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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Determining Power Law parameter(s) using Bayesian modeling with PyMC"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Model declaration\n",
      "\n",
      "To begin with, I define the model that we want to use for our Bayesian inference approach. As the power law distribution is not already included in the PyMC library, we have to define it ourself. For doing so, I resort to the probability density and mass functions defined by Clauset et al. in http://arxiv.org/abs/0706.1062.\n",
      "\n",
      "We have to differ between continiuous and discrete distributions. \n",
      "\n",
      "For the continuious case we use the following definition:\n",
      "\n",
      "$p(x) = C * f(x) = (\\alpha-1)*x_{min}^{\\alpha-1} * x^{-\\alpha}$\n",
      "\n",
      "And for the discrete the following where $\\zeta$ is the Hurwitz zeta function:\n",
      "\n",
      "$p(x) = C * f(x) = {\\zeta(\\alpha,x_{min})}^{-1}  * x^{-\\alpha}$\n",
      "\n",
      "Note that at the moment, only $\\alpha$ can be determined and $x_{min}$ is fixed. For $\\alpha$ an exponential prior distribution is chosen, but it also works with other distributions like the uniform."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys\n",
      "import pymc as mc\n",
      "from scipy.special import zeta\n",
      "\n",
      "def _model(data, discrete=True, xmin=1.):\n",
      "\n",
      "    alpha = mc.Uniform('alpha', 0.,10.) \n",
      "    #alpha = mc.Exponential('alpha', 1. / 1.5)\n",
      "    #xmin = mc.Uniform('xmin', min(data), max(data))\n",
      "    #xmin = mc.Exponential('xmin', 1.)\n",
      "    #print xmin.value\n",
      "\n",
      "    @mc.stochastic(observed=True)\n",
      "    def custom_stochastic(value=data, alpha=alpha, xmin=xmin, discrete=discrete):\n",
      "        value = value[value >= xmin]\n",
      "        if discrete == True:\n",
      "            return np.sum(np.log(value**-alpha / zeta(alpha,xmin)))\n",
      "        else:\n",
      "            return np.sum(np.log((alpha-1) * xmin**(alpha-1) * value**-alpha))\n",
      "\n",
      "    return locals()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def analyze(data, discrete=True, xmin=1.):\n",
      "    model = mc.MCMC(_model(data,discrete,xmin)) \n",
      "    model.sample(5000) \n",
      "\n",
      "    print\n",
      "    print(model.stats()['alpha']['mean'])\n",
      "\n",
      "    mc.Matplot.plot(model) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Applying and evaluating the model\n",
      "\n",
      "We start by generating random power law data with specific parameters using the power law library https://pypi.python.org/pypi/powerlaw.\n",
      "\n",
      "First, using discrete data with $\\alpha=1$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import powerlaw\n",
      "\n",
      "test = powerlaw.Power_Law(xmin = 1., parameters = [2.], discrete=True)\n",
      "simulated = test.generate_random(5000)\n",
      "analyze(simulated, discrete=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    34%                  ] 1727 of 5000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------51%                  ] 2596 of 5000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------90%--------------    ] 4515 of 5000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 5000 of 5000 complete in 1.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1.94561399584\n",
        "Plotting alpha\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gRUQOp0ePHjh69Cjy8/Nx+vRpHD16FMePH8eGDRsQGhqK8+fPY9KkSdiwYQMA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\nsSIiIiKSCBMrIiIiIon8P9P/HHgv9ksvAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bfd5dd0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Second, using continuous data with $\\alpha=3$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test = powerlaw.Power_Law(xmin = 1., parameters = [3.], discrete=False)\n",
      "simulated = test.generate_random(5000)\n",
      "analyze(simulated, discrete=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     32%                  ] 1618 of 5000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------65%----              ] 3284 of 5000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------98%----------------- ] 4913 of 5000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 5000 of 5000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "2.95652161755\n",
