-bd2a-4b1b-9f29-564fa0599722",
"metadata": {},
"source": [
"Die Normalverteilung wird durch zwei Parameter beschrieben, den Mittelwert $\\mu$ und die Standardabweichung $\\sigma$. Jeder unterschiedliche Satz von Werten für $\\mu$ und $\\sigma$ ergibt eine andere Normalverteilung. Der Wert von $\\mu$ bestimmt den Mittelpunkt einer Normalverteilungskurve auf der horizontalen Achse, und der Wert von $\\sigma$ gibt die Streuung der Werte um den Mittelpunkt an."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "4b775795-b864-4ed9-a73b-5b4223051954",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"(-0.003, 0.031)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(14, 6))\n",
"x = np.linspace(-100, 100, 1000)\n",
"sigma = 15\n",
"mu = -45\n",
"ax.plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax.vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"ax.text(mu, -0.002, s=f\"$\\mu$ = {mu}\", horizontalalignment=\"center\", size=14)\n",
"ax.text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05,\n",
" s=f\"$\\sigma$ = {sigma}\",\n",
" horizontalalignment=\"center\",\n",
" size=14,\n",
")\n",
"mu = 15\n",
"ax.plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax.vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"ax.text(mu, -0.002, s=f\"$\\mu$ = {mu}\", horizontalalignment=\"center\", size=14)\n",
"ax.text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05,\n",
" s=f\"$\\sigma$ = {sigma}\",\n",
" horizontalalignment=\"center\",\n",
" size=14,\n",
")\n",
"mu = 55\n",
"ax.plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax.vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"ax.text(mu, -0.002, s=f\"$\\mu$ = {mu}\", horizontalalignment=\"center\", size=14)\n",
"ax.text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05,\n",
" s=f\"$\\sigma$ = {sigma}\",\n",
" horizontalalignment=\"center\",\n",
" size=14,\n",
")\n",
"ax.set_title(\n",
" \"Drei Wahrscheinlichkeitsdichtefunktionen der Normalverteilung\\nmit unterschiedlichen Millelwerten aber mit identischen Standardabweichungen\",\n",
" size=18,\n",
")\n",
"ax.set_ylim(-0.003, 0.031)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "982dbbf9-3c7c-4d62-af7f-bcd4668b9858",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Drei Wahrscheinlichkeitsdichtefunktionen der Normalverteilung\\nmit unterschiedlichen Standardabweichungen aber mit identischen Mittelwerten')"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(14, 6))\n",
"x = np.linspace(-100, 100, 1000)\n",
"\n",
"mu = 7\n",
"ax.text(mu, -0.003, s=f\"$\\mu$ = {mu}\", horizontalalignment=\"center\", size=14)\n",
"\n",
"sigma = 4\n",
"ax.plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax.vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"ax.text(mu * 2.5, 0.06, s=f\"$\\sigma$ = {sigma}\", horizontalalignment=\"center\", size=14)\n",
"\n",
"sigma = 9\n",
"ax.plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax.vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"ax.text(mu * -1.3, 0.03, s=f\"$\\sigma$ = {sigma}\", horizontalalignment=\"center\", size=14)\n",
"\n",
"sigma = 20\n",
"ax.plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax.vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"ax.text(mu * 4.5, 0.015, s=f\"$\\sigma$ = {sigma}\", horizontalalignment=\"center\", size=14)\n",
"\n",
"ax.set_title(\n",
" \"Drei Wahrscheinlichkeitsdichtefunktionen der Normalverteilung\\nmit unterschiedlichen Standardabweichungen aber mit identischen Mittelwerten\",\n",
" size=18,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "4ec62186-e74c-488d-a909-3911caa16a60",
"metadata": {},
"source": [
"Eine Normalverteilung ist unter anderem durch die folgenden Merkmale gekennzeichnet ({cite:t}`fahrmeirstatistik` s.272):"
]
},
{
"cell_type": "markdown",
"id": "3723ffb9-a87d-43a0-8405-7ca411279508",
"metadata": {},
"source": [
"1) Die Gesamtfläche unter einer Normalverteilungskurve beträgt $1,0$, also $100 \\%$.\n",
"2) Eine Normalverteilungskurve ist symmetrisch um den Mittelwert. Folglich liegen $50 \\%$ der Gesamtfläche unter einer Normalverteilungskurve auf der linken Seite des Mittelwerts und $50 \\%$ liegen auf der rechten Seite des Mittelwerts.\n",
"3) Die Ausläufer einer Normalverteilungskurve erstrecken sich unendlich weit in beide Richtungen, ohne die horizontale Achse zu berühren oder zu kreuzen. Obwohl eine Normalverteilungskurve niemals die horizontale Achse berührt, kommt sie jenseits der Punkte, durch $\\mu-3\\sigma$\n",
"und $\\mu+3\\sigma$ dargestellten Punkte so nahe an diese Achse heran, dass die Fläche unter der Kurve jenseits dieser Punkte in beiden Richtungen praktisch als Null angenommen werden kann."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "72deed3b-680f-4d29-b107-727ef07bde19",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"(-5.0, 5.0)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x = np.linspace(-5, 5, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\")\n",
"\n",
"x = [-3, -2, -1, 0, 1, 2, 3]\n",
"for _x in x:\n",
" ax.vlines(_x, ymin=-0.02, ymax=norm.pdf(_x, mu, sigma), linestyle=\"dashed\")\n",
"\n",
"ax.set_xticks(x)\n",
"ax.set_xticklabels([f\"$\\mu$ {x}$\\sigma$\" if x != 0 else f\"$\\mu$\" for x in x])\n",
"\n",
"\n",
"ax.text(\n",
" -3.6,\n",
" 0.06,\n",
" s=r\"$\\int_{-\\infty}^{\\mu-3\\sigma} f(x)dx \\approx 0.001$\",\n",
" horizontalalignment=\"center\",\n",
" size=22,\n",
")\n",
"ax.arrow(-5, 0.02, 1.7, 0, head_width=0.01, head_length=0.3, color=\"k\")\n",
"\n",
"\n",
"ax.text(\n",
" -2.5,\n",
" 0.36,\n",
" s=\"$\\int_{-\\infty}^\\mu f(x)dx=0.5$\",\n",
" horizontalalignment=\"center\",\n",
" size=22,\n",
")\n",
"ax.arrow(-5, 0.4, 4.7, 0, head_width=0.01, head_length=0.3, color=\"k\")\n",
"\n",
"ax.text(\n",
" 2.5,\n",
" 0.36,\n",
" s=\"$\\int_\\mu^\\infty f(x)dx=0.5$\",\n",
" horizontalalignment=\"center\",\n",
" size=22,\n",
")\n",
"ax.arrow(0, 0.4, 4.7, 0, head_width=0.01, head_length=0.3, color=\"k\")\n",
"\n",
"ax.text(\n",
" 3.5,\n",
" 0.06,\n",
" s=r\"$\\int_{\\mu+3\\sigma}^\\infty f(x)dx \\approx 0.001$\",\n",
" horizontalalignment=\"center\",\n",
" size=22,\n",
")\n",
"ax.arrow(3, 0.02, 1.7, 0, head_width=0.01, head_length=0.3, color=\"k\")\n",
"\n",
"ax.set_xlim(-5, 5)"
]
},
{
"cell_type": "markdown",
"id": "358c8c9f-0056-4c88-b427-c9e7dfa6b857",
"metadata": {},
"source": [
"## Die Standard-Normalverteilung"
]
},
{
"cell_type": "markdown",
"id": "3bed4a55-ab6d-42e5-9752-e8b4efb34c1c",
"metadata": {},
"source": [
"Die Standardnormalverteilung ist ein Spezialfall der Normalverteilung. Bei der Standardnormalverteilung ist der Wert des Mittelwerts gleich Null $(\\mu=0)$ und der Wert der Standardabweichung gleich $1$ $(\\sigma=1)$."
