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Last active November 7, 2020 06:45
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RandomWalkArcSine
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "RandomWalkArcSine",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyM+j+f7I+SsNqQ8S6xdjdol",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/neoyipeng2018/bd07eaf9e28a5bfec5f7b9d948d26439/randomwalkarcsine.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "CnkcDUWvWrs4"
},
"source": [
"import random\n",
"from numpy import arcsin, pi, sqrt"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "XiNz8wJrXGJd"
},
"source": [
"def toss(): return 1 if random.random() < 0.5 else -1\n",
"\n",
"def randomwalk(sims=10_000,ntoss=20,leadthres=0.5):\n",
" leadsims=0\n",
" for i in range(sims):\n",
" cum,leadtoss=0,0\n",
" for _ in range(ntoss):\n",
" cum+=toss()\n",
" if cum >= 0: leadtoss+=1\n",
" if leadtoss == ntoss*leadthres: leadsims+=1\n",
" return leadsims/sims"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "OxsLmbz1YtXM"
},
"source": [
"Verifying arcsine law"
]
},
{
"cell_type": "code",
"metadata": {
"id": "JePUptx7tjA1"
},
"source": [
"import matplotlib.pyplot as plt\n",
"plt.style.use('seaborn-dark-palette')\n",
"plt.rcParams[\"figure.figsize\"] = (11,7)"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "IhuhFjOFtSlf",
"outputId": "3812be90-29a7-4e2f-91ee-0ae0b24f3b00",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
}
},
"source": [
"leadpct=[1,0.9,0.75,0.5,0.75,0.9,1.0] #assuming if one player is not in lead, the other is, so the distribution will be symmetrical\n",
"plt.plot([randomwalk(sims=10_000,ntoss=20,leadthres=lead) for lead in leadpct])\n",
"plt.ylabel('Simulated Probability')\n",
"plt.xlabel('% of time in the lead')\n",
"plt.xticks([0,1,2,3,4,5,6],['0%','10%','25%','50%','75%','90%','100%'])\n",
"plt.title('Distribution of who stays in the lead in a fair coin toss ')\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 792x504 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_7lPcVnrRJ5G"
},
"source": [
"From Arcsine Wikipedia page\n",
"https://en.wikipedia.org/wiki/Arcsine_distribution"
]
},
{
"cell_type": "code",
"metadata": {
"id": "5oSHM-fcQ8qE",
"outputId": "8b73cb66-34f8-41ce-c259-144bd7d8bd13",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 549
}
},
"source": [
"from IPython.display import Image\n",
"from IPython.core.display import HTML \n",
"Image(url= \"https://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Arcsin_density.svg/700px-Arcsin_density.svg.png\")"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Arcsin_density.svg/700px-Arcsin_density.svg.png\"/>"
],
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {
"tags": []
},
"execution_count": 2
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "AukUgpGPRHF2"
},
"source": [
"**References:** Understanding Probability by Henk Tijms"
]
}
]
}
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