{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats\n", "\n", "np.random.seed(42)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "def cauchy_inverse_cdf(p, mu, sigma):\n", " return mu + sigma * np.tan(np.pi * (p - 0.5))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "def get_cauchy_deviate(mu, sigma):\n", " \"\"\"Get a random cauchy deviate using the transformation method.\"\"\"\n", " uniform_deviate = np.random.random()\n", " return cauchy_inverse_cdf(uniform_deviate, mu, sigma)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "cauchy_mu = -2\n", "cauchy_sigma = 0.5\n", "\n", "samples = np.array([get_cauchy_deviate(cauchy_mu, cauchy_sigma) for _ in xrange(10000000)])\n", "samples.sort()\n", "print 'First 5', samples[:5]\n", "print 'Last 5', samples[-5:]\n", "print 'Sample Median', np.median(samples)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "First 5 [-472102.55301209 -421651.84579584 -415302.55927885 -411290.46997529\n", " -407346.13437632]\n", "Last 5 [ 340251.58424335 551800.27483741 701783.98767175 1178281.1345642\n", " 1906305.9508952 ]\n", "Sample Median " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "-1.99996602588\n" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(8, 8))\n", "\n", "ax.hist(samples, bins=100, range=(-6, 2), label='Deviates', normed=True, alpha=0.5)\n", "\n", "scipy_cauchy_pdf = scipy.stats.cauchy(loc=cauchy_mu, scale=cauchy_sigma).pdf\n", "xs = np.linspace(-6, 2, num=1000)\n", "ax.plot(xs, scipy_cauchy_pdf(xs), color='red', label='Scipy PDF', linewidth=3)\n", "\n", "ax.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAegAAAH0CAYAAAD2RL7sAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQgghLJAkaCGEEMICSYIWQgghLND/B8MlUSnnXT3bAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 5 } ], "metadata": {} } ] }