        "Plotting alpha\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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r4MHy39Xhw/LzBZBH1bZula9fviz/nb36qgFVVQYA5o9jZ3H8+HGsXLkSZWVlqKioQHBw\ncIPtIiMjAQCjR4/Gr7/+irKyMkiShEmTJsHR0RH9+vWDi4sLiouLMWDAAGzYsAG7d+8GIL/G5ubm\nIiAgoN5xH3/8cQByTeq///1v0/baN6oPPfQQoqKiEB4ebmorhOCHd6hNdJZ1rCCacO7cOXHhwgUh\nhBCXLl0So0ePFnv37jVr8+mnn4qQkBAhhBD/93//JwICAho8Vu2pXnlFiJ49hejaVf75yivy9YsX\nhXjkESH+/Gch7r5biNmzhZg1q+7Sr99IMWuWELffLsQzz8iTF1On1l0CA+Vtzz1XO7EhX6qqhHjp\nJSFOnxaioECIP/5RiDvuEMLNzbydj48Qb78txF13yfH++99CDBokxOOPC9GlixC33VbXdtYs+afB\nIJ/Xx0eIrKzafgrh7FwX3wsvmJ+n9jJqlBBOTkJ8/LEQ48bVPU6rVsn7u3UT4sQJIRYtki9z5ggR\nHCyEh4f8ONUe57nnhBg4UAitVr49caLcv6QkIbZsEcLPTz7uhx8K8fvfy+cMDJT7tWuXEBUVdZcz\nZ+qO+8svQoSGyr+P6+NWKISYN0+IFSuEWL5cvjz8sLzv0iUh7rtPvt/f/ibEmjXm933+eSH+8hf5\n97FokRBjxghx9aq875//FKKkRIhTp4QoKqp7PNatkx/vP/xBiAEDhJg7V4hz54SIiJAf98GD5XMO\nGCA/jmq1EI6OQvTrJ8Qbbwjh6irEzJlCREcL0bt3XSxubkJcuCC3dXGRL4AQe/YIkZoqP14ffijH\neffd5v3o3l0IjUaIF1+Ub3/+ufnfxp49QmzeLMQ99wjx5Zd1lwcfFCI2Vn7cMzLkxyg6Wohjx+r/\nfTg41D/vjZfFi81vT58u/25mzJCPvXNnw/e7776mj3vjxcdH/unuLv8cN06IhQvN20iSEN7e5tuS\nk+ue97aupf1wd3cXx44dE0II8eGHH4pZs2YJIYTQ6XTi9ddfF0IIodVqRXp6uuk+d999tygrKxM6\nnU689tprpu1Dhw4VP/30k0hPTxcPP/ywqKysNN1/3759DZ77l19+EUIIcejQIaHVaoUQQnzwwQdi\n4cKFpnYZGRnir3/9q6n9jfuJbkVqaqpwdg5u4esLrl2uf+1bIl555ZX27oYQovWvX02OWBUVFSEq\nKgo1NTWoqanBjBkzMHbsWGzatAkAEB0djdDQUKSmpsLDwwPdu3fHBx980GQi99VX8rtoZ2dg9255\nOmjdOvlde2UlcPfd8gjDuXPySEmtffskPPKIvE2tBt56S74vAKSny+/U//AH+R127QdrFiyQRzpW\nrqw7jqenPJrz6KNyDL/8AmRnyyMm48fLoyI//QSsXSuPJsyfL0+HjRwpT8OsWydPj3z4ofwO/8sv\nzfv34YdyH557Th4t2btXjqegALj3Xrlfvr7A7NlyXG5uwHff1Y2c1M60Dhggv+Nfv978+GfOAGlp\n8mjFa68BkyYBTz9dNwqSlSVPzYSFyaMrMTHAI48Ax48Dzz8vj8ydPQvMmSP3q2tXeWSk1tix8lRc\n377Ap5/Kf+o+PnWP9ZIl8lRm797yCEZ1tXwdAJyc5Gmlt96SR4vOngVWrJCvBwfLj11jnJ3l+/br\nZ759xAjg3XflkaOpU4HkZPnvpl8/ecTrjjsAR0d5xOToUTneSZPk0aP//U+e0kxMlEfgsrPlkRxA\njqV3b7lN7XTrhAny34CTkzzaBAB//3v9WJ9/Xj73Aw8AQ4bI12tH+P7f/5N/14D8GAcG1t1vyRJ5\ndGnnTvmxB4CXX5Yf308+kf8ejh6Vf+8//AAsWgR89BFw8CDw1FNAbWnNsGHy4xIRUff3ERNTN0W7\nZIk8inj4cN25n35afhzHjpWnMF97TT6Oh4d5344ckUf0nniiblt6ujzCeO4ccNtt8khrly7yc87N\nTe732bPy6N31wsIa/l3bs4qKCri6uqKqqgrbt2831Z+K60aFhBBISkqCVqvFN998g969e6NXr14N\njhoJIfDrr7+iT58+6Nq1K06cOIGDBw+2Or4ff/wR/v7+8Pf3R1paGgoKCtCrV696n54motZrMrHy\n8fHB4etfna+Jjo42u52QkNCik6WkyInBkiXAmDHyPwtAnpapTazuvx/473/l5KRnz7r7zp5tvvbU\n9a9B06bJ/+xvu02+HRMj/9MfPbp+DIMHy0nL+PHm/zxqj6lWy4nIzz/LSZVKJe/r2VOemlq0SI4X\nkKflbnTtw4po4GEzM3Wq/PPyZfkfdVWVfDs8XJ6Wuffehu/n7i73r6ZGnm574AE5ubh4UZ6yycwE\nevWSEyaVCvj6a/lxdXCQH9suXeRzDhkiJ3h33NF0nJJUN2UUEiIfJz9fnqasXdasvFw+5/r18uNT\nq29fuf3HH9clfo1p7NNvY8fKNVF//7uc+Li6Nn6MoUPrrisUcvIkSXKiBMjJrBByclObUNQmhYA8\ntQfIiYS/v3z9t9/k6TsHh7op0D//uW6K7Zln5GT2tdfkv8N+/eRzNuSxx+RLQyZNkqcGY2Pl6di+\nfeVk/k9/kn9ntf3u1UveX5u0DB8u/63Nnl13rJ49zf/+XnhB/t29+678tzZ+fN2+cePkBOs//5Hv\n5+tbN2X9ww9ykt27t/zcuvGxLyyU/24lSX5M77pLTuCLioBGqgHs3ksvvYSAgADcddddCAgIQMW1\nB1OSJFPZgiRJ6Nq1K4YPH46rV69iy5Yt9drUkiQJwcHBeOedd6BWqzF48GA88MADDZ77+vveeL7a\n688//zxyc3MhhMC4ceMwbNgwuLm5IT4+HhqNBitWrGCdFdEtkkRDb5OscSJJwrhxAr16yUXed91V\nt8/XV34xPn9e/udy3YcM240kyf9gH3pI/ofyu98B117/TPuPHq1fp2SPhJD/ifbvLyfGn30mJ4a1\nicityssDBg5sPCFpjatX5Vh79Gg6GbteVZWcNN53X922X3+VE0dHR+Avf5Hr5ZpLmlvr6FF5tO+N\nN+QEqtbf/y4n0IMGyYXlc+fW7bt40Tx5BORRuv/+V4713nvlkdab8csv8khafHzDbx5uRmNLANga\nS/YjMDAQr7/+OoYPH26R4xF1JGlpaYiM3Iiysvpro9Wvsap90Rdm+52cnJr81pW20trnfZsmVoWF\nAv37199XXi5fbr9d/oSULTh2TB4h4fJV1FYOH5anDR0d2zuSlmNiVR8TK7JnTSVW9ZknVgCurWPl\nYtOJVZt+CXNjIxI9e5pP+9mCzjBSRR0L/w/bh/T09PYOgYisqE3HWzi6Q0RERPasQ4xYERERkX3r\nLOtYtWlixRErIiKizonfFWgFHLEiIiIie8YaKyIiIiILYY0VERERWR1rrKyAI1ZERESdE2usrHEy\nJlZERERkx1i8TkRERGQhnAokIiIiq+ssNVbNpjr5+fkIDAzEkCFDMHToUGzcuLFeG4PBAGdnZ2g0\nGmg0GqxevbrBY3HEioiIqHPS6VY1WWel063C6tUVbRiRdTQ7YuXo6Ig333wTfn5+qKiowIgRIxAU\nFARvb2+zdmPGjEFKSkqTx+KIFREREdmzZlMdV1dX+Pn5AQB69OgBb29vFBYW1mvXkm+A5ogVERER\n2bObqrE6c+YMsrOzERAQYLZdkiQcOHAAvr6+UCqVeO2116BWq+vdnyNWREREnVNnqbFqcWJVUVGB\nadOmYcOGDejRw7zjw4cPR35+PpycnJCWloYpU6bg5MmT9Y4RF6czjVpptVpotdpbCp6IOhaDwQCD\nwdDeYRBRB9RZ1rGSRAvm8KqqqjBp0iSEhIRg8eLFzR703nvvRVZWFvr27Vt3Iklq0XQhEdkPe3ne\n20s/iKwtLS0NkZEbUVaW1oLWtfVBdc8tObFywdKlS60S381o7fO+2ck5IQTmzp0LtVrdaFJVXFxs\nOnlmZiaEEGZJFREREVFn0OxU4P79+7F9+3YMGzYMGo0GALBmzRr8/PPPAIDo6Gh8/PHHePvtt+Hg\n4AAnJyfs3LnTulETERGRTeksNVYtmgq0yIk4lE7U6djL895e+kFkbZwKbOOvtCEiIiKyZ0ysiIiI\niCykTb8rkIiIiDqnzlJjxcSKiIiIrK6zrGPFqUAiIiIiC2FiRURERGQhnAokIiIiq2ONFREREZGF\nsMaKiIiIiG4KEysiIiIiC+FUIBEREVkda6yIiIiILIQ1VgDy8/MRGBiIIUOGYOjQodi4cWOD7WJj\nY+Hp6QlfX19kZ2dbJVAiIiKijq7JEStHR0e8+eab8PPzQ0VFBUaMGIGgoCB4e3ub2qSmpiIvLw+5\nubnIyMhATEwMDh48aPXAiYiIiDqaJkesXF1d4efnBwDo0aMHvL29UVhYaNYmJSUFUVFRAICAgACU\nlpaiuLjYSuESEdWprq6GRqPB5MmTAQDnz59HUFAQBg0ahPHjx6O0tNTUdu3atfD09ISXlxf27Nlj\n2p6VlQUfHx94enpi0aJFbd4Hos5Cp4sz1Vk1tn/lStuvsWrxpwLPnDmD7OxsBAQEmG03Go1wc3Mz\n3VapVCgoKLBchEREjdiwYQPUajUkSQIAxMfHIygoCCdPnsTYsWMRHx8PAMjJyUFSUhJycnKg1+sx\nf/58CCEAADExMdi8eTNyc3ORm5sLvV7fbv0hsmc63aom66x0ulVYvbqiDSOyjhYlVhUVFZg2bRo2\nbNiAHj3qZ5O1L1C1al/kiIispaCgAKmpqZg3b57pNej6EfSoqCjs3r0bAJCcnIzIyEg4OjrC3d0d\nHh4eyMjIQFFREcrLy+Hv7w8AmDlzpuk+RESt0eynAquqqjB16lQ8+eSTmDJlSr39SqUS+fn5ptsF\nBQVQKpUNHkun05mua7VaaLXam4+YiDosg8EAg8HQJuf605/+hFdffRW//vqraVtxcTEUCgUAQKFQ\nmMoSCgsLcf/995vaqVQqGI1GODo6QqVSmbYrlUoYjcY2iZ+I7FOTiZUQAnPnzoVarcbixYsbbBMW\nFoaEhARERETg4MGD6N27t+mF7UbXJ1ZEZH9ufMMUF9d4PcWt+M9//gMXFxdoNJpGEzlJkjh6TtSB\ncB0rAPv378f27dsxbNgwaDQaAMCaNWvw888/AwCio6MRGhqK1NRUeHh4oHv37vjggw+sHzURdWoH\nDhxASkoKUlNTcfnyZfz666+YMWMGFAoFzp49C1dXVxQVFcHFxQVAwyPrKpUKSqXSrCaUI+5E1tPR\n17Gy1Ii7JG4skLISSZLq1WIRkX1ri+f9vn378Nprr+GTTz7B888/j379+mHZsmWIj49HaWkp4uPj\nkZOTgyeeeAKZmZkwGo0YN24c8vLyIEkSAgICsHHjRvj7+2PixImIjY1FcHBwm/eDyB6kpaUhMnIj\nysrSWtC6dkS57rklJ1YuWLp0qVXiuxmtfd5z5XUisnm1U37Lly9HeHg4Nm/eDHd3d+zatQsAoFar\nER4eDrVaDQcHByQmJpruk5iYiFmzZqGyshKhoaH1kioiopvBESsishp7ed7bSz+IrK2pEav6NVbm\nI1a1+52cnDhiRURERNSUjl5jZSktXiCUiIiIiJrGxIqIiIjIQjgVSERERFbHdayIiIiILIQ1VkRE\nRER0U5hYEREREVkIpwKJiIjI6lhjRURERGQhrLEiIiIiopvCxIqIiIjIQppNrObMmQOFQgEfH58G\n9xsMBjg7O0Oj0UCj0WD16tUWD5KIiIhsm04XZ6qzamz/ypWdoMZq9uzZeOaZZzBz5sxG24wZMwYp\nKSkWDYyIiIjsB2usrhk9ejT69OnTZBt+6zsRERGRBWqsJEnCgQMH4Ovri9DQUOTk5FgiLiIiIiKb\nc8vLLQwfPhz5+flwcnJCWloapkyZgpMnT1oiNiIiIrITXMeqhXr27Gm6HhISgvnz5+P8+fPo27dv\nvbY6nc50XavVQqvV3urpiagDMRgMMBgM7R0GEXVAnaXG6pYTq+LiYri4uECSJGRmZkII0WBSBZgn\nVkRkf258wxQX1/gngIiI7FGziVVkZCT27duHkpISuLm5IS4uDlVVVQCA6OhofPzxx3j77bfh4OAA\nJycn7Ny50+pBExEREXVEzSZWO3bsaHL/ggULsGDBAosFRERERPaHNVZEREREFtJZaqz4lTZERERE\nFsLEiogqo8A3AAAgAElEQVSIiMhCOBVIREREVscaKyIiIiILYY0VEREREd0UJlZEREREFsKpQCIi\nIrI61lgRERERWQhrrIiIiIjopjCxIiIiIrIQTgUSERGR1bHGioiIiMhCWGN1zZw5c6BQKODj49No\nm9jYWHh6esLX1xfZ2dkWDZCIiIjIVjSbWM2ePRt6vb7R/ampqcjLy0Nubi7effddxMTEWDRAIiIi\nIlvR7FTg6NGjcebMmUb3p6SkICoqCgAQEBCA0tJSFBcXQ6FQWCxIIiIism2ssWoho9EINzc3022V\nSoWCggImVkRERGTCGqubIIQwuy1JkiUOS0RERGRTbnnESqlUIj8/33S7oKAASqWywbY6nc50XavV\nQqvV3urpiagDMRgMMBgM7R0GEVG7ueXEKiwsDAkJCYiIiMDBgwfRu3fvRqcBr0+siMj+3PiGKS4u\nrv2CIaIOhTVW10RGRmLfvn0oKSmBm5sb4uLiUFVVBQCIjo5GaGgoUlNT4eHhge7du+ODDz6wetBE\nRERkWzpLjVWzidWOHTuaPUhCQoJFgiEiIiKyZfyuQCIiIiIL4VfaEBERkdWxxoqIiIjIQjpLjRWn\nAomIiIgshIkVERERkYVwKpCIiIisjjVWRERERBbCGisiIiIiuilMrIiIiIgshFOBREREZHWssSIi\nIiKyENZYEREREdFNYWJFREREZCHNJlZ6vR5eXl7w9PTEunXr6u03GAxwdnaGRqOBRqPB6tWrrRIo\nERER2S6dLs5UZ9XY/pUr7bzGqrq6GgsXLsTevXuhVCoxatQohIWFwdvb26zdmDFjkJKSYtVAiYiI\nyHaxxgpAZmYmPDw84O7uDkdHR0RERCA5ObleOyGE1QIkIiIishVNJlZGoxFubm6m2yqVCkaj0ayN\nJEk4cOAAfH19ERoaipycHOtESkR0zeXLlxEQEAA/Pz+o1Wq88MILAIDz588jKCgIgwYNwvjx41Fa\nWmq6z9q1a+Hp6QkvLy/s2bPHtD0rKws+Pj7w9PTEokWL2rwvRGRfmpwKlCSp2QMMHz4c+fn5cHJy\nQlpaGqZMmYKTJ0822Fan05mua7VaaLXamwqWiDo2g8EAg8Fg9fN07doV6enpcHJywtWrV/Hwww/j\nm2++QUpKCoKCgvD8889j3bp1iI+PR3x8PHJycpCUlIScnBwYjUaMGzcOubm5kCQJMTEx2Lx5M/z9\n/REaGgq9Xo/g4GCr94Gos+E6VgCUSiXy8/NNt/Pz86FSqcza9OzZ03Q9JCQE8+fPx/nz59G3b996\nx7s+sSIi+3PjG6a4uMYLVW+Vk5Nch3HlyhVUV1ejT58+SElJwb59+wAAUVFR0Gq1iI+PR3JyMiIj\nI+Ho6Ah3d3d4eHggIyMD99xzD8rLy+Hv7w8AmDlzJnbv3s3EisgKWGMFYOTIkcjNzcWZM2dw5coV\nJCUlISwszKxNcXGxqcYqMzMTQogGkyoiIkuqqamBn58fFAoFAgMDMWTIEBQXF0OhUAAAFAoFiouL\nAQCFhYVmbwpryxpu3K5UKuuVOxAR3YwmR6wcHByQkJCACRMmoLq6GnPnzoW3tzc2bdoEAIiOjsbH\nH3+Mt99+Gw4ODnBycsLOnTvbJHAi6ty6dOmCI0eOoKysDBMmTEB6errZfkmSWlTOQERkSc1+pU1I\nSAhCQkLMtkVHR5uuL1iwAAsWLLB8ZERELeDs7IyJEyciKysLCoUCZ8+ehaurK4qKiuDi4gKgfllD\nQUEBVCoVlEolCgoKzLYrlcoGz8MaUaJb09FrrCxVIyqJNlorQZIkLstA1MlY63lfUlICBwcH9O7d\nG5WVlZgwYQJWrVqFzz77DP369cOyZcsQHx+P0tJSU/H6E088gczMTFPxel5eHiRJQkBAADZu3Ah/\nf39MnDgRsbGx9Wqs+PpF1DJpaWmIjNyIsrK0FrSuHVGue27JNVYuWLp0qVXiuxmtfd7zS5iJyOYU\nFRUhKioKNTU1qKmpwYwZMzB27FhoNBqEh4dj8+bNcHd3x65duwAAarUa4eHhUKvVcHBwQGJiomma\nMDExEbNmzUJlZSVCQ0NZuE5Et4QjVkRkNfbyvLeXfhBZG0esOGJFREREbaCj11hZChMrIiIisjqu\nY0VEREREN4WJFREREZGFcCqQiIiIrI41VkREREQWwhorIiIiIropTKyIiIiILIRTgURERGR1naXG\nqtkRK71eDy8vL3h6emLdunUNtomNjYWnpyd8fX2RnZ1t8SCJiIjItul0q5qss9LpVmH16oo2jMg6\nmkysqqursXDhQuj1euTk5GDHjh34/vvvzdqkpqYiLy8Pubm5ePfddxETE2PVgDsCS3z7dUdgL/0A\n2BciIuoYmkysMjMz4eHhAXd3dzg6OiIiIgLJyclmbVJSUhAVFQUACAgIQGlpKYqLi60XcQdgL//4\n7KUfAPtCREQdQ5M1VkajEW5ubqbbKpUKGRkZzbYpKCiAQqGwcKhERERkq1hjBfmbnVvixm9/bun9\niIhqzZw5E2lpae0dBhFZSWepsWpyxEqpVCI/P990Oz8/HyqVqsk2BQUFUCqV9Y41cOBAu0q44uLi\n2jsEi7CXfgDsS0c0cODAFrd97733kJSUhN///vd48MEHMW/ePHTv3t2K0RERWV6TidXIkSORm5uL\nM2fOYMCAAUhKSsKOHTvM2oSFhSEhIQERERE4ePAgevfu3eA0YF5enmUjJyK78ssvv+DUqVNwdnaG\nQqHAnDlzkJSU1N5hERHdlCYTKwcHByQkJGDChAmorq7G3Llz4e3tjU2bNgEAoqOjERoaitTUVHh4\neKB79+744IMP2iRwIrIvr7/+OubPn28a5bq+dpOIbF9nqbGSxI0FUkRE7eCTTz7B5MmTAQCffvop\nJk6c2M4R1ZEkqV4tKRHVl5aWhsjIjSgra0m9ZG15UN1zS/6uQBcsXbrUKvHdjNY+763+lTYtWWC0\nvc2ZMwcKhQI+Pj6mbefPn0dQUBAGDRqE8ePHo7S01LRv7dq18PT0hJeXF/bs2WPanpWVBR8fH3h6\nemLRokVt2gdAroELDAzEkCFDMHToUGzcuNFm+3L58mUEBATAz88ParUaL7zwgs32pVZ1dTU0Go0p\nebDVvri7u2PYsGHQaDTw9/cHYJm+7Nu3z7Tv66+/brsOERFZkrCiq1evioEDB4rTp0+LK1euCF9f\nX5GTk2PNU