{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "I show that the log-normal distribution converges to 1/x as sigma approaches infinity by plotting \n", "1/x along with the log-normal distribution for increasing values of sigma. Since the log-normal distribution is normalized to sum to one but 1/x is not, I plot the log-normal distributions unnormalized so they can be visually compared to 1/x." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "def unnormalized_lognormal_pdf(x, mu, sigma):\n", " \"\"\"Unnormalized probability density function for the log-normal distribution.\n", " \n", " The 'np.sqrt(2*np.pi) * sigma' has been removed from the denominator, so the\n", " result is no longer a valid probability distribution because it does not sum\n", " to one. The shape is still the same though because the missing normalizer\n", " was just a constant wrt x.\n", " \"\"\"\n", " normalizer = 1.0 / x\n", " exp_part = np.exp(-((np.log(x) - mu)**2)/(2 * sigma**2))\n", " return normalizer * exp_part\n", "\n", "vectorized_lognormal_pdf = np.vectorize(unnormalized_lognormal_pdf)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_unnormalized_lognormal(x, mu, sigma):\n", " \"\"\"Plots the unnormalized log-normal distribution with the specified parameters.\"\"\"\n", " label = \"unnormalized ln N(mu={0}, sigma={1})\".format(mu, sigma)\n", " plt.plot(x, vectorized_lognormal_pdf(x, mu, sigma), label=label)\n", "\n", "NUM_X_POINTS = 10000\n", "\n", "# Plot 1/x along with unnormalized lognormals with increasing sigma.\n", "x = np.linspace(1e-6, 1, num=NUM_X_POINTS)\n", "plt.loglog()\n", "one_over_x = 1.0 / x\n", "plt.plot(x, one_over_x, label='1/x')\n", "for sigma in (2, 3, 4, 8, 16):\n", " plot_unnormalized_lognormal(x, 0, sigma)\n", "plt.legend(loc='lower right')\n", "plt.xlabel('x')\n", "plt.ylabel('p(x)')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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PY+jfDIXjqAOfj/8cpx48hcv/+zLcX7l79Y/OjIwRGDnyBTz44NcYN64GohjA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KWlISYmhuPtLSoqQvfu3REcHIyUlBSpbaampiIpKQn+/v7o3r07qqurkZKSAiUlJYwfP15qvQUL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\nCwCoqalBfX09DA0NlRwRkYW5uTmcnZ0BAH379oWRkREqKiqUHBVpi4CAA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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another way to show the result is to calculate the mean absolute difference between 1/x and the unnormalized log-normal distribution at several points between 0 and 1. The difference approaches zero as sigma increases." ] }, { "cell_type": "code", "collapsed": false, "input": [ "sigmas = []\n", "mean_abs_errors = []\n", "for exponent in xrange(0, 20):\n", " sigmas.append(2**exponent)\n", " # Average the difference between 1/x and the lognormal at `NUM_X_POINTS` points.\n", " mean_abs_errors.append(np.mean(np.abs(one_over_x - vectorized_lognormal_pdf(x, 0, 2**exponent))))\n", "\n", "for sigma, mean_abs_error in zip(sigmas, mean_abs_errors):\n", " print \"sigma {0}, error {1}\".format(sigma, mean_abs_error)\n", "\n", "plt.loglog()\n", "plt.plot(sigmas, mean_abs_errors)\n", "plt.xlabel(\"sigma\")\n", "plt.ylabel(\"mean absolute error from 1/x\")" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "sigma 1, error 108.516971028\n", "sigma 2, error 107.263781685\n", "sigma 4, error 104.57058235\n", "sigma 8, error 79.4518416827\n", "sigma 16, error 31.6909090087\n", "sigma 32, error 9.04754313241\n", "sigma 64, error 2.34061429391\n", "sigma 128, error 0.590218129844\n", "sigma 256, error 0.147873369473\n", "sigma 512, error 0.0369883058605\n", "sigma 1024, error 0.00924832474948\n", "sigma 2048, error 0.00231215921399\n", "sigma 4096, error 0.000578044680308\n", "sigma 8192, error 0.00014451147488\n", "sigma 16384, error 3.6127887772e-05\n", "sigma 32768, error 9.03197313323e-06\n", "sigma 65536, error 2.25799335929e-06\n", "sigma 131072, error 5.64498345743e-07\n", "sigma 262144, error 1.41124589157e-07\n", "sigma 524288, error 3.52811502797e-08\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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GDpS6djUeSO3Y0Vhtj4iwOhUAAKiIixeCU1JSTLu25T3sQFXWuLH07rvGzPZf/1qaM0ei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\nS6tLAgAAaJebK+3aJb36qnTZZdLBg1ZXBH8SEA3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