]
},
{
"cell_type": "markdown",
"id": "ef19aec4-6333-4583-bc84-407443a13792",
"metadata": {},
"source": [
"Wenn man also $\\mu =0$ und $\\sigma =1$ in die PDF der Normalverteilung einsetzt, vereinfacht sich die Gleichung zu"
]
},
{
"cell_type": "markdown",
"id": "804dd126-9a70-47fd-bbcc-0e3ea40c08b6",
"metadata": {},
"source": [
"$$ \\begin{align}\n",
"f(x)& = \\frac{1}{\\sigma \\sqrt{2 \\pi}}e^{-\\frac{1}{2}\\left(\\frac{x-\\mu}{\\sigma}\\right)^2} \\\\\n",
" & =\\frac{1}{1 \\times \\sqrt{2 \\pi}}e^{-\\frac{1}{2}\\left(\\frac{x-0}{1}\\right)^2} \\\\\n",
" & = \\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{1}{2}x^2} \n",
"\\end{align} $$"
]
},
{
"cell_type": "markdown",
"id": "f8bc00b0-7636-47ad-80b2-62ec2757982d",
"metadata": {},
"source": [
"Die Zufallsvariable, die die Standardnormalverteilung erfüllt, wird mit $z$ bezeichnet. Folglich werden die Einheiten für die Kurve der Standardnormalverteilung mit $z$ bezeichnet und als $z$-**Werte**, $z$-**Scores** oder $z$-**Statistik** bezeichnet."
]
},
{
"cell_type": "markdown",
"id": "b1ce9549-baa4-48ad-af10-172788fa0d68",
"metadata": {},
"source": [
"Die **kumulative Verteilungsfunktion (CDF)** der Standardnormalverteilung, die der Fläche unter der Kurve für das Intervall $]-\\infty \\ $,$ \\ z]$ entspricht und gewöhnlich mit dem griechischen Großbuchstaben *$\\phi$* bezeichnet wird, ist gegeben durch"
]
},
{
"cell_type": "markdown",
"id": "bc3e8017-7a4c-4a95-8907-86efecc993d9",
"metadata": {},
"source": [
"$$F(x"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x = np.linspace(-4, 4, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=4)\n",
"\n",
"z = 0.5\n",
"ticks = [-3, -2, -1, 0, z, 1, 2, 3]\n",
"for _x in ticks:\n",
" if _x != z:\n",
" ax.vlines(_x, ymin=-0, ymax=norm.pdf(_x, mu, sigma), linestyle=\"dashed\")\n",
"\n",
"ax.set_xticks(ticks)\n",
"ax.set_xticklabels([\"z\" if x == z else str(x) for x in ticks])\n",
"ax.fill_between(x, norm.pdf(x), where=x <= z, color=\"r\", alpha=0.5)\n",
"\n",
"ax.set_ylabel(r\"$f(x)$\")\n",
"ax.set_xlabel(r\"z-score\")\n",
"ax.annotate(\n",
" r\"$\\phi(z)$\",\n",
" xy=(-0.5, 0.15),\n",
" xytext=(-2, 0.3),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=28,\n",
")\n",
"ax.annotate(\n",
" r\"$f(x) = \\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{1}{2}x^2}$\",\n",
" xy=(1.2, 0.2),\n",
" xytext=(2.2, 0.3),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=28,\n",
")\n",
"ax.set_title(\"Die Wahrscheinlichkeitsdichtefunktion der Normalverteilung\", size=22)"
]
},
{
"cell_type": "markdown",
"id": "2436dfb2-4c16-42ed-ba47-7e6e60b2cb12",
"metadata": {},
"source": [
"Die $z$-Werte auf der rechten Seite des Mittelwerts sind positiv und die auf der linken Seite sind negativ. Der $z$-Wert für einen Punkt auf der horizontalen Achse gibt den Abstand zwischen dem Mittelwert $(z=0)$ und diesem Punkt in Form der Standardabweichung an. Ein Punkt mit einem Wert von $z=2$ liegt zum Beispiel zwei Standardabweichungen rechts vom Mittelwert. Ebenso liegt ein Punkt mit einem Wert von $z=-2$ zwei Standardabweichungen links vom Mittelwert."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "fe3f66bc-306f-4b49-832e-ae9d2c774a74",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Die kumulative Wahrscheinlichkeitsdichtefunktion der Normalverteilung')"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x = np.linspace(-4, 4, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.cdf(x), color=\"C0\", linewidth=4)\n",
"\n",
"z = 0.5\n",
"ticks = [-3, -2, -1, 0, z, 1, 2, 3]\n",
"for _x in ticks:\n",
" if _x != z:\n",
" ax.vlines(_x, ymin=-0, ymax=norm.cdf(_x, mu, sigma), linestyle=\"dashed\")\n",
"\n",
"ax.set_xticks(ticks)\n",
"ax.set_xticklabels([\"z\" if x == z else str(x) for x in ticks])\n",
"ax.fill_between(x, norm.cdf(x), where=x <= z, color=\"r\", alpha=0.5)\n",
"\n",
"ax.set_ylabel(r\"$f(x)$\")\n",
"ax.set_xlabel(r\"z-score\")\n",
"\n",
"ax.annotate(\n",
" r\"$\\phi(z) = \\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^ze^{-\\frac{1}{2}x^2}dx$\",\n",
" xy=(-0.2, 0.2),\n",
" xytext=(-4, 0.7),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=28,\n",
")\n",
"ax.set_title(\n",
" \"Die kumulative Wahrscheinlichkeitsdichtefunktion der Normalverteilung\", size=22\n",
")"
]
},
{
"cell_type": "markdown",
"id": "5e49f81d-08a7-43b1-a8ef-06940aa70026",
"metadata": {},
"source": [
"Das Methode die Wahrscheinlichkeiten durch Berechnung der Fläche unter der Standardnormalkurve zu bestimmen, kommt häufig zur Anwendung. Aus diesem Grund gibt es Wahrscheinlichkeitstabellen, um die Fläche für einen bestimmten $z$-Wert zu ermitteln. Python ist jedoch ein so leistungsfähiges Werkzeug, dass wir die Fläche unter der Kurve für einen bestimmten $z$-Wert berechnen können."
]
},
{
"cell_type": "markdown",
"id": "3e782fca-9c2b-447b-a274-b03a25aa84fb",
"metadata": {},
"source": [
"Um die Fläche unter der Kurve für eine Standardnormalverteilung zu berechnen, verwenden wir zunächst die Funktion `norm` aus dem `scipy.stats` Paket um eine Standardnormalverteilung zu generieren und wenden darauf die Methode `cdf` an um die kumulative Wahrscheinlichkeit zu berechnen. Die Funktion `norm` ist definiert als `norm(loc = Mittelwert , scale = Standardabweichung)`. Um die Standardwerte zu Erhalten setzen wir den Mittelwert und die Standardabweichung jeweils auf $0$ und $1$ sind. Wenden wir die Methode `cdf` an bekommen wir die kumulative Wahrscheinlichkeit bis zum angegebenen Punkt. Wir berechnen die Fläche unter der Kurve für $z=-3,-2,-1,0,1,2,3$ oder formeller geschrieben:"
]
},
{
"cell_type": "markdown",
"id": "c36759da-59eb-45c0-8df2-fef7240c8a19",
"metadata": {},
"source": [
"$$P(x\\le z) \\qquad \\forall \\ z \\in (-3, -2, -1, 0, 1, 2, 3)$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "852081fe-0ef6-404f-8718-e57b15cc0982",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.0013498980316300933"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(-3)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "b98633a1-00bd-4dae-a04e-6f544d154237",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.022750131948179195"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(-2)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "15276c42-3ff6-420a-bee7-eb82b58949a8",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.15865525393145707"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(-1)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "c848dfae-ee50-4ff7-9f59-ca2f6be50d3f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.5"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(0)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "764d6bb0-9625-4e04-bbcd-bf68ad158286",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.8413447460685429"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(1)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "0cdeef72-b741-477c-bcb3-7532bd85b12e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9772498680518208"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(2)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "9ff674c0-5f49-424e-ad49-95e6f08a61c9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9986501019683699"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(3)"
]
},
{
"cell_type": "markdown",
"id": "f466b90f-755b-4ad0-be76-cae46ab5193a",
"metadata": {
"tags": []
},
"source": [
"Perfekt! Wir haben einige der oben genannten Eigenschaften einer Standardnormalkurve bestätigt. Wir erinnern uns, dass wir die Fläche unter der Kurve für das Intervall $]-\\infty \\ $,$ \\ z]$ berechnet haben. Der Aufruf von `norm.cdf(-3)` ergibt eine sehr geringe Zahl. Nur etwa $0,1 \\%$ der gesamten Fläche unter der Kurve befinden sich links von $z=-3$, was dem Abstand der dreifachen Standardabweichung vom Mittelwert entspricht. Außerdem ergibt `norm.cdf(0)` $50 \\%$. Fantastisch! Daraus schließen wir, dass die Fläche unter der Kurve für das Intervall $]-\\infty \\ $,$ \\ 0]$ die gleiche ist wie die Fläche unter der Kurve für das Intervall $[0 \\ $,$ \\ \\infty[$ und dass die Fläche unter der Kurve sich zu $1$ aufsummiert. Auch hier haben wir eine der oben genannten Eigenschaften einer Standardnormalkurve bestätigt. Und schließlich ergibt der Aufruf von `norm.cdf(3)` eine hohe Zahl nahe bei $1$. Somit sind etwa $99,9 \\%$ der Fläche unter der Kurve im Intervall $]-\\infty \\ $,$ \\ 3]$ zu finden. Für den Bereich jenseits von $z=3$ bleibt nur wenig übrig."