7bKV199JQ4fPiyGDh1q2rZ06VKxbt06IYQQ8fHxYtmyZUIIIb777jvh6+srrly5Ik6f\nPi0GDhwoampqhBBCjBo1SmRkZAghhAgJCRFpaWlt2o+ioiKRnZ0thBCivLxcDBo0SOTk5NhkX4QQ\n4uLFi0IIIaqqqkRAQID4+uuvbbYvQgjx+uuviyeeeEJMnjxZCGGbf2NCCOHu7i5++eUXs22W6MvY\nsWPF3r17xRdffCFmzZrVhj1qnpVfKonsRmpqqnB2DhaAaMEF1y512xwclohXXnmlvbshhGj9896q\nI1YtWWC0Ixg9ejT69Oljtu36hU+joqKwe/duAEBycjIiIyPh6OgId3d3eHh4ICMjA0VFRSgvLze9\ng585c6bpPm3F1dUVfn5+AIAePXrA29sbRqPRJvsCAE5OTgCAK1euoLq6Gn369LHZvhQUFCA1NRXz\n5s0zDS3bal+A+kusWKIvbm5uOHnyJE6cOIH169e3bYeIyOp0ujhTnVVj+1eutP0aK6smVg0tHmo0\nGq15SospLi42fbpRoVCYVpMvLCw0W3Kitk83blcqle3a1zNnziA7OxsBAQE225eamhr4+flBoVCY\npjhttS9/+tOf8Oqrr6JLl7qnnK32RZIkjBs3DiNHjsR7770HwDJ9OXXqFMrKynDu3Dls2LChDXtE\nRG2B61hZgL2sWyVJkk31paKiAlOnTsWGDRvQs2dPs3221JcuXbrgyJEjKCsrw4QJE5Cenm6231b6\n8p///AcuLi7QaDSNfl2NrfQFAPbv34/+/fvj3LlzCAoKgpeXl9n+1vbl1KlTmDRpEhwdHS0VKhFR\nm7NqYtWSBUY7KoVCgbNnz8LV1RVFRUVwcXEB0PCCqCqVCkqlEgUFBWbbG1oo1dqqqqowdepUzJgx\nA1OmTAFgu32p5ezsjIkTJyIrK8sm+3LgwAGkpKQgNTUVly9fxq+//ooZM2bYZF8AoH///gCAu+66\nC4899hgyMzMt0heVSoWhQ4e2bWeIiCzMqlOB1y8weuXKFSQlJSEsLMyap7SYsLAwbN26FQCwdetW\nU5ISFhaGnTt34sqVKzh9+jRyc3Ph7+8PV1dX9OrVCxkZGRBCYNu2bab7tBUhBObOnQu1Wo3Fixfb\ndF9KSkpMnyyrrKzE559/Do1GY5N9WbNmDfLz83H69Gns3LkTjz76KLZt22aTfbl06RLKy8sBABcv\nXsSePXvg4+Njkb7U1NRg8uTJmD59OqZPn96m/SIi6+ssNVZW/6hLamqqGDRokBg4cKBYs2aNtU/X\nKhEREaJ///7C0dFRqFQqsWXLFvHLL7+IsWPHCk9PTxEUFCQuXLhgav/yyy+LgQMHisGDBwu9Xm/a\n/u2334qhQ4eKgQMHimeeeabN+/H1118LSZKEr6+v8PPzE35+fiItLc0m+3Ls2DGh0WiEr6+v8PHx\nMX1KxBb7cj2DwWD6VKAt9uXUqVPC19dX+Pr6iiFDhpie05boS3l5ucjMzBRCCJGfn9+2HWtGG7xU\nEtkFfipQCC4QSkQdwlNPPYXbb78df/vb3zB//nwkJia2d0gmXCCUqGW4QKiVa6yIiFqqR48epmVP\nunXr1s7REBG1DhMrIuoQ7rzzTnz99dd47rnnzJalICL7wO8KJCJqYydOnEBNTQ3UanV7h2KGU4FE\nLcOpQI5YEVEHERkZCUD+FCiAdltVnojoVjCxIqIOYceOHQDkZUPefPPNdo6GiKh1mFgRUYfw3Xff\nQZIkVFVV4bvvvmvvcIjIwjpLjRUTKyLqED7++GMAwB133IHY2Nh2joaILK2p7wms3S/XWDm1UUTW\nwcSKiDqEkSNHmq4XFBSgoKAAEydObMeIiIhuHhMrIuoQ3n//fTz00EOQJAnffPNNm39dDxGRJTCx\nIqIOwcvLC0uWLAEAnDt3DlFRUe0cERFZEmusiIja2Ny5cyFJEhQKRXuHQkQWxhorIqI29PLLL6Og\noAC9e/fGHXfc0d7hEBG1Cr83gog6hMWLFyMuLg69evXCM888097hEBG1CkesiKhD6NKlC+655x4A\nQO/evds5GiKyNNZYERG1oTvuuAM5OTl46623cOHChfYOh4gsjDVWRERtRAiBadOmoaSkBEIIzJ8/\nv71DIiJqFSZWRNTuJElCeno6nn/++fYOhYjoljCxIqJ2l5ycjOTkZHz22Wfo27cvAOCjjz5q56iI\nyJJYY2Vhfn5+OHr0aFudjog6AF9fXxw5cqTZdnq9Hvv370dMTAzefvvtNoiMiNpaZ6mxarPlFo4e\nPQohhF1cVq1a1e4xsB/siy1cWvpm6ueff8ann36Kn3/+GampqUhNTbXyKxIRkXVwKpCI2t306dNR\nUlKC8PBwnDt3rr3DISJqNSZWRNTuZs2a1d4hEJGVscaKGqXVats7BIuwl34A7AsRUUfHGitqlL38\n47OXfgDsCxERdQxMrIiIiIgspNnEas6cOVAoFPDx8Wm0TWxsLDw9PeHr64vs7GyLBkhERES2T6eL\nM9VZNbZ/5Urbr7FqNrGaPXs29Hp9o/tTU1ORl5eH3NxcvPvuu4iJibFogERERGT7dLpVTdZZ6XSr\nsHp1RRtGZB3NJlajR49Gnz59Gt2fkpKCqKgoAEBAQABKS0tRXFxsuQiJiIiIbMQt11gZjUa4ubmZ\nbqtUKhQUFNzqYYmIiIhsjkWWWxBCmN2WJMkShyUiIiI7wXWsWkipVCI/P990u6CgAEqlssG2Op3O\ndF2r1fJj5UR2xmAwwGAwtHcYRNQBdZZ1rG45sQoLC0NCQgIiIiJw8OBB9O7dGwqFosG21ydWRGR/\nbnzDFBfX+CeAbkV+fj5mzpyJ//3vf5AkCU8//TRiY2Nx/vx5/P73v8dPP/0Ed3d37Nq1C7179wYA\nrF27Flu2bMFtt92GjRs3Yvz48QCArKwszJo1C5cvX0ZoaCg2bNhglZiJqHNotsYqMjISDz74IH74\n4Qe4ublhy5Yt2LRpEzZt2gQACA0NxX333QcPDw9ER0cjMTHR6kETUefm6OiIN998E9999x0OHjyI\nv/3tb/j+++8RHx+PoKAgnDx5EmPHjkV8fDwAICcnB0lJScjJyYFer8f8+fNNJQwxMTHYvHkzcnNz\nkZub2+SnoImImtPsiNWOHTuaPUhCQoJFgiEiaglXV1e4uroCAHr06AFvb28YjUakpKRg3759AICo\nqChotVrEx8cjOTkZkZGRcHR0hLu7Ozw8PJCRkYF77rkH5eXl8Pf3BwDMnDkTu3fvRnBwcLv1jche\ndZYaqw698rrBYMDSpUsb3a/T6fDpp5+2YURE1NGcOXMG2dnZCAgIQHFxsakUQaFQmJZ+KSwshEql\nMt1HpVLBaDTW265UKmE0Gtu2A0SdBNex6gCa+3Rhe3768PpPQt74qUgiahsVFRWYOnUqNmzYgJ49\ne5rtkySJn1AmojZnkeUWLOG///0vFi5ciCtXrmDEiBF46623zBKW4cOHY9SoUTh+/Dgef/xxLFmy\nBACQlJSExMREXLx4EXq9HrfffjsmTJiAqqoq3H777fjXv/5l9oLb2HkWLlyI48ePw8HBAbt27UJR\nUZGpDmPSpElYvnw5dDodzpw5g3PnzmHNmjV45plnMGDAAPj5+WH58uVt/pgRdWZVVVWYOnUqZsyY\ngSlTpgCQR6nOnj0LV1dXFBUVwcXFBUDDn15WqVRQKpVm6+7xU81EnZelPtXcYRIrDw8PU4emTJmC\nvLw8s3ebpaWlWLJkCTw8PKDVak2rvQ8aNAgrV67E8uXL8fnnn2Py5MlISUlBt27dsH79eiQlJWHe\nvHlNnicnJwe33XYbvvrqKwDyCNScOXPw/vvvY/DgwZgwYQIiIyMhSRLuuecefPjhhzhz5gwKCwvx\n5ZdfwsGhwzyMRJ2CEAJz586FWq3G4sWLTdvDwsKwdetWLFu2DFu3bjUlXGFhYXjiiSfw7LPPwmg0\nIjc3F/7+/pAkCb169UJGRgb8/f2xbds2xMbGNnhOfqqZ6NZ09BorS32qucNkBKdOncKSJUtw6dIl\nnDp1CoWFhWb7e/ToAU9PTwCAr68vTp8+DQDQaDQAADc3N1y4cAEXL17E008/DaPRiPPnz2P69OnN\nnufEiRMYM2aMqY0kSTh79iwGDx4MQB4t+/HHHwEAI0eONLXz9fVlUkXUDvbv34/t27dj2LBhpteA\ntWvXYvny5QgPD8fmzZtNyy0AgFqtRnh4ONRqNRwcHJCYmGh645aYmIhZs2ahsrISoaGhLFwnshKu\nY9XG3nnnHTz33HMYO3Ysfve739WrW6qoqEBeXh4GDhyIY8eOwd3dvd4xhBD47LPPcN999+Ef//gH\n3njjDZSXlzd7Hm9vb+zduxdTp04FANTU1EChUODEiRMYPHgwDh8+jD/+8Y/4+uuv0aVLXVna9deJ\nqO08/PDDqKmpaXDf3r17G9y+YsUKrFixot72ESNG4Pjx4xaNj4g6rw6TWE2ePBmLFi2Cl5cXhBCQ\nJMn0EwD69OmD9evXIysrC48//ripduL66UJJknD//fdjzZo1yM7OhkKhwD333NPseSZPngy9Xo/R\no0fD0dERu3btwssvv4x58+aZaqxqj1N7PhbGEhER0Y0k0UYfaatNlFpr1KhROHTokAUjIiJru9Xn\nfUdhL/0gsra0tDRERm5EWVlavX31a6xqByeE2X4nJ6cml1pqK6193neYEavmcHSIiIjIdnWWGiub\nKRLKzMxs7xCIiIiImmQziRURERFRR2czU4FERERkuzr6OlaW0uYjVlxkj4iIqPPhdwVaSWtXMiUi\nIiLq6FhjRURERGQhrLEiIiIiq+ssNVZMrIiIiMjquI7VNXq9Hl5eXvD09MS6devq7S8pKUFwcDD8\n/PwwdOhQfPjhh9aIk4iIiKjDazKxqq6uxsKFC6HX65GTk4MdO3bg+++/N2uTkJAAjUaDI0eOwGAw\n4LnnnsPVq1etGjQRERFRR9TkVGBmZiY8PDzg7u4OAIiIiEBycjK8vb1Nbfr3749jx44BAH799Vf0\n69cPDg6cYSQiIqI6rLECYDQa4ebmZrqtUqmQkZFh1uapp57Co48+igEDBqC8vBy7du2yTqRERERk\ns1hjhZZ98fGaNWvg5+eHwsJCHDlyBAsWLEB5ebnFAiQiIiKyFU2OWCmVSuTn55tu5+fnQ6VSmbU5\ncOAA/vznPwMABg4ciHvvvRc//PADRo4cWe94tauu63Q6aLVaaLXaWwyfiDoSg8EAg8HQ3mEQEbUb\nSQghGtt59epVDB48GF988QUGDBgAf39/7Nixw6zG6tlnn4WzszNWrVqF4uJijBgxAseOHUPfvn3N\nTyRJEEKYfhKR/bOX57u99IPI2tLS0hAZuRFlZWn19tWvsaqdFRNm+52cnLB06VJrh9qs1j7vmxyx\ncnBwQEJCAiZMmIDq6mrMnTsX3t7e2LRpEwAgOjoaK1aswOzZs+Hr64uamhq88sor9ZIqIiIi6tw6\nS41Vsx/fCwkJQUhIiNm26Oho0/U777wTn3zyieUjIyIiIrIx/K5AIiIiIgvhglNERERkdVzHioiI\niMhCOkuNFacCiYiIiCyEiRURERGRhbRrYlW7YCgRERHZN50uzlRn1dj+lSttv8aqyQVCLXqiBhYI\n5aJ7RPbNXp7j9tIPImtraoHQ+swXCAVwrcbKxaYXCOVUIBEREZGFMLEiIiIishAut0BERERWx3Ws\niIiIiCyE61gRERER0U1hYkVERERkIZwKJCIiIqtjjRURERGRhbDGioiIiIhuSrOJlV6vh5eXFzw9\nPbFu3boG2xgMBmg0GgwdOhRardbSMRIRERHZhCanAqurq7Fw4ULs3bsXSqUSo0aNQlhYGLy9vU1t\nSktLsWDBAnz22WdQqVQoKSmxetBERERkW1hjBSAzMxMeHh5wd3cHAERERCA5OdkssfrnP/+JqVOn\nQqVSAQDuvPNO60VLRERENok1VgCMRiPc3NxMt1UqFYxGo1mb3NxcnD9/HoGBgRg5ciS2bdtmnUiJ\niIiIOrgmR6wkSWpqNwCgqqoKhw8fxhdffIFLly7hgQcewP333w9PT0+LBUlERERkC5pMrJRKJfLz\n80238/PzTVN+tdzc3HDnnXeiW7du6NatGx555BEcPXq0wcRKp9OZfrLIncj+GAwGGAyG9g6DiDqg\nzlJjJQkhRGM7r169isGDB+OLL77AgAED4O/vjx07dpjVWJ04cQILFy7EZ599ht9++w0BAQFISkqC\nWq02P5EkQQhh+nn9NiKyT/byHLeXfhBZW1paGiIjN6KsLK0FrWtnxeqeW3KNlQuWLl1qlfhuRmuf\n902OWDk4OCAhIQETJkxAdXU15s6dC29vb2zatAkAEB0dDS8vLwQHB2PYsGHo0qULnnrqqXpJFRER\nEVFn0OSIlUVPxBErok7HXp7j9tIPImvjiBW/0oaIiIjaQGepsWJiRURERFbHdayIiIiI6KZ0mMSq\ndikGIiIiIlvVYRKruLi49g6BiIiIrESnizPVWTW2f+VK1lgRERERNYs1VkRERER0U5hYEREREVkI\npwKJiIjI6riOFREREZGFsMaKiIiIiG4KEysiIiIiC+FUIBEREVldZ6mx4ogVEdmkOXPmQKFQwMfH\nx7Tt/PnzCAoKwqBBgzB+/HiUlpaa9q1duxaenp7w8vLCnj17TNuzsrLg4+MDT09PLFq0qE37QNSZ\n6HSrmqyz0ulWYfXqijaMyDqYWBGRTZo9ezb0er3Ztvj4eAQFBeHkyZMYO3Ys4uPjAQA5OTlISkpC\nTk4O9Ho95s+fDyEEACAmJgabN29Gbm4ucnNz6x2TiOhmMLEiIps0evRo9OnTx2xbSkoKoqKiAABR\nUVHYvXs3ACA5ORmRkZFwdHSEu7s7PDw8kJGRgaKiIpSXl8Pf3x8AMHPmTNN9iIhagzVWRGQ3iouL\noVAoAAAKhQLFxcUAgMLCQtx///2mdiqVCkajEY6OjlCpVKbtSqUSRqOxbYMm6iRYY3WNXq+Hl5cX\nPD09sW7dukbbHTp0CA4ODvj3v/9t0QCJiFpDkiRIktTeYRDRNZ2lxqrJEavq6mosXLgQe/fuhVKp\nxKhRoxAWFgZvb+967ZYtW4bg4GBT3QIRUVtTKBQ4e/YsXF1dUVRUBBcXFwDySFR+fr6pXUFBAVQq\nFZRKJQoKCsy2K5XKBo+t0+lM17VaLbRarVX6QETtw2AwwGAw3PJxmkysMjMz4eHhAXd3dwBAREQE\nkpOT6yVWb731FqZNm4ZDhw7dckBERK0VFhaGrVu3YtmyZdi6dSumTJli2v7EE0/g2WefhdFoRG5u\nLvz9/SFJEnr16oWMjAz4+/tj27ZtiI2NbfDY1ydWRGR/bnzDFBcX16rjNJlYGY1GuLm5mW6rVCpk\nZGTUa5OcnIwvv/wShw4d4tA7EbWJyMhI7Nu3DyUlJXBzc8OLL76I5cuXIzw8HJs3b4a7uzt27doF\nAFCr1QgPD4darYaDgwMSExNNr1WJiYmYNWsWKisrERoaiuDg4PbsFpHd6iw1Vk0mVi1JkhYvXoz4\n+HhIkgQhRJNTgbXv+HQ6HYfRieyQpYbSW2LHjh0Nbt+7d2+D21esWIEVK1bU2z5ixAgcP37corER\nUX2d5bsCm0ysbqxLyM/PN/sEDSAvrhcREQEAKCkpQVpaGhwdHREWFlbveDqdDnFxcU0Oqet0Og65\nE9koSw2lExHZqiY/FThy5Ejk5ubizJkzuHLlCpKSkuolTKdOncLp06dx+vRpTJs2DW+//XaDSVVL\n8YFwmGcAAA9qSURBVIWYiIiIbFWTI1YODg5ISEjAhAkTUF1djblz58Lb2xubNm0CAERHR7dJkERE\nRGTbOkuNlSTaaH2E2hqs2p/Xb2tsPxHZNnt5PttLP4isLS0tDZGRG1FWltaC1rV13HXPLbnGygVL\nly61Snw3o7XPe36lDREREZGFMLEiIiIishB+VyARERFZXWepsWJiRURERFbXWdax4lQgERERkYUw\nsSIiIiKykA6dWHEFdiIiIvug08WZ6qwa279ype3XWHXoday4dgyRbbOX57C99IPI2riOVQcfsarF\nkSsiIiKyBTaRWPH7A4mIiMgWcLkFIiIisjquY0VERERkIVzHioiIiIhuis0lVixkJyIioo7K5hIr\nFrITERHZns6yjhVrrIiIiMjqWGN1Hb1eDy8vL3h6emLdunX19v/jH/+Ar68vhg0bhoceegjHjh2z\neKBEREREHV2zI1bV1dVYuHAh9u7dC6VSiVGjRiEsLAze3t6mNvfddx+++uorODs7Q6/X4+mnn8bB\ngwetGjgRERFRR9NsYpWZmQkPDw+4u7sDACIiIpCcnGyWWD3wwAOm6wEBASgoKLB8pERERGSzOss6\nVs1OBRqNRri5uZluq1QqGI3GRttv3rwZoaGhlomuCfx0IBERke3Q6VY1WWel063C6tUVbRiRdTSb\nWEmS1FwTk/T0dGzZsqXBOixL46cDiYiIqKNpdipQqVQiPz/fdDs/Px8qlapeu2PHjuGpp56CXq9H\nnz59GjxW7SiTTqeDVqttXcRE1GEZDAYYDIb2DoOIqN1IQgjRVIOrV69i8ODB+OKLLzBgwAD4+/tj\nx44dZjVWP//8Mx599FFs374d999/f8MnkiQIIUw/r9/W3P7mthFRx2Qvz1N76QeRtaWlpSEyciPK\nytLq7atfY1U7IybM9js5OWHp0qXWDrVZrX3eNzti5eDggISEBEyYMAHV1dWYO3cuvL29sWnTJgBA\ndHQ0XnzxRVy4cAExMTEAAEdHR2RmZt50MERERGSfOss6Vi1aIDQkJAQhISFm26Kjo03X33//fbz/\n/vuWjYyIiIjIxtjcV9oQERERdVR2kVhx6QUiIqKOrbN8V2CzxesWO5EVi9dZWErUMdnLc9Ne+kFk\nbU0Vr9dnXrwO4FqNlYtNF6/bxYgVERERUUfAxIqIiIjIQlr0qUAiIiL6/+3dfUxb9RoH8G8R/tkb\nOONA1pktpbwUWOmCazQxd2iQywyNOmJgcVvcNPi6+HKXxb/cTSaFGY1b+GOaTJ2awP7bFu2ITsWR\nQEcmTBMxEU1JKGz4MjvHXizU5/6x0duOtpyynnM49PtJTkJPD+3zPD09fXp6zvnRreBYgQbEg9iJ\niIjmJ44VaEAcP5CIiIj0tKAaKyIiIiI98RgrIiIiUl26HGPFxoqIiIhUly5jBfKnQCIiIqIUWbCN\n1fQZgpFnCvKsQSIiIlLTgm2sps8QjDxTcPpvNltERETaSpexAhdsY5VIrGYL4F4uIiIitfA6Vmko\n2b1cbLqIiIgo0qyNVWdnJ4qLi2G1WtHa2hpzmZ07d8JqtcJut2NgYCDlQc4HsZotpXu7uAeMiIgo\nPSRsrEKhEF544QV0dnZicHAQ7e3t+PHHH6OW8Xg8+PnnnzE0NIT33nsPzz77rKoBz1eJ9nYlc5xX\nsg2aFvNu/puIiChZ6XKMFSSBnp4eqampCd92u93idrujlmlqapKOjo7w7aKiIjl//vyMx5p+qsin\njPW3XvMYg7K4Xn/99fC86b+VzqP0M8smxjAWSh5EavN4PJKd/W8BRMGEG9P/52Vm/kf27dundxoi\nMvf3fcI9VqOjo1i1alX4ttlsxujo6KzL+P3+hM0cGZfSPXI8G9N4UrVXk68tEaWzhI2VyWRS9CDX\nG7vk/4/Sy1xOCkjHD+lUNTXJzruVpjne/URE6cYkN3dFEbxeL/bs2YPOzk4AgNvtRkZGBnbv3h1e\n5plnnsGGDRvQ0NAAACguLsY333yD3Nzc6CcymQBEnma54cZERAtH141p2n9nfPEyIpPJtCDyIFLb\niRMn0Nh4ABcvnphx38yxAqd3wkjU/YsWLcKuXbvUDnVWc33fJxwrsLKyEkNDQxgeHkZ+fj6OHDmC\n9vb2qGVcLhfa2trQ0NAAr9eLnJycGU3VNJE9SQdIREayAZFfmEwm7r0iouvSZazAhI1VZmYm2tra\nUFNTg1AohB07dqCkpATvvvsuAKCpqQkbN26Ex+NBQUEBFi9ejA8++ECTwImIiIjmm4SNFQDU1tai\ntrY2al5TU1PU7ba2ttRGRURERGRAszZWRERERLdq5jFWse43/nWs2FgRERGR6tLlGCuOFUhERESU\nImysiIiIiFKEjRURpT0lg80T0a1Jl7EC2VjNQVdXl94hpMRCyQNgLjR3Sgabn4/m23rCeBJjPNeP\noUp0nNWePf/C3r0TGkakDjZWczDf3iBztVDyAJgLzV1fXx8KCgqwevVqZGVloaGhAceOHdM7rFnN\nt/WE8STGeJTo0juAlOBZgUSU1mINJH/69GkdI6J0NzU1hV9//XXO/3/bbbfFHQGF1MfGiojSmpqD\nxv/2229YsWKFao8/3wa8ZjyJpVM8y5bVzZj3yiuVAIC33z4DAPjrr+hlHY5LqKqqQkaGwX9ME43Y\n7XbB9ZEWOXHilCaT3W7XahMzZ729vVJTUxO+3dzcLC0tLVHLWCwW3WvJiRMnbSeLxTKnbYpJhEO2\nE1H6mpqaQlFREb788kvk5+dj/fr1aG9vR0lJid6hEZEB8adAIkpr8QabJyKaC+6xIiIiIkoR1Y8Q\nM/KF90ZGRlBVVYXS0lKUlZXhwIEDAIALFy6guroahYWFeOihhxAIBHSOVLlQKASHw4G6uusHCxo1\nl0AggPr6epSUlMBms+H06dOGzMXtdqO0tBTl5eXYvHkz/v77b8PksX37duTm5qK8vDw8L1Hsbrcb\nVqsVxcXF+Pzzz/UIeVZKtlc7d+6E1WqF3W7HwMCArvF0dXUhOzsbDocDDocDe/fuVTWeWK/5zbSs\nz2zxaF2feJ8ZN9OqRkri0bJG165dg9PpREVFBWw2G1577bWYy2m5DimJKekazfmITwWmpqbEYrGI\nz+eTYDAodrtdBgcH1XzKlDp37pwMDAyIiMilS5eksLBQBgcHZdeuXdLa2ioiIi0tLbJ79249w0zK\nW2+9JZs3b5a6ujoREcPmsnXrVjl06JCIiExOTkogEDBcLj6fT9asWSPXrl0TEZHHH39cPvzwQ8Pk\ncerUKenv75eysrLwvHix//DDD2K32yUYDIrP5xOLxSKhUEiXuONRsr367LPPpLa2VkREvF6vOJ1O\nXeP5+uuvw+9lLcR6zSNpWR8l8Whdn3ifGZG0rJGSeLSu0eXLl0Xk+nbb6XRKd3d31P1ar0NKYkq2\nRqrusTLqhfem5eXloaKiAgCwZMkSlJSUYHR0FMePH8e2bdsAANu2bcPRo0f1DFMxv98Pj8eDp556\nCnLjF2Aj5nLx4kV0d3dj+/btAK4fI5OdnW24XJYtW4asrCxcuXIFU1NTuHLlCvLz8w2Tx/3334/b\nb789al682I8dO4bGxkZkZWVh9erVKCgoQF9fn+YxJ6JkexWZn9PpRCAQwPj4uG7xAAi/l7UQ6zWP\npGV9lMQDaFufWJ8ZY2NjUctoWSMl8QDa1mjRokUAgGAwiFAohOXLl0fdr/U6pCQmILkaqdpYxbrw\n3ujoqJpPqZrh4WEMDAzA6XRifHw8fPG13Nxc1V/0VHn55Zfx5ptvRl0jxIi5+Hw+3HnnnXjyySex\nbt06PP3007h8+bLhclm+fDleffVV3H333cjPz0dOTg6qq6sNl0ekeLGPjY3BbDaHl5uP2wIl26tY\ny/j9ft3iMZlM6Onpgd1ux8aNGzE4OKhKLEppWR8l9KxP5GdGJL1qFC8erWv0zz//oKKiArm5uaiq\nqoLNZou6X4/6zBZTsjVStbFS88J7WpqYmMCmTZuwf/9+LF26NOo+k8lkiDw//fRTrFixAg6HI27n\nbZRcpqam0N/fj+eeew79/f1YvHgxWlpaopYxQi6//PIL3nnnHQwPD2NsbAwTExP45JNPopYxQh7x\nzBb7fMtLaTw3v3/UykPJ465btw4jIyP47rvv8OKLL+KRRx5RJZZkaFUfJfSqz8TEBOrr67F//34s\nWTJzUGGta5QoHq1rlJGRgbNnz8Lv9+PUqVMxh9bRuj6zxZRsjVRtrFauXImRkZHw7ZGRkahvrUYw\nOTmJTZs2YcuWLeFi5ubm4vz58wCAc+fOqXpl5VTp6enB8ePHsWbNGjQ2NuKrr77Cli1bDJmL2WyG\n2WzGPffcAwCor69Hf38/8vLyDJXLmTNncN999+GOO+5AZmYmHnvsMfT29houj0jx1qebtwV+vx8r\nV67UJcZ4lGyvtMxDSTxLly4N/4xRW1uLyclJXLhwQZV4lJhvr7Me9Zn+zHjiiSdifgBrXaPZ4tFr\nHcrOzsbDDz+MM2fORM3Xcx2KF1OyNVK1saqsrMTQ0BCGh4cRDAZx5MgRuFwuNZ8ypUQEO3bsgM1m\nw0svvRSe73K5cPjwYQDA4cOH58W3xNk0NzdjZGQEPp8PHR0deOCBB/Dxxx8bMpe8vDysWrUKP/30\nEwDg5MmTKC0tRV1dnaFyKS4uhtfrxdWrVyEiOHnyJGw2m+HyiBRvfXK5XOjo6EAwGITP58PQ0BDW\nr1+vZ6gzKNleuVwufPTRRwAAr9eLnJwc1cZkUxLP+Ph4+Nt9X18fRCTm8SFa0bI+Smhdn3ifGZG0\nrJGSeLSs0e+//x4+U/jq1av44osv4HA4opbReh1SElPSNZrjQfSKeTweKSwsFIvFIs3NzWo/XUp1\nd3eLyWQSu90uFRUVUlFRISdOnJA//vhDHnzwQbFarVJdXS1//vmn3qEmpaurK3yGg1FzOXv2rFRW\nVsratWvl0UcflUAgYMhcWltbxWazSVlZmWzdulWCwaBh8mhoaJC77rpLsrKyxGw2y/vvv58w9jfe\neEMsFosUFRVJZ2enjpHHF2t7dfDgQTl48GB4meeff14sFousXbtWvv32W13jaWtrk9LSUrHb7XLv\nvfdKb2+vqvHc/JofOnRI1/rMFo/W9Yn1meHxeHSrkZJ4tKzR999/Lw6HQ+x2u5SXl8u+fftERN/3\nmJKYkq0RLxBKRERElCIGH0KaiIiIaP5gY0VERESUImysiIiIiFKEjRURERFRirCxIiIiIkoRNlZE\nREREKcLGioiIiChF2FgRERERpcj/AJLGV389DMInAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c07ccd0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In both examples, we can clearly see that the posterior distributions of the $\\alpha$ values are very certain in regard to the value of the parameter which is very similar to the initital parameter set when generating the random power law data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we will evaluate our approach by also applying it to some examples used in Aaron Clauset's famous power law paper (http://arxiv.org/abs/0706.1062). The data can be found at http://tuvalu.santafe.edu/~aaronc/powerlaws/data.htm. \n",
      "\n",
      "We begin by using the classic Moby Dick word frequency data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import urllib\n",
      "\n",
      "data = list()\n",
      "for line in urllib.urlopen(\"http://tuvalu.santafe.edu/~aaronc/powerlaws/data/words.txt\"):\n",
