Distribution.ipynb

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  "signature": "sha256:006719e533ecc1441c68b13072ede12faca63dc73cf07931bcf628df28184843"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy\n",
      "import scipy\n",
      "import scipy.stats\n",
      "import matplotlib.pylab as plt\n",
      "import pylab"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def convert(loc, scale):\n",
      "    m, v = loc, scale * scale\n",
      "    mean = numpy.log(m * m / numpy.sqrt(v + m * m))\n",
      "    sigma = numpy.sqrt(numpy.log(1 + v / (m * m)))\n",
      "    return mean, sigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 1000\n",
      "Xmean, Ymean = 1.0, 1.0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m = 1\n",
      "X = numpy.zeros(N, numpy.double)\n",
      "for _ in range(m):\n",
      "    mean, sigma = convert(Xmean / m, 0.5)\n",
      "    X += numpy.random.lognormal(mean, sigma, size=N)\n",
      "    # X += numpy.random.normal(Ymean, 0.5, size=N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# mean, sigma = convert(Ymean, 0.5)\n",
      "# Y = numpy.random.lognormal(mean, sigma, size=N)\n",
      "# Y = numpy.random.normal(Ymean, 0.5, size=N)\n",
      "Y = Ymean * numpy.ones(N, numpy.double)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pylab.hist(X, bins=numpy.linspace(0, Xmean * 5, 50))\n",
      "print \"Mean of X = %g, STD of X = %g\" % (numpy.mean(X), numpy.std(X))\n",
      "print \"Skewness of X = %g\" % (scipy.stats.skew(X))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mean of X = 1.03394, STD of X = 0.555739\n",
        "Skewness of X = 2.06638\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f3f52fa1a10>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B = X / Y\n",
      "Bmean = Xmean / Ymean\n",
      "pylab.hist(B, bins=numpy.linspace(0, Bmean * 5, 50))\n",
      "print \"Mean of B = %g, STD of B = %g\" % (numpy.mean(B), numpy.std(B))\n",
      "print \"Skewness of B = %g\" % (scipy.stats.skew(B))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mean of B = 1.03394, STD of B = 0.555739\n",
        "Skewness of B = 2.06638\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f3f64096390>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}