]
},
{
"cell_type": "markdown",
"id": "0a7e2ded-5abe-4c93-8ee7-905867137528",
"metadata": {},
"source": [
"Es sei daran erinnert, dass wir die Fläche unter der Kurve für jedes beliebige Intervall explizit berechnen können"
]
},
{
"cell_type": "markdown",
"id": "596a880f-ca29-49c7-89f5-3029390a2ae6",
"metadata": {},
"source": [
"$ P(a \\le z \\le b) = P(z \\le b) - P(z \\le a) $\n",
"\n",
"$ =\\int_{a}^{b}f(z)dz$\n",
"\n",
"$ = \\int_{-\\infty}^{b}f(x)dx - \\int_{-\\infty}^{a}f(x)dx $"
]
},
{
"cell_type": "markdown",
"id": "5dc9c6cf-f3ac-46ae-b192-8d2d0b576b99",
"metadata": {},
"source": [
"Berechnen wir die Fläche unter der Kurve für die folgenden Intervalle: $[−1 \\ $,$ \\ 1],[−2 \\ $,$ \\ 2],[−3 \\ $,$ \\ 3]$. Oder in Worten: Bestimmen wir die Fläche unter der Kurve für $±1$ Standardabweichung, für $±2$ Standardabweichungen und für $±3$ Standardabweichungen."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "60e16368-d9b1-4b7b-bc10-28413a830371",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.6826894921370859"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(1) - norm.cdf(-1)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "b041f6c9-60c0-4659-9c95-1f2ddf69903f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9544997361036416"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(2) - norm.cdf(-2)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "8345e9a2-d7ec-451b-8919-e252edcaf2b0",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9973002039367398"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(3) - norm.cdf(-3)"
]
},
{
"cell_type": "markdown",
"id": "91e6e34d-d9fd-4fb9-bedd-4a25d13bdde6",
"metadata": {},
"source": [
"Toll, wir haben soeben die Empirische Regel ({cite:t}`fahrmeirstatistik` s.86), auch bekannt als **$68-95-99,7$-Regel**, bestätigt, die sich auf den Tschebyscheffsche Ungleichung bezieht. Für eine glockenförmige Verteilung sind die $3$ Regeln dass ungefähr"
]
},
{
"cell_type": "markdown",
"id": "29fb49c4-049f-42db-af42-5d566098a7ef",
"metadata": {},
"source": [
"\n",
" 1) $68 \\%$ der Beobachtungen liegen innerhalb einer Standardabweichung des Mittelwerts,\n",
" 2) $95 \\%$ der Beobachtungen liegen innerhalb von zwei Standardabweichungen des Mittelwerts, und\n",
" 3) $99,7 \\%$ der Beobachtungen liegen innerhalb von drei Standardabweichungen des Mittelwerts."
]
},
{
"cell_type": "markdown",
"id": "0c8c9582-6e00-44d4-a714-95563683c017",
"metadata": {},
"source": [
"Um unsere Intuition zu stärken, wird die empirische Regel im Folgenden veranschaulicht."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "06295b3d-d49c-4392-a889-1576c03aebdb",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Die Fläche des Intervalls $z=[-1,1]$')"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x = np.linspace(-4, 4, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=4)\n",
"\n",
"\n",
"for _x in [-1, 1]:\n",
" ax.vlines(_x, ymin=-0, ymax=norm.pdf(_x, mu, sigma))\n",
"\n",
"ticks = [-3, -2, -1, 0, 1, 2, 3]\n",
"ax.set_xticks(ticks)\n",
"ax.fill_between(x, norm.pdf(x), where=(x >= -1) & (x <= 1), color=\"r\", alpha=0.5)\n",
"\n",
"\n",
"ax.text(\n",
" -2.5,\n",
" 0.36,\n",
" s=\"$\\phi(z) = \\int_{-1}^1 f(z)dz=P(z \\leq 1) - P(z \\leq-1)$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"ax.text(\n",
" 0,\n",
" 0.15,\n",
" s=r\"$\\phi(z) \\approx 0.68$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"\n",
"ax.set_xlabel(r\"z-score\")\n",
"ax.set_yticks([])\n",
"\n",
"ax.set_title(r\"Die Fläche des Intervalls $z=[-1,1]$\", size=22)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "b02c0477-383b-4201-b7fe-ed109b283f12",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Die Fläche des Intervalls $z=[-2,2]$')"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x = np.linspace(-4, 4, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=4)\n",
"\n",
"\n",
"for _x in [-2, 2]:\n",
" ax.vlines(_x, ymin=-0, ymax=norm.pdf(_x, mu, sigma))\n",
"\n",
"ticks = [-3, -2, -1, 0, 1, 2, 3]\n",
"ax.set_xticks(ticks)\n",
"ax.fill_between(x, norm.pdf(x), where=(x >= -2) & (x <= 2), color=\"r\", alpha=0.5)\n",
"\n",
"\n",
"ax.text(\n",
" -2.5,\n",
" 0.36,\n",
" s=\"$\\phi(z) = \\int_{-2}^2 f(z)dz=P(z \\leq 2) - P(z \\leq-2)$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"ax.text(\n",
" 0,\n",
" 0.15,\n",
" s=r\"$\\phi(z) \\approx 0.95$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"\n",
"ax.set_xlabel(r\"z-score\")\n",
"ax.set_yticks([])\n",
"\n",
"ax.set_title(r\"Die Fläche des Intervalls $z=[-2,2]$\", size=22)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "2479e6cf-9263-44a8-a3b2-21354c1440e0",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Die Fläche des Intervalls $z=[-3,3]$')"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x = np.linspace(-4, 4, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=4)\n",
"\n",
"\n",
"for _x in [-3, 3]:\n",
" ax.vlines(_x, ymin=-0, ymax=norm.pdf(_x, mu, sigma))\n",
"\n",
"ticks = [-3, -2, -1, 0, 1, 2, 3]\n",
"ax.set_xticks(ticks)\n",
"ax.fill_between(x, norm.pdf(x), where=(x >= -3) & (x <= 3), color=\"r\", alpha=0.5)\n",
"\n",
"\n",
"ax.text(\n",
" -2.5,\n",
" 0.36,\n",
" s=\"$\\phi(z) = \\int_{-3}^3 f(z)dz=P(z \\leq 3) - P(z \\leq-3)$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"ax.text(\n",
" 0,\n",
" 0.15,\n",
" s=r\"$\\phi(z) \\approx 0.97$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"\n",
"ax.set_xlabel(r\"z-score\")\n",
"ax.set_yticks([])\n",
"\n",
"ax.set_title(r\"Die Fläche des Intervalls $z=[-3,3]$\", size=22)"
]
},
{
"cell_type": "markdown",
"id": "24b34b8b-b248-4ae8-9d29-c042b7c43973",
"metadata": {
"tags": []
},
"source": [
"## Bestimmung des z-Wertes, bei bekannter Fläche unter der Normalverteilungskurve\n",
"----------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "cae1da31-fe42-491a-819a-829da17a31d8",
"metadata": {},
"source": [
"Bisher haben wir $z$-Scores verwendet, um die Fläche unter der Kurve zu berechnen. Jetzt machen wir es andersherum. Wir berechnen den oder die $z$-Score(s), die einer bestimmten Fläche unter der Standardnormalkurve entsprechen. Das Auffinden des $z$-Scores, der eine bestimmte Fläche hat, ist so häufig, dass es eine spezielle Notation gibt. Das Symbol $z_{\\alpha}$ wird verwendet, um den $z$-Score zu bezeichnen, der eine Fläche von $ \\alpha $ (alpha) zu seiner Rechten unter der Standardnormalkurve aufweist."
