{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"hide": true
},
"source": [
"# Distributions example - elections\n",
"\n",
"##### Keywords: bernoulli distribution, binomial, normal distribution, central limit theorem, uniform distribution, empirical distribution, elections"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Contents\n",
"{:.no_toc}\n",
"* \n",
"{: toc}"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"hide": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"//anaconda/envs/py35/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
" warnings.warn(self.msg_depr % (key, alt_key))\n"
]
}
],
"source": [
"# The %... is an iPython thing, and is not part of the Python language.\n",
"# In this case we're just telling the plotting library to draw things on\n",
"# the notebook, instead of on a separate window.\n",
"%matplotlib inline\n",
"# See all the \"as ...\" contructs? They're just aliasing the package names.\n",
"# That way we can call methods like plt.plot() instead of matplotlib.pyplot.plot().\n",
"import numpy as np\n",
"import scipy as sp\n",
"import matplotlib as mpl\n",
"import matplotlib.cm as cm\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import time\n",
"pd.set_option('display.width', 500)\n",
"pd.set_option('display.max_columns', 100)\n",
"pd.set_option('display.notebook_repr_html', True)\n",
"import seaborn as sns\n",
"sns.set_style(\"whitegrid\")\n",
"sns.set_context(\"poster\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the last section, we made a simple simulation of a coin-toss on the computer from a fair-coin model which associated equal probability with heads and tails. Let us consider another model here, a table of probabilities that [PredictWise](http://www.predictwise.com/results/2012/president) made on October 2, 2012 for the US presidential elections. \n",
"PredictWise aggregated polling data and, for each state, estimated the probability that the Obama or Romney would win. Here are those estimated probabilities:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Obama | \n",
" Romney | \n",
" Votes | \n",
"
\n",
" \n",
" | States | \n",
" | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" | Alabama | \n",
" 0.000 | \n",
" 1.000 | \n",
" 9 | \n",
"
\n",
" \n",
" | Alaska | \n",
" 0.000 | \n",
" 1.000 | \n",
" 3 | \n",
"
\n",
" \n",
" | Arizona | \n",
" 0.062 | \n",
" 0.938 | \n",
" 11 | \n",
"
\n",
" \n",
" | Arkansas | \n",
" 0.000 | \n",
" 1.000 | \n",
" 6 | \n",
"
\n",
" \n",
" | California | \n",
" 1.000 | \n",
" 0.000 | \n",
" 55 | \n",
"
\n",
" \n",
"
\n",
"
\n",
"
\n",
" \n",
" \n",
" | \n",
" Democrat | \n",
" Republican | \n",
" Dem_Adv | \n",
" N | \n",
" Unknown | \n",
"
\n",
" \n",
" | State | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" | Alabama | \n",
" 36.0 | \n",
" 49.6 | \n",
" -13.6 | \n",
" 3197 | \n",
" 14.4 | \n",
"
\n",
" \n",
" | Alaska | \n",
" 35.9 | \n",
" 44.3 | \n",
" -8.4 | \n",
" 402 | \n",
" 19.8 | \n",
"
\n",
" \n",
" | Arizona | \n",
" 39.8 | \n",
" 47.3 | \n",
" -7.5 | \n",
" 4325 | \n",
" 12.9 | \n",
"
\n",
" \n",
" | Arkansas | \n",
" 41.5 | \n",
" 40.8 | \n",
" 0.7 | \n",
" 2071 | \n",
" 17.7 | \n",
"
\n",
" \n",
" | California | \n",
" 48.3 | \n",
" 34.6 | \n",
" 13.7 | \n",
" 16197 | \n",
" 17.1 | \n",
"
\n",
" \n",
"
\n",
"
\n",
"
\n",
" \n",
" \n",
" | \n",
" Democrat | \n",
" Republican | \n",
" Dem_Adv | \n",
" N | \n",
" Unknown | \n",
" SE_percentage | \n",
"
\n",
" \n",
" | State | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" | Alabama | \n",
" 36.0 | \n",
" 49.6 | \n",
" -13.6 | \n",
" 3197 | \n",
" 14.4 | \n",
" 0.849059 | \n",
"
\n",
" \n",
" | Alaska | \n",
" 35.9 | \n",
" 44.3 | \n",
" -8.4 | \n",
" 402 | \n",
" 19.8 | \n",
" 2.395543 | \n",
"
\n",
" \n",
" | Arizona | \n",
" 39.8 | \n",
" 47.3 | \n",
" -7.5 | \n",
" 4325 | \n",
" 12.9 | \n",
" 0.744384 | \n",
"
\n",
" \n",
" | Arkansas | \n",
" 41.5 | \n",
" 40.8 | \n",
" 0.7 | \n",
" 2071 | \n",
" 17.7 | \n",
" 1.082971 | \n",
"
\n",
" \n",
" | California | \n",
" 48.3 | \n",
" 34.6 | \n",
" 13.7 | \n",
" 16197 | \n",
" 17.1 | \n",
" 0.392658 | \n",
"
\n",
" \n",
"
\n",
"