      "    data.append(line.strip())\n",
      "analyze(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            14%                  ] 727 of 5000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 1293 of 5000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    35%                  ] 1766 of 5000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  40%                  ] 2002 of 5000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------52%                  ] 2621 of 5000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------62%---               ] 3134 of 5000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------77%---------         ] 3860 of 5000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------92%---------------   ] 4638 of 5000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 5000 of 5000 complete in 4.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1.77235083893\n",
        "Plotting alpha\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MrIjI6Vy/fh0REREIDQ1FUFAQXnnlFQBAeXk5oqKi0K9fP4wePRoVFRXm+yQl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\nAAAAQd4BEbdWCuZZ6sMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c2364d0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In Clauset et al. the authors find a value for $x_{min} = 7$ and $\\alpha = 1.95$. As we currently do not have a working function to also determining the best $x_{min}$ value, we will set the same $x_{min}$ value and find the appropriate $\\alpha$ value. We end up with close to the exact same $\\alpha$ of around $1.95$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "analyze(data,xmin=7)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------55%                  ] 2754 of 5000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------95%----------------  ] 4760 of 5000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 5000 of 5000 complete in 1.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1.95864984427\n",
        "Plotting alpha\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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59pWVGf9zmT373n8gd4Maa4/a9gkBfPaZMYC6kxt752cBzJwJtG9vHpjV9Xzz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\nkzANiqeQAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c028710>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we use a dataset capturing the size of acres of wildfire (this time continuous) occurring in the US between 1986 and 1996."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = list()\n",
      "for line in urllib.urlopen(\"http://tuvalu.santafe.edu/~aaronc/powerlaws/data/fires.txt\"):\n",
      "    data.append(line.strip())\n",
      "analyze(data, discrete=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 408 of 5000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 779 of 5000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         22%                  ] 1114 of 5000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       27%                  ] 1351 of 5000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     32%                  ] 1609 of 5000 complete in 2.5 sec"
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      },
      {
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       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   37%                  ] 1855 of 5000 complete in 3.0 sec"
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      {
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       "stream": "stdout",
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        "\r",
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      {
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       "stream": "stdout",
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        "\r",
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      {
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       "stream": "stdout",
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        "\r",
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
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        "\r",
        " [-----------------55%-                 ] 2778 of 5000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
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        "\r",
        " [-----------------60%--                ] 3008 of 5000 complete in 5.5 sec"
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      {
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       "stream": "stdout",
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        "\r",
        " [-----------------63%----              ] 3195 of 5000 complete in 6.0 sec"