]
},
{
"cell_type": "markdown",
"id": "7ea8a928-3c3f-4b3a-83e5-2c1d965c2b01",
"metadata": {},
"source": [
"Ermitteln wir $z_{0,05}$, den $z$-Wert, der unter der Standardnormalkurve eine Fläche von $0,05$ zu seiner Rechten hat. Der Wert von $\\alpha$ entspricht der Wahrscheinlichkeit, einen bestimmten Wert zu erhalten, der dem Intervall $[z \\ $,$ \\ \\infty[$entspricht. Denn die Fläche rechts davon ist $0,05$. Die Fläche links davon ist $1-0,05=0,95$, was dem Intervall $]- \\alpha \\ $,$ \\ z]$ (siehe Grafik unten)."
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "3bc0ba78-33ad-4d63-8732-39ef0cbd02b4",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x = np.linspace(-4, 4, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=4)\n",
"\n",
"\n",
"for _x in [norm.ppf(0.95)]:\n",
" ax.vlines(_x, ymin=-0, ymax=norm.pdf(_x, mu, sigma))\n",
"z = norm.ppf(0.95)\n",
"ticks = [-3, -2, -1, 0, 1, z, 2, 3]\n",
"\n",
"ax.set_xticks(ticks)\n",
"ax.set_xticklabels([np.round(x, 2) if x == z else x for x in ticks])\n",
"ax.fill_between(x, norm.pdf(x), where=(x >= norm.ppf(0.95)), color=\"r\", alpha=0.5)\n",
"\n",
"\n",
"ax.text(\n",
" 0,\n",
" 0.15,\n",
" s=r\"$Fläche = 0.95$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"ax.text(\n",
" 1.85,\n",
" 0.11,\n",
" s=r\"$z_{0.05}$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"ax.annotate(\n",
" r\"$Fläche=0.05$\",\n",
" xy=(2, 0.02),\n",
" xytext=(2.4, 0.1),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"\n",
"\n",
"ax.set_xlabel(r\"z-score\")\n",
"ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"id": "0cd6132c-e779-4088-ba4d-2f2b2afa63e6",
"metadata": {
"tags": []
},
"source": [
"Um den entsprechenden $z$-Score zu erhalten, kann man ihn in einer Wahrscheinlichkeitstabelle nachschlagen oder Python verwenden. Daher wenden wir die Funktion `norm.ppf` an. Die `norm.ppf`-Funktion wird geschrieben als `norm.ppf(p, mean = 0, scale = 1, loc = 0)`. Wir behalten die Standardwerte für die Argumente `mean`, `sd` und `loc` bei. Allerdings müssen wir vorsichtig sein auf welchen Bereich der Fläche unter der Normalverteilung wir uns beziehen. Für `norm.ppf(p)` erhalten wir den $z$-Score, bei dem das p-Argument der Bereich links von $z$ ist. Wenn wir dagegen `norm.ppf(1-p)` berechnen, erhalten wir den $z$-Score, bei dem das p-Argument der Bereich rechts von $z$ ist. Wenden wir uns an Python um dies zu verdeutlichen."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "c77210f0-e7b5-402a-868d-5691f1bc56f8",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"-1.6448536269514729"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.ppf(0.05)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "8f06e246-8d05-4b78-8aab-ca3d0fb228c5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.6448536269514722"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.ppf(0.95)"
]
},
{
"cell_type": "markdown",
"id": "3db8f7cf-a38d-4f20-87b0-b8c34f7bff09",
"metadata": {},
"source": [
"Es ist interessant zu erwähnen das die Perzentile Punkt Funktion `norm.ppf` die inverse Funktion der kumulativen Wahrscheinlichkeitsfunktion `norm.cdf` ist"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "5ca4478d-0310-43e9-8e63-50165d9ed976",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.95"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(norm.ppf(0.95))"
]
},
{
"cell_type": "markdown",
"id": "6a229df2-cb6d-44b7-b889-51edb71fb3f7",
"metadata": {},
"source": [
"Da die Standardnormalverteilung symmetrisch ist, erhalten wir zweimal die gleiche Zahl, aber mit einem anderen Vorzeichen. Das bedeutet, dass bei einem z-Wert von etwa $1,64 \\ $ $ 95 \\%$ aller Werte links von $z_{0,05}$ und $5 \\%$ aller Werte rechts davon liegen. Im Gegensatz dazu liegen für einen $z$-Wert von etwa $-1,64 \\ $ $5 \\%$ aller Werte links von $z_{0,05}$ und $95 \\%$ aller Werte rechts davon. Kombiniert man diese, erhält man das Intervall $z \\in [-1,64 \\ $,$ \\ 1,64 ]$, das $90 \\%$ aller Werte abdeckt."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "8abdfeec-1b54-41b6-8663-b4fb6eb13704",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 8))\n",
"x = np.linspace(-4, 4, 1000)\n",
"\n",
"mu = 0\n",
"sigma = 1\n",
"ax.plot(x, norm.pdf(x), color=\"C0\", linewidth=4)\n",
"\n",
"z1 = norm.ppf(0.05)\n",
"z2 = norm.ppf(0.95)\n",
"\n",
"\n",
"for _x in [norm.ppf(0.05), norm.ppf(0.95)]:\n",
" ax.vlines(_x, ymin=-0, ymax=norm.pdf(_x, mu, sigma))\n",
"\n",
"ticks = [-3, -2, z1, -1, 0, 1, z2, 2, 3]\n",
"ax.set_xticks(ticks)\n",
"ax.set_xticklabels([np.round(x, 2) if (x == z1) or (x == z2) else x for x in ticks])\n",
"ax.fill_between(x, norm.pdf(x), where=(x >= norm.ppf(0.95)), color=\"r\", alpha=0.5)\n",
"ax.fill_between(x, norm.pdf(x), where=(x <= norm.ppf(0.05)), color=\"r\", alpha=0.5)\n",
"\n",
"\n",
"ax.text(\n",
" 0,\n",
" 0.15,\n",
" s=r\"$Fläche = 0.9 = 90\\%$\",\n",
" horizontalalignment=\"center\",\n",
" size=19,\n",
")\n",
"\n",
"\n",
"ax.annotate(\n",
" r\"$Fläche=0.05$\",\n",
" xy=(2, 0.02),\n",
" xytext=(2.4, 0.1),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"\n",
"ax.annotate(\n",
" r\"$Fläche=0.05$\",\n",
" xy=(-2, 0.02),\n",
" xytext=(-3.7, 0.1),\n",
" # textcoords=\"data\",\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"\n",
"ax.set_xlabel(r\"z-score\")\n",
"ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"id": "c0dd72ff-211c-4ef6-86b4-e0a3718a5eff",
"metadata": {},
"source": [
"## Standardisierung einer normalverteilten Variable\n",
"----------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "350e66e1-ad74-4054-ad55-47368982d0f0",
"metadata": {},
"source": [
"Bevor wir das Konzept der Standardnormalverteilung auf einen realen Datensatz anwenden können, müssen wir das Konzept der **Standardisierung einer Normalverteilung** diskutieren. Wir wissen, dass eine Normalverteilung durch zwei Parameter parametrisiert ist, ihren Mittelwert $\\sigma \\in \\mathbb R>0$ und ihre Standardabweichung $\\sigma \\in \\mathbb R>0,X \\sim N(\\mu,\\sigma)$. Der tatsächliche Wert dieser Parameter hängt von der Population und den zur Beschreibung ihrer Merkmale verwendeten Metriken ab. Um ein bestimmtes $\\mu$ und $\\sigma$, das sich auf eine bestimmte Zufallsvariable X bezieht, in $\\mu=0$ und $\\sigma=1$ umzuwandeln, müssen wir den $x$-Wert in einen $z$-Wert umwandeln, indem wir die folgende Gleichung anwenden."
