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@wasade
Created July 14, 2013 23:46
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Beta distributions for your viewing pleasure. This notebook can be viewed using the IPython Notebook Viewer: http://nbviewer.ipython.org/5996603
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{
"metadata": {
"name": "Beta distribution figures"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Based on Dan Knights' distribution figures, and matplotlib example code (http://matplotlib.org/examples/pylab_examples/subplots_demo.html)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from cogent.maths.stats.special import Gamma as GammaLn\n",
"\n",
"beta_complete = lambda a_, b_: exp(GammaLn(a_) + GammaLn(b_) - GammaLn(a_ + b_))\n",
"\n",
"xx = arange(0.01,1,0.01)\n",
"shapes = [.1, .9, 1, 1.1, 1.9, 2, 5]\n",
"\n",
"f, axarr = plt.subplots(len(shapes), len(shapes), figsize=(10,10))\n",
"f.text(0.3,0.3, \"beta(x; alpha, beta)\", horizontalalignment='center', verticalalignment='top', fontsize=25)\n",
"f.tight_layout() # better spacing\n",
"x_pad = 7\n",
"\n",
"for a_idx, a in enumerate(shapes):\n",
" for b_idx, b in enumerate(shapes):\n",
" bc = beta_complete(a,b)\n",
" if b_idx < a_idx or bc == 0.0: \n",
" axarr[a_idx, b_idx].set_visible(False)\n",
" else:\n",
" # beta distribution PDF\n",
" dist = (xx**(a-1) * (1 - xx)**(b-1)) / bc\n",
" \n",
" # matplotlib displays max yval when large, not sure how to control explicitly. Easy workaround...\n",
" dist = dist / dist.max() \n",
"\n",
" # plot\n",
" axarr[a_idx, b_idx].plot(dist, linewidth=3, color='k')\n",
" \n",
" # set properties\n",
" axarr[a_idx, b_idx].set_title(\"a=%0.1f, b=%0.1f\" % (a, b), fontsize=12)\n",
" axarr[a_idx, b_idx].set_xlim(-x_pad, xx.size + x_pad)\n",
" axarr[a_idx, b_idx].set_ylim(0,dist.max() * 1.1)\n",
"\n",
" # hide axes labels and ticks\n",
" plt.setp(axarr[a_idx, b_idx].get_xticklabels(), visible=False)\n",
" plt.setp(axarr[a_idx, b_idx].get_yticklabels(), visible=False)\n",
" \n",
" plt.setp(axarr[a_idx, b_idx].get_xticklines(), visible=False)\n",
" plt.setp(axarr[a_idx, b_idx].get_yticklines(), visible=False)\n",
"savefig('betas.pdf') "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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6d+6Mdu3aoVWrVmjRogUaN24s/Jl60TIBaq9pzZo1GDNmjM4dUKKjo/HKK6/g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\n2LBhPBHz8vLCv//9b4wdO1ZnOENWVhY++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SGEEPJKFy5c4NvjNm/eHO7u7jJHJA1x4nvm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\nK1DiSwghhBBCagVKfAkhhBBCSK3w/wBHMPSAvRWcDwAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 184
}
],
"metadata": {}
}
]
}
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