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      },
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       "stream": "stdout",
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        "\r",
        " [-----------------67%-----             ] 3379 of 5000 complete in 6.5 sec"
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      {
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       "stream": "stdout",
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        "\r",
        " [-----------------71%-------           ] 3567 of 5000 complete in 7.0 sec"
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      },
      {
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       "stream": "stdout",
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        "\r",
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       "stream": "stdout",
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        "\r",
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      {
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       "stream": "stdout",
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        "\r",
        " [-----------------82%-----------       ] 4132 of 5000 complete in 8.5 sec"
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      },
      {
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       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------86%------------      ] 4308 of 5000 complete in 9.0 sec"
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      },
      {
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       "stream": "stdout",
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        "\r",
        " [-----------------89%--------------    ] 4484 of 5000 complete in 9.5 sec"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------93%---------------   ] 4659 of 5000 complete in 10.0 sec"
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      },
      {
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       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------96%----------------  ] 4827 of 5000 complete in 10.5 sec"
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 5000 of 5000 complete in 11.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1.49052367336\n",
        "Plotting alpha\n"
       ]
      },
      {
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       "output_type": "display_data",
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NBi+//HKb6y1ZsgShoaHQarUoKipySKBERNS2tLS0Fn1W6dY+KyJyvnab12+77Tbs27cP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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c1ef710>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, Clauset et al. find a much higher $x_{min}$ value of $6324$. Hence, we set $x_{min}$ to this value and again apply the MCMC process. The posterior distribution of $\\alpha$ again resembles the value found by Clauset et al. -- $\\alpha=2.2$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "analyze(data, discrete=False, xmin=6324.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      30%                  ] 1507 of 5000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------49%                  ] 2469 of 5000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------65%----              ] 3255 of 5000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------80%----------        ] 4014 of 5000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------98%----------------- ] 4948 of 5000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 5000 of 5000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "2.16074260841\n",
        "Plotting alpha\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FWdZMJ8rHbylANxdY/fij4W32BFaLFxvfVqEQF3jesMF0UG3Na6G/jRTgy8fa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\nrJSVrUNZ2Tq5Y5CCeCysHA4HVq1aBZPJhMbGRuzYsQOnT59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R3Nwsuru7hcFgEI2NjVI+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\nsCIiIiIKkv8H3bfHEwvO3yoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c26b910>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Whats next?\n",
      "\n",
      "First of all, I want to incorporate the process of also determining the appropriate $x_{min}$ value. If anyone has a hint or idea of how to solve this, please let me know. Furthermore, I want to analyze the goodness-of-fit and also compare the power law distribution to other candidate distributions like the Weibull distribution. This is a crucial step needed for gaining insights into the underlying processes of the data. I previously blogged about this issue at http://www.philippsinger.info/?p=247."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}