]
},
{
"cell_type": "markdown",
"id": "7d68e408-4285-43f9-ab76-aaaa20d59f72",
"metadata": {},
"source": [
"$$z = \\frac{x-\\mu}{\\sigma}$$"
]
},
{
"cell_type": "markdown",
"id": "a1cd247e-b5dc-4fa7-ad46-8336061f6e7b",
"metadata": {},
"source": [
"Als Ergebnis erhalten wir eine Standardnormalverteilung für eine bestimmte Normalverteilung. Dieses Verfahren ist unerlässlich, wenn Sie die $z$-Scores oder eine auf einen $z$-Score bezogene Wahrscheinlichkeit $(P(z))$ bestimmen müssen indem man sie in einer Tabelle nachschlägt. Wir werden später sehen, dass Python ein so mächtiges Werkzeug ist, dass der Schritt der Standardisierung überflüssig ist."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "8a37eb16-4267-4d91-bc95-97fb77b41ec1",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(14, 12), nrows=2)\n",
"\n",
"# axis 0\n",
"x = np.linspace(-100, 100, 1000)\n",
"mu = -45\n",
"sigma = 10\n",
"\n",
"ax[0].plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax[0].vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"ax[0].text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05 + 0.005,\n",
" s=f\"$\\mu$ = {mu}\",\n",
" horizontalalignment=\"center\",\n",
" size=16,\n",
")\n",
"\n",
"ax[0].text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05,\n",
" s=f\"$\\sigma$ = {sigma}\",\n",
" horizontalalignment=\"center\",\n",
" size=16,\n",
")\n",
"\n",
"mu = 12\n",
"sigma = 7\n",
"ax[0].plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax[0].vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"\n",
"ax[0].text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05 + 0.005,\n",
" s=f\"$\\mu$ = {mu}\",\n",
" horizontalalignment=\"center\",\n",
" size=16,\n",
")\n",
"\n",
"ax[0].text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05,\n",
" s=f\"$\\sigma$ = {sigma}\",\n",
" horizontalalignment=\"center\",\n",
" size=16,\n",
")\n",
"\n",
"mu = 36\n",
"sigma = 18\n",
"ax[0].plot(x, norm.pdf(x, mu, sigma), color=\"C0\")\n",
"ax[0].vlines(mu, ymin=0, ymax=norm.pdf(mu, mu, sigma), linestyle=\"dashed\")\n",
"ax[0].text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05 + 0.005,\n",
" s=f\"$\\mu$ = {mu}\",\n",
" horizontalalignment=\"center\",\n",
" size=16,\n",
")\n",
"\n",
"ax[0].text(\n",
" mu,\n",
" norm.pdf(mu, mu, sigma) * 1.05,\n",
" s=f\"$\\sigma$ = {sigma}\",\n",
" horizontalalignment=\"center\",\n",
" size=16,\n",
")\n",
"\n",
"ax[0].set_ylim(-0.003, 0.07)\n",
"\n",
"# axis 1\n",
"x = np.linspace(-4, 4, 1000)\n",
"mu = 0\n",
"sigma = 1\n",
"ax[1].plot(x, norm.pdf(x), color=\"C0\")\n",
"\n",
"ax[1].text(\n",
" 0,\n",
" 0.2,\n",
" s=f\"$\\mu$ = {mu}\",\n",
" horizontalalignment=\"center\",\n",
" size=16,\n",
")\n",
"\n",
"ax[1].text(\n",
" 0,\n",
" 0.17,\n",
" s=f\"$\\sigma$ = {sigma}\",\n",
" horizontalalignment=\"center\",\n",
" size=16,\n",
")\n",
"\n",
"ax[1].text(\n",
" -3,\n",
" 0.25,\n",
" s=r\"$z = \\frac{X-\\mu}{\\sigma}$\",\n",
" horizontalalignment=\"center\",\n",
" size=26,\n",
")\n",
"\n",
"ax[1].text(\n",
" -2.1,\n",
" 0.45,\n",
" s=r\"$z = \\frac{X-(-45)}{10}$\",\n",
" horizontalalignment=\"center\",\n",
" size=20,\n",
")\n",
"\n",
"ax[1].text(\n",
" -0.3,\n",
" 0.5,\n",
" s=r\"$z = \\frac{X-12}{7}$\",\n",
" horizontalalignment=\"center\",\n",
" size=20,\n",
")\n",
"\n",
"ax[1].text(\n",
" 1.7,\n",
" 0.35,\n",
" s=r\"$z = \\frac{X-36}{18}$\",\n",
" horizontalalignment=\"center\",\n",
" size=20,\n",
")\n",
"\n",
"# Add line from one subplot to the other\n",
"from matplotlib.patches import ConnectionPatch\n",
"\n",
"for xy in [\n",
" ([45, 0.01], [1, 0.28]),\n",
" ([14, 0.005], [0.2, 0.42]),\n",
" ([-50, 0.005], [-1, 0.3]),\n",
"]:\n",
" xyA = xy[0]\n",
" xyB = xy[1]\n",
" # ConnectionPatch handles the transform internally so no need to get fig.transFigure\n",
" arrow = ConnectionPatch(\n",
" xyA,\n",
" xyB,\n",
" coordsA=ax[0].transData,\n",
" coordsB=ax[1].transData,\n",
" # Default shrink parameter is 0 so can be omitted\n",
" color=\"black\",\n",
" arrowstyle=\"-|>\", # \"normal\" arrow\n",
" mutation_scale=30, # controls arrow head size\n",
" linewidth=2,\n",
" )\n",
" fig.patches.append(arrow)\n",
"\n",
"ax[1].set_ylim(-0.003, 0.6)\n",
"for _ax in ax:\n",
" _ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"id": "d715a953-47cb-43e7-9ba5-2596fe459fbf",
"metadata": {
"tags": []
},
"source": [
"## Die Standard-Normalverteilung: Ein Beispiel in Python"
]
},
{
"cell_type": "markdown",
"id": "cb2c0c99-c8fc-4fd9-bff9-4df8db4ff359",
"metadata": {},
"source": [
"### Vorbereitung der Daten"
]
},
{
"cell_type": "markdown",
"id": "2c21ecbd-58f6-480f-a051-9538961919b8",
"metadata": {},
"source": [
"Jetzt sind wir bereit, einige Übungen zu machen. Dazu laden wir den `students` Datensatz. Sie können die Datei `students.csv` hier herunterladen. Zuerst laden wir den Datensatz und geben ihm einen passenden Namen."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "58ca09db-5c70-46f8-bda8-24a413ac2c87",
"metadata": {},
"outputs": [],
"source": [
"# Lese Datei students.csv als Dataframe ein\n",
"students = pd.read_csv(\"../../data/students.csv\")\n",
"# Lese Spalte 'height' ein\n",
"height = students[\"height\"]"
]
},
{
"cell_type": "markdown",
"id": "8ffa4048-ab19-4bed-85a7-e2af46667ea0",
"metadata": {},
"source": [
"Der `students` Datensatz besteht aus $8239$ Zeilen, von denen jede einen bestimmten Studenten repräsentiert, und $16$ Spalten, von denen jede einer Variable/einem Merkmal entspricht, das sich auf diesen bestimmten Studenten bezieht. Diese selbsterklärenden Variablen sind: *stud_id, Name, Geschlecht, Alter, Größe, Gewicht, Religion, nc_score, Semester, Hauptfach, Nebenfach, score1, score2, online_tutorial, graduated, salary*. In diesem Abschnitt verwenden wir die Variable `height`, um das bisher Besprochene zu üben.\n",
"\n",
