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@kforeman
Last active August 31, 2017 06:24
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20170830 - Distribution rescaling.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/kforeman/anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
" warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
]
}
],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simulate some independent normal distributions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ a = \\mathcal{N}(0, 1) $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ b = \\mathcal{N}(3, 2) $$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"a = np.random.normal(0, 1, size=1000)\n",
"b = np.random.normal(3, 2, size=1000)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x116628fd0>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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V+7I7KqebvLZqfGU0GdcWQhSZhLYouom1uScuj6o01W4bigLDQQltIURxSWiL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\n2oIgCIKQJkTSFgRBEIQ08f/J+BJLGeKlugAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11411ec10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.distplot(a, label='$a$')\n",
"sns.distplot(b, label='$b$')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"<seaborn.axisgrid.PairGrid at 0x11667aad0>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ugODa+Rp3X+zBj3NFdIH96KOP8N///d/YvXu32FshiLxAAgnWryqb0YovPbdYndIQ0FRT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\no85MI3rzjAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1166fd290>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.pairplot(pd.DataFrame(np.vstack([a,b]).T, columns=['$a$','$b$']))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Adjust using mean and standard deviation\n",
"$$\n",
"\\hat{b} = \\bar{a} + \\frac{\\sigma_{a}}{\\sigma_{b}} \\times (b - \\bar{b})\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def mean_sd_adjust(target, raw):\n",
" sd_ratio = target.std() / raw.std()\n",
" adjusted = target.mean() + (sd_ratio * (raw - raw.mean()))\n",
" return adjusted\n",
"b_adj = mean_sd_adjust(a, b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Confirm that $a$ and $\\hat{b}$ share the same distribution"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1176ab550>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Fvv/977Nv3z4Mw+Dpp5/mwIEDPPjggwDs2bOnvtGLlqbMDELrdTaQOQp4NQJe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\nz8/erhwb98QoczMs7HoDcIlOmoU3GCZwKEmns2fWcMWWHPY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gwIEDB7jhhhuIRqMsXbo0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\nSNqCIAiCUCT+P/a5r00Te9MAAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1176ab510>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.distplot(a, label='$a$')\n",
"sns.distplot(b, label='$b$')\n",
"sns.distplot(b_adj, label='$\\hat{b}$')\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Show that $a$ and $\\hat{b}$ have the same summary values, yet $\\hat{b}$ maintains the draw order of $b$ so that correlation isn't broken"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"<seaborn.axisgrid.PairGrid at 0x116695bd0>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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b7Dh+fgytdcWoKDHi5Ecj6O6ohEalRJFFi0AoDq1aiZQsXazJZUU6ncGD95RD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\nAiGEEEKsoiCBEEIIIVb9P5eSPLCZFxwBAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1177e9d10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.pairplot(pd.DataFrame(np.vstack([a,b,b_adj]).T, columns=['$a$','$b$','$\\hat{b}$']))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Now test for non-normal distributions\n",
"e.g. log-normal"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ \\mathrm{log}(x) = \\mathcal{N}(.1, .1) $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ \\mathrm{log}(y) = \\mathcal{N}(.25, .25) $$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x = np.random.lognormal(0.1, 0.1, size=1000)\n",
"y = np.random.lognormal(0.25, 0.25, size=1000)\n",
"y_adj = mean_sd_adjust(x, y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### The adjustment isn't quite right, because it assumes normality\n",
"The further from normal the distribution is, the worse the approximation..."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x119243a50>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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w/T+ZxXztoOtf7Nd/uuZcxX3gwAE++9nPcvvtt/ORj3xk9vFcLke5XJ79ulKp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\nf/RkIrqxyLS6AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119243fd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.distplot(x, label='$x$')\n",
"sns.distplot(y, label='$y$')\n",
"sns.distplot(y_adj, label='$\\hat{y}$')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"<seaborn.axisgrid.PairGrid at 0x1177c5ed0>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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NZtVAcDgcOHLkCF5++WXifblcjmPHjkEulwMAYrEYFApFpktQKJQpxJNXPJFA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\ncv/PqIHw1FNP4amnnhq1fffu3di9e3cGRzT3SY12vS1nalvFsTiDxjY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Lr5UYZmmEc59J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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x118ff9c10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.pairplot(pd.DataFrame(np.vstack([x,y,y_adj]).T, columns=['$x$','$y$','$\\hat{y}$']))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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