"Zunächst wollen wir sicherstellen, dass wir es mit normalverteilten Daten zu tun haben. Wenn eine Variable normalverteilt ist, sollte ein Histogramm der Beobachtungen bei einer großen Stichprobe in etwa die Form einer Glocke haben."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "3d1372cb-f342-4497-bf98-541aa67be0eb",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'Größe in cm')"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plotte die Werte als Histogramm\n",
"fig, ax = plt.subplots()\n",
"ax.hist(height, bins=14, edgecolor=\"k\")\n",
"# Erzeuge Labels\n",
"ax.set_ylabel(\"Häufigkeit\")\n",
"ax.set_xlabel(\"Größe in cm\")"
]
},
{
"cell_type": "markdown",
"id": "a2afe112-6dd0-4e9d-9a19-d36b56165f8b",
"metadata": {},
"source": [
"Aus dem Diagramm kann man schließen, dass die Variable `height` normalverteilt ist. Allerdings ist es vor allem bei kleinen Stichproben oft schwierig, eine klare Form in einem Histogramm festzustellen, insbesondere, ob sie glockenförmig ist. Daher ist eine empfindlichere grafische Technik zur Beurteilung der Normalität erforderlich. **Normal-Quantil-Plot** bieten eine solche Technik. Die Idee hinter einem Normal-Quantil-Plot oder kurz Q-Q Plot ist einfach: Man vergleicht die beobachteten Werte der Variablen mit den Beobachtungen, die für eine normalverteilte Variable erwartet werden. Genauer gesagt ist ein Q-Q Plot eine Darstellung der beobachteten Werte der Variablen im Vergleich zu den Werten, die für eine Variable mit der Standardnormalverteilung erwartet werden. Wenn die Variable normalverteilt ist, sollte der Q-Q Plot in etwa linear sein (d. h. in etwa auf einer Geraden liegen) ({cite:t}`fahrmeirstatistik` s.88)."
]
},
{
"cell_type": "markdown",
"id": "8c5ed57b-dba5-4610-98b1-01be0c9f1cba",
"metadata": {},
"source": [
"Bei der Verwendung eines Normal-Quantil-Plots zur Beurteilung der Normalität einer Variablen sind zwei Dinge zu beachten:"
]
},
{
"cell_type": "markdown",
"id": "28584205-79c5-447f-a4cf-87fbb1a6d0c1",
"metadata": {},
"source": [
"1) Die Entscheidung, ob eine normale Wahrscheinlichkeitsverteilung annähernd linear ist, ist eine subjektive Entscheidung, und\n",
"2) dass wir nur eine begrenzte Anzahl von Beobachtungen dieser bestimmten Variablen verwenden, um ein Urteil über alle möglichen Beobachtungen der Variablen zu fällen."
]
},
{
"cell_type": "markdown",
"id": "e172aa12-45ef-46ef-baaa-2af447ff402a",
"metadata": {},
"source": [
"In Python können wir die Funktion `qqplot()` verwenden, um Normalwahrscheinlichkeitsplots zu erstellen, die auch als Q-Q-Plots bezeichnet werden."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "71680aa3-3f5b-4ad9-b80e-7849acf68059",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Erzeuge Q-Q Plot\n",
"_ = smi.qqplot(height, line=\"r\")"
]
},
{
"cell_type": "markdown",
"id": "fcd53d07-0e7a-4f3f-96a2-5717a7f10a71",
"metadata": {},
"source": [
"Bei der Betrachtung des Diagramms sehen wir, dass die Quantile der Stichprobe im Vergleich zu den theoretischen Quantilen am unteren und oberen Ende etwas abweichen. Dieser Tatsache muss etwas mehr Aufmerksamkeit geschenkt werden! Was könnte der Grund für die Abweichung am oberen und unteren Ende der Verteilung sein? Irgendeine Vermutung?"
]
},
{
"cell_type": "markdown",
"id": "de9b1fe6-f8bf-4d33-8cae-d8cc284b6884",
"metadata": {},
"source": [
"Was ist mit dem Geschlecht? Ehrlich gesagt scheint es natürlich zu sein, dass die durchschnittliche Körpergröße von Männern und Frauen unterschiedlich ist. Stellen wir ein Histogramm der Körpergröße von Männern und Frauen auf."
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "768f9b88-cb4e-403d-b382-b12d62e181e2",
"metadata": {},
"outputs": [],
"source": [
"male_height = students.loc[students[\"gender\"] == \"Male\", \"height\"]\n",
"female_height = students.loc[students[\"gender\"] == \"Female\", \"height\"]"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "9745ac24-63da-4257-ab03-ae89f38db0a3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'Größe in cm')"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plotte die Werte als Histogramm\n",
"fig, ax = plt.subplots()\n",
"# Bestimme Anzahl Bins\n",
"bins_male = male_height.max() - male_height.min()\n",
"ax.hist(male_height, bins_male, edgecolor=\"k\", alpha=0.5)\n",
"# Bestimme Anzahl Bins\n",
"bins_female = female_height.max() - female_height.min()\n",
"ax.hist(female_height, bins_female, edgecolor=\"r\", alpha=0.5)\n",
"# Erzeuge Labels\n",
"ax.set_ylabel(\"Häufigkeit\")\n",
"ax.set_xlabel(\"Größe in cm\")"
]
},
{
"cell_type": "markdown",
"id": "871c5c7e-d096-49a0-a2b0-9688057d06b8",
"metadata": {},
"source": [
"Das ist es! Offensichtlich haben die beiden Gruppen unterschiedliche Mittelwerte, so dass die Zusammenfassung zu einer Gruppe dazu führt, dass die linken und rechten Ausläufer der sich ergebenden Verteilung weiter reichen, als bei einer normalverteilten Variablen zu erwarten wäre. Um fortzufahren, betrachten wir also nur die Körpergröße der Studentinnen. Der Klarheit halber zeichnen wir noch einmal den Normalwahrscheinlichkeitsplit der Größenvariablen, um sicherzustellen, dass unsere Zielvariablen normalverteilt sind."
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "026f082d-17ab-4a33-aa41-24da2f2ca479",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Erzeuge Q-Q Plot\n",
"_ = smi.qqplot(female_height, line=\"r\")"
]
},
{
"cell_type": "markdown",
"id": "d25d9269-8ef5-4369-87a0-9bf4f11248c6",
"metadata": {},
"source": [
"Bevor wir mit den eigentlichen Übungen beginnen, berechnen wir zunächst den Mittelwert $\\bar{x}$ und die Standardabweichung $s$ der Zielvariablen. Außerdem standardisieren wir die Variable, um eine Standardnormalverteilung mit $\\bar{x}=0$ und $s=1$ zu erhalten, und weisen ihr einen geeigneten Variablennamen zu."
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "829cf0a1-9cb6-44fa-ba6d-892f6f2c9e1c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"163.65328467153284"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Heights\n",
"height_mean = female_height.mean()\n",
"height_mean"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "d85b21b5-e96f-4850-9926-885dc8b98989",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"7.919725792052593"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"height_sd = female_height.std()\n",
"height_sd"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "62f6e6bd-41d2-4de2-9963-9d4109511325",
"metadata": {},
"outputs": [],
"source": [
"height_z = (female_height - height_mean) / height_sd"
]
},
{
"cell_type": "markdown",
"id": "cd50da71-dcca-4ddc-9f14-e0c44414a238",
"metadata": {},
"source": [
"Die Variable `height` hat einen Mittelwert von $163,7$ cm und eine Standardabweichung von $7,9$ cm."
]
},
{
"cell_type": "markdown",
"id": "bcff45ff-276d-41c0-97cd-9ca8f915f695",
"metadata": {},
"source": [
"### Suche nach dem Bereich links von einem angegebenen $z$-Scores oder $x$-Wertes"
]
},
{
"cell_type": "markdown",
"id": "ac0f4ec3-03fa-45ad-8628-a3a2930aa938",
"metadata": {},
"source": [
"**Frage 1**"
]
},
{
"cell_type": "markdown",
"id": "2519569f-2db8-4a7c-a7dc-39521fd30021",
"metadata": {},
"source": [
"Wie hoch ist die Wahrscheinlichkeit, dass eine zufällig ausgewählte Studentin aus dem `students` Datensatz eine Körpergröße von $168$ cm oder weniger hat? Wir suchen also nach $P(x \\le 168)$.\n",
"\n",
"Zunächst berechnen wir die Wahrscheinlichkeit für die standardisierte Variable. Dazu müssen wir den Wert, der uns interessiert ($168$ cm), in einen $z$-Score umwandeln."
]
},
{
"cell_type": "markdown",
"id": "fa02a707-cf7d-4dfb-95f7-79ecd0edbe5c",
"metadata": {},
"source": [
"$$z = \\frac{x-\\mu}{\\sigma} = \\frac{ 168- 163,7}{7,9} = 0,55$$"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "04a7c3d5-31bd-4f3d-9239-0f0f220e0623",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.5488466952768823"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"height_z2 = (168 - height_mean) / height_sd\n",
"height_z2"
]
},
{
"cell_type": "markdown",
"id": "95eab9fa-276d-4c77-aafe-2a95de0afd08",
"metadata": {},
"source": [
"Dann müssen wir die Fläche unter der Kurve links neben dem erhaltenen $z$-Wert berechnen. Zur Erinnerung: Die Fläche unter der Kurve einer normalverteilten Variablen kann mit Hilfe der Funktion `norm.cdf()` berechnet werden. Die `norm.cdf()` -Funktion wird als `norm.cdf(q, loc = 0, scale = 1)` geschrieben. Für dieses spezielle Beispiel können wir alle Standardargumente akzeptieren."
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "0249fb67-af8a-4932-bcd0-ec2b0b77a4cd",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.7084446690628331"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.cdf(height_z2)"
]
},
{
"cell_type": "markdown",
"id": "42a4d61e-ba50-4214-8ab7-c010871b6312",
"metadata": {},
"source": [
"Genial, wir haben ein Ergebnis: $P(z\\le 0,55) \\approx 0,71$\n",
"\n",
"Nun führen wir die gleiche Berechnung durch, überspringen aber diesmal den Schritt der Standardisierung. Dank der Leistungsfähigkeit von Python müssen wir uns nicht auf Tabellen verlassen, sondern können den Stichprobenmittelwert $\\bar x$ und die Standardabweichung der Stichprobe, $s$, in die Funktion `stats.norm.cdf` eingeben."
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "e40fe4ca-2083-4ba4-b07f-8f1e0ee37d18",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.7084446690628331"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = 168\n",
"norm.cdf(x, loc=height_mean, scale=height_sd)"
]
},
{
"cell_type": "markdown",
"id": "0a095e43-b90e-4fd2-aaab-ef2ab954c308",
"metadata": {},
"source": [
"Perfekt! Die Zahlen stimmen überein: $P(x \\le 168) \\approx 0,71$. Um sicherzustellen, dass wir verstehen, was vor sich geht, werden unten sowohl die Fläche unter der Kurve für die standardisierte Variable in $z$-Werten (linkes Feld) als auch die Fläche für die nicht standardisierte Variable in cm (rechtes Feld) dargestellt."
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "fac4012c-4dbb-4383-b810-eaca70d45af2",
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy.stats import norm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots(figsize=(16, 6), ncols=2)\n",
"# axis 0\n",
"x = np.linspace(-3.2, 3.2, 1000)\n",
"mu = 0\n",
"sigma = 1\n",
"ax[0].plot(x, norm.pdf(x), color=\"C0\", linewidth=4)\n",
"\n",
"z = 0.55\n",
"ticks = [-3, -2, -1, 0, z, 1, 2, 3]\n",
"ax[0].vlines(z, ymin=0, ymax=norm.pdf(z, mu, sigma))\n",
"\n",
"ax[0].set_xticks(ticks)\n",
"ax[0].set_xticklabels([np.round(x, 2) if x == z else str(x) for x in ticks])\n",
"ax[0].fill_between(x, norm.pdf(x), where=x <= z, color=\"r\", alpha=0.5)\n",
"\n",
"ax[0].annotate(\n",
" r\"$Fläche \\approx 0.71$\",\n",
" xy=(-0.2, 0.25),\n",
" xytext=(-3.45, 0.3),\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"ax[0].set_title(r\"$P(z \\leq 0.55)$\", size=18)\n",
"\n",
"# axis 1\n",
"x = np.linspace(height_mean + height_sd * -3.2, height_mean + height_sd * 3.2, 1000)\n",
"mu = height_mean\n",
"sigma = height_sd\n",
"ax[1].plot(x, norm.pdf(x, mu, sigma), color=\"C0\", linewidth=4)\n",
"\n",
"z = 168\n",
"ax[1].vlines(z, ymin=0, ymax=norm.pdf(z, mu, sigma))\n",
"\n",
"ticks = ax[1].get_xticks().tolist()\n",
"ticks.pop(ticks.index(170))\n",
"ticks = ticks + [z]\n",
"ax[1].set_xticks(ticks)\n",
"ax[1].fill_between(x, norm.pdf(x, mu, sigma), where=x <= z, color=\"r\", alpha=0.5)\n",
"\n",
"ax[1].annotate(\n",
" r\"$Fläche \\approx 0.71$\",\n",
" xy=(163, 0.03),\n",
" xytext=(137, 0.04),\n",
" arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n",
" size=19,\n",
")\n",
"ax[1].set_title(r\"$P(z \\leq 168)$\", size=18)\n",
"\n",
"for _ax in ax:\n",
" _ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"id": "63f2fe6c-dde1-4faf-9a99-fcd14a48db53",
"metadata": {},
"source": [
"### Ermitteln der Fläche rechts von einem bestimmten $x$-Wert"
]
},
{
"cell_type": "markdown",
"id": "8ef2a328-704b-4559-8882-0d72a9d1c407",
"metadata": {},
"source": [
"**Frage 2**"
]
},
{
"cell_type": "markdown",
"id": "863bf65d-b571-4d09-846f-6ec8354b9d5a",
"metadata": {},
"source": [
"Wie hoch ist die Wahrscheinlichkeit, dass eine zufällig ausgewählte Studentin aus dem `students` Datensatz eine Körpergröße von $185$ cm oder mehr hat? Wir suchen also nach $P(x \\ge 175)$. Um die Fläche unter der Kurve rechts vom interessierenden Wert zu erhalten, müssen wir in die Funktion `stats.norm.sf()` oder `1-stats.norm.cdf` verwenden."
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "fad0ecf8-b438-4419-a9d7-45826474e0bb",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.07596955321865"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = 175 # height in cm\n",
"norm.sf(x, loc=height_mean, scale=height_sd)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "9b15ec3c-6697-49d2-b3ab-4b94c27b80b7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.92403044678135"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = 175 # height in cm\n",
"norm.cdf(x, loc=height_mean, scale=height_sd)"
]
},
{
"cell_type": "markdown",
"id": "64451e26-01b3-48ce-a5be-d775db085957",
"metadata": {},
"source": [
"Antwort: : $P(x \\ge 175) \\approx 0,08$"
]
},
{
"cell_type": "markdown",
"id": "3e47bf4c-a614-4386-8b25-f8fb9f3e0911",
"metadata": {},
"source": [
"### Ermitteln der Fläche zwischen zwei angegebenen $x$-Werten"
]
},
{
"cell_type": "markdown",
"id": "1ba8429d-8e1e-4fdf-8fb6-8f47a04beafa",
"metadata": {},
"source": [
"Um die Fläche unter einer Kurve für ein Intervall $[a \\ $,$ \\ b]$ zu bestimmen, verwenden wir die Gleichung"
]
},
{
"cell_type": "markdown",
"id": "6781980e-1795-4743-810c-8a52b31c4806",
"metadata": {},
"source": [
"$$P(a \\le x \\le b) = \\int_{a}^{b}f(x)dx = P(x \\le b)- P(x \\le a)\\text{.}$$"
]
},
{
"cell_type": "markdown",
"id": "9e625f97-bf08-42ba-af7e-a41383550c76",
"metadata": {},
"source": [
"**Frage 3**"
]
},
{
"cell_type": "markdown",
"id": "5fdb8c34-cc75-49bb-9e51-487258177be0",
"metadata": {},
"source": [
"Wie hoch ist die Wahrscheinlichkeit, dass eine zufällig ausgewählte Studentin aus dem `students` Datensatz eine Körpergröße zwischen $155$ und $165$ cm hat, $P(155≤x≤165)$?"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "061328a1-4fb5-48db-bacf-f1db9892d5fc",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.4302335028797312"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x_lower = 155 # height in cm\n",
"x_upper = 165 # height in cm\n",
"\n",
"cdf_upper = norm.cdf(x_upper, loc=height_mean, scale=height_sd)\n",
"cdf_lower = norm.cdf(x_lower, loc=height_mean, scale=height_sd)\n",
"cdf_upper - cdf_lower"
]
},
{
"cell_type": "markdown",
"id": "bfa85ad0-6dec-4452-a267-3c578345f6b3",
"metadata": {},
"source": [
"Antwort: : $P(155≤x≤165)≈0,43$"
]
},
{
"cell_type": "markdown",
"id": "7a2e5abf-f87e-42c2-848f-a38002f3c51a",
"metadata": {},
"source": [
"**Frage 4**"
]
},
{
"cell_type": "markdown",
"id": "04a9a377-8113-4c97-b3a7-a28509308f9f",
"metadata": {},
"source": [
"Wie hoch ist die Wahrscheinlichkeit, dass eine zufällig ausgewählte Studentin aus dem Studentendatensatz eine Körpergröße zwischen $170$ und $180$ cm hat, $P(170≤x≤180)$?"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "ced2c61f-134e-4f12-aaeb-5cfe9589535c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.19194918877717126"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x_lower = 170 # height in cm\n",
"x_upper = 180 # height in cm\n",
"\n",
"cdf_upper = norm.cdf(x_upper, loc=height_mean, scale=height_sd)\n",
"cdf_lower = norm.cdf(x_lower, loc=height_mean, scale=height_sd)\n",
"cdf_upper - cdf_lower"
]
},
{
"cell_type": "markdown",
"id": "7f48cba9-4000-41b3-a98f-d306a41656cd",
"metadata": {},
"source": [
"Antwort: : $P(170≤x≤180)≈0,19$"
]
},
{
"cell_type": "markdown",
"id": "5a5a0f6f-632d-47a5-b9fe-dcc1f020bfe4",
"metadata": {},
"source": [
"### $z_\\alpha$ finden"
]
},
{
"cell_type": "markdown",
"id": "2a225890-a7b4-4e64-8af2-0fd60db57b00",
"metadata": {},
"source": [
"**Frage 5**"
]
},
{
"cell_type": "markdown",
"id": "3cb62eec-4423-409e-8217-aa84e7b98582",
"metadata": {},
"source": [
"Wir möchten wissen, welche Körpergröße der Studentinnen in unserem `students` Datensatz mit einer Wahrscheinlichkeit von $0,60$ übereinstimmt. Oder anders ausgedrückt: Wenn wir eine Anzahl von $n$ Studenten aus dem `students` Datensatz zufällig auswählen, welche Größe teilt die Stichprobe in $60 \\%$ der $n$ Studierenden, die kleiner sind, und $40 \\%$ der n Studentinnen, die größer als diese bestimmte Größe sind. Wir suchen also nach $P(X)=0,60$.\n",
"\n",
"Um $P(X)=0,60$ zu lösen, werden wir zwei Ansätze wählen. Der erste Ansatz verwendet den $z$-Score, und der zweite verwendet Python, um den Standardisierungsschritt überflüssig zu machen. .\n",
"\n",
"Für beide Ansätze verwenden wir die `norm.ppf()`-Funktion, die wie folgt geschrieben wird: `norm.ppf(p, loc = 0, scale = 1)`.\n",
"\n",
"Für den ersten Ansatz müssen wir die Gleichung für die Standardisierung von oben umstellen und sie für $x$ lösen"
]
},
{
"cell_type": "markdown",
"id": "35e537b6-9bce-41eb-b1d0-641c50d14b41",
"metadata": {},
"source": [
"$$z = \\frac{x-\\mu}{\\sigma} \\implies x = z \\sigma + \\mu$$"
]
},
{
"cell_type": "markdown",
"id": "93ba3ec8-c066-41c5-9e11-888732925ac5",
"metadata": {},
"source": [
"Für die Berechnung von $x$ benötigen wir den Mittelwert (`height_mean`) und die Standardabweichung (`height_sd`) für die Variable `height`, die $163,7$ cm bzw. $7,9$ cm beträgt. Außerdem müssen wir einen $z$-Score für die gegebene Wahrscheinlichkeit von $0,60$ erhalten. Wir können diesen $z$-Score in einer Tabelle nachschlagen oder die `norm.ppf()`-Funktion in Python anwenden. Wir wollen den $z$-Score ermitteln, bei dem der Bereich links von diesem $z$-Score $0,60$ entspricht; erinnern Sie sich, dass wir nach $P(X)=0,60$ suchen."
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "dc8fd5d1-9125-4154-af16-538b17ccb58b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.2533471031357997"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"z = norm.ppf(0.6, loc=0, scale=1)\n",
"z"
]
},
{
"cell_type": "markdown",
"id": "eda9c45d-89c7-4798-a319-dfbe509bda77",
"metadata": {},
"source": [
"Da wir nun $z$ kennen, können wir in die Gleichung von oben einsetzen"
]
},
{
"cell_type": "markdown",
"id": "96cd666a-3465-4b69-8383-9282400f743e",
"metadata": {},
"source": [
"$ x = z \\sigma + \\mu $\n",
"\n",
"$ = 0,25 \\times 7,9 + 163,7 $\n",
"\n",
"$ \\approx 165,66 $"
]
},
{
"cell_type": "markdown",
"id": "0e08a1cf-f323-471f-92c3-fe69871d4015",
"metadata": {},
"source": [
"Perfekt, wir sind fertig: $P(X<165,66)=0,60$\n",
"\n",
"Nun gehen wir den zweiten Ansatz durch, bei dem wir den Schritt der $z$-Berechnung überspringen. Alles, was wir tun müssen, ist, die `norm.ppf()`-Funktion mit dem Mittelwert und der Standardabweichung unserer Variablen `height` zu füttern."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9a53c641-9050-45fb-a552-fc2fb2f7a7c5",
"metadata": {},
"outputs": [],
"source": [
"x = norm.ppf(0.6, loc=height_mean, scale=height_sd)\n",
"x"
]
},
{
"cell_type": "markdown",
"id": "6e1741b2-39f1-4cc4-8bbe-5395a5f21017",
"metadata": {},
"source": [
"Keine Überraschung, die Zahlen stimmen überein: $P(X<165,66)=0,60$."
]
}
],
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