wiso/Poisson2

## Poisson2
{
 "metadata": {
  "name": "poisson"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy as np\nimport ROOT\nimport rootnotes",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Definitions\n============"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "NEVENTS_PER_CAT = [1, 2, 4] # first category 1 event on average, second category 2 events on average, ...\nNCAT = len(NEVENTS_PER_CAT) # numbers of categories\nNTOYS = 1000000\nweights = np.random.random(NCAT) / 100. # weights for every categories\nprint \"weights: \", weights",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "weights:  [ 0.00633232  0.00998537  0.00152294]\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Toys\n====\nI generate `NTOYS`. I fill the histogram with the sum of the weights."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "nw = (NEVENTS_PER_CAT * weights).sum()\nnw2 = (NEVENTS_PER_CAT * weights ** 2).sum()\nlambda_tilde = nw ** 2 / nw2\nscale = nw2 / nw\nprint \"lambda_tilde: \", lambda_tilde\nprint \"scale: \", scale\nscaled_poisson = ROOT.TF1(\"scaled_poisson\", \"[0] * TMath::Poisson(x / [2], [1])\", 0, 100)\nscaled_poisson.SetParameter(0, NTOYS*100.)\nscaled_poisson.FixParameter(1, lambda_tilde)\nscaled_poisson.FixParameter(2, scale)\nscaled_poisson.SetLineColor(ROOT.kGreen)\n\nx = ROOT.RooRealVar(\"x\", \"x\", 0, 0.2)\nlambda_tilde_var = ROOT.RooRealVar(\"lambda_tilde\", \"lambda_tilde\", lambda_tilde)\nscale_var = ROOT.RooRealVar(\"scale\", \"scale\", scale)\nx_scaled = ROOT.RooFormulaVar(\"x_scaled\", \"x_scaled\", \"@0/@1\", ROOT.RooArgList(x, scale_var))\n#scaled_poisson_pdf = ROOT.RooGenericPdf(\"scaled_poisson_pdf\", \"scaled poisson\", \"TMath::Poisson(x / @0, @1)\",\n#                                        ROOT.RooArgList(scale_var, lambda_tilde_var))\nscaled_poisson_pdf = ROOT.RooPoisson(\"scaled_poisson_pdf\", \"scaled_poisson_pdf\", x_scaled, lambda_tilde_var)\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "lambda_tilde:  4.21810232008\nscale:  0.00767995660764\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "TClass::TClass:0: RuntimeWarning: no dictionary for class stack<RooAbsArg*,deque<RooAbsArg*> > is available\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "histo = ROOT.TH1F(\"histo\", \"histo\", 20, 0, 0.2)\n\nvars_set = ROOT.RooArgSet(x)\ndataset = ROOT.RooDataSet(\"dataset\", \"dataset\", vars_set)\nfor itoy in xrange(NTOYS):\n    n = [np.random.poisson(n) for n in NEVENTS_PER_CAT]\n    b = (n * weights).sum()\n    histo.Fill(b)\n    x.setVal(b)\n    set_to_add = ROOT.RooArgSet(x)\n    dataset.add(set_to_add)    \n\nhisto.Fit(scaled_poisson, \"\", \"goff\")\n\nprint \"expected sum of weights\", (NEVENTS_PER_CAT * weights).sum()\nprint \"average sum of weights\", histo.GetMean()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": " expected sum of weights 0.0323948427848\naverage sum of weights 0.032373085747\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "TROOT::Append:0: RuntimeWarning: Replacing existing TH1: histo (Potential memory leak).\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "canvas = rootnotes.default_canvas()\nhisto.Draw()\nscaled_poisson.Draw(\"same\")\ncanvas",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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DLVEBsCi7C1ViEwAwBt1/Y9GOAgC7IlSNy3wKALATQhXrpkUQgIUQqlgrrYAA\nLIpQBQCQgFAFAJCAUAUAkIBQNQqjp6fkbAOwBELViIykHpszDMByCFUAAAkIVQAACQhVbIFhVQDM\nTqhi3QyrAmAhhCoAgASEqvR0RQHADglVY9EtBQC7srtQlQ2au3a8oP567hoAsGvv5q7A1OpaA9LW\n1KHW5QrA7HbXUgUAMAahCgAgAaGK7dAJCMCMhKrE3Ndn4VlLAGYnVI3CPR4A9kaoAgBIQKgCAEhA\nqGJTjGkDYC5CFVuRfT93DQDYNaEqKSulAMBeCVXpefQPAHZIqGJrDKsCYBZCFduhjRCAGQlVAAAJ\nCFUAAAm8m7sCU8uyoQE3da3/aAuykOkKBGBiuwtV48Um46OXoA61HwQAs9D9l5gGEgDYJ6EKACAB\noYpt0gkIwMSEKrZGDywAsxCqAAASEKoAABIQqtIwgmeB/FAAmJJQlVT2/dw1IATDqgCYg1AFAJDA\n+kJVVVVVVT23FQBgJIsLVVmWZVlWluX1pqIosiw7HA6Hw+G6TFVV7a3Da/yxE4ZVATCZBYWqsiwH\nklBRFJfL5Xg81nV9Pp/zPD+dTu1GqcPhEEI4n8+xQHhr7WS2zbAqACa2lFBVVdXpdDoejzEPXbtc\nLnmex9apoihinIpBKoQQXz+fz0VRxALH4zG+7ehV1xwCACwnVBVFcT6fe3v9wufM1Nma53nz79Pp\nFN9keJdRaRpZJpEXgGksJVSFX0aijtjg1CkQv2zaotoZq3G5XBLVjvURcwGY0oJC1aMGQhgAwMRW\nHKqigVFTvW1X2bNGPAYAYP3ezV2BVw20V/X2/dW1LqHdyUKmKxCAsa2jpao3OZnkkzfJUgBMZk2h\nqpOiOqPXe9ulensA0/JwGQAQ1hWqOvMjxJmr4r+vZ6WaeEoFLSIAsHPZQsYYtdfsO51OeZ4303g2\niSq+HnNSM39601IVx5LHuUPjVKJ5nncat7Is/fHGlqoYqrLsQ11/lfb9udOtk980JQq+ABMb47a7\nZEsZqB5jUPPl5XKJ3XlN2IpZ6nQ6NbOotxNVCKGu66Iomq3XiYp9qkOtixaACewrQmqp2rCBk9/+\nGQEwmb21VK1jTBW8TnsVAKMSql7iPr0K2qgAmIBQlYB7NgAgVAEAJCBUsSO6awEYj1DFLuiiBWBs\nQhUAQAJC1fP0JQEADaHqVfqV1kUUBmAkS1mmZjJxicBbdjXx695YrwaAUeOCmaUAAA7vSURBVO0u\nVIlNAMAYdP8BACQgVD1JR9J6+dkBMAah6iVGqa+LnxcA4xGqAAASEKoAABIQqtgjw6oASE6oeoZb\n8noZVgXASISq57k9AwANoQoAIAGhip3ShwtAWkIVu6PfFoAx7G7tPzYsyz7cW7R+sHzcqf7qwRoB\nsCNC1cN0Gy3TQ4knC1+HEEL99f2tVo8mMAD2Rvffk3QhrZofHwDJCVUAAAkIVeyazlwAUtndmKos\nG7qJ1rVeob2oQy1RAZDQ7kLVi7HJbRgA6KX77xmGOW+JoAxAEkIV+yUcA5CQUAUAkIBQBQCQgFAF\nhlUBkIBQ9QC33u0xrAqAVISqh7kNAwDXhCoIQTMkAC8Tqtg7TY8AJCFUAQAkIFTdS/fQ5vkRA/AK\noeoxuoo2yY8VgNcJVQAACQhV8C96AAF4mlAFIegBBOBl7+auwNSybKgpoq7dWQGAZ+wuVD0Xm/QK\n7UcWMq1WADxB998D3Gu3zc8XgFcIVQAACQhV0KW3F4AnCFXwL3oAAXiaUAUAkIBQ9TadQTvkhw7A\no4Sqe+kY2gk/aACeI1QBACQgVAEAJCBUQT/DqgB4iFD1BnfWHTKsCoAnCFV3cZcFAIYJVXCTdkoA\n7idUQQ9tkwA8SqgCAEhAqIIhegABuNO7uSswtSwbukfW9S86fdxQ96wOtQ8AAPfbXajqxKa7djG8\nBgB4i+4/eIP2KgDusbuWqiz78EDp+vFd2BA9gADcL3uiO2y9suyx4403VN1/e9Z8BrLsQ11/NXd1\nANbk0dvu2un+g7dprwLgTULVTe6jBO2UANxNqHqDeyoAcI99dXY+1LlrQBVR02bpwwDwEGOqgF+Q\npQC4x9ZCVVVVVVXNXQu2yTA7AAasI1SVZZn1aZcpiiLLssPhcDgcsiwry/KV7+j2SZvGKgDetKbJ\nP4/HY1EUvZuKorhcLsfjsSzLqqrKsjydTkVR3Cp/J7dSAOBO6xhBFjPTQFWzLMvzvN3xF9uxugsk\n3z1izih1OgxXB3iUgerrE3v6Ov19eZ7PUhk2K/t+7hoAsGgrC1XVZ50XQwidnr74pUHrAMA01jGm\n6nK5hM89eo3z+TwwZKooitPp9Ny3M0qdAVnI9AACcG1NLVXH47Gu67quz+dzCOFwOLzZEHVdoPcp\nwv6HCrPQ8yI7JksBMGAdLVWdYW5FUZzP58PhEJ/1G9jxuinrnhFz/xylvqexdQDAi9bUUtXWTku9\nnYBGUzEeHcQAXFtrqGrrHZPeO3odXqQHEIBb1hGqsizrxKM4gUJ8Mf5vZ0qFy+Xy3KwKGiG4h88J\nAB3rCFV5nl8ul6Io4nwKccL00ApSx+OxXSCOK39lpRoNEtziswFAr9VMddoEqagzf/p1gd4JF+6Z\n2tVc6vTKsg91/dU//212dYA77G1G9Z0drVDFs9qhKvicANxhb6FqHd1/kzFQhof4wADQEKp6aH7g\nTT4kAHQIVfASjVUAREIVPEljFQBtQhW8SmMVAEGoanNr5FEaqwBoCFVdbpM8QSIHQKiCl0jhAERC\nFaShsQpg597NXYGpxWUB+2lx4Cl1qCUqAHYXqm7Nl++myOuykOkNBNgt3X+/4I7Ic3xyABCqICVN\nngC7JVRBGhqrAHZOqApB6wJJ+TgB7JNQ9S9aGniRjxDAnglVkJ7GKoAdEqrc/0hJYxXAbu1unqpb\n3At5U5Z9uKtcHUIM69n3D71/XX/1eKUAWIrs1mSYm5RlPccbW6qEKhJ64kOVZR+EKmBjem+7G6b7\nD8aiZxlgV/Yeqtz2GIOGT4Ad2nuoitwCGYnUDrAfQhWMQlIH2JtdhyqtCEzAxwxgJ3YdqiItCozE\nRwtgV4QqGJ3GKoA92N3kn1n2+fZWX70Swq6m02ACdaglKoCd2F2oamLTv6ZnlKMYXxYyHzWAbdP9\nB+OSpQB2QqiCiegHBNi2nYYqtzem1DRW+eABbNhOQ1WkX4bJyFUAm7frUAVTEuIBtm2PoUpTAfPy\nCQTYpD2GqkizAdPTCQiwYfsNVTALuQpgq/YYqupQa6ZiRj5+AJu0x1AFC6GxCmBLhCqYgU5AgO0R\nqmAechXAxghVMBu5CmBLsrre0ZjZLNvX8bIKTaIygB3YmL3ddrVUwcxkKYBteDd3BaaWZUP9LLsK\n1CxNFjIBC2C9dheqxCYWqA517ASUqwDWS/cfLEP2/T//36B1gHUSqmApPAwIsGpCFSyIXAWwXkIV\nLItcBbBSQhUsjlwFsEZCFSyRXAWwOkIVLJRcBbAuQhUsl1wFsCJCFSyaXAWwFkIVLF07V4lWAIsl\nVMEKtNeukasAlinb1Vp4Wbav42VFsuzDXeXqrz/v8P2j36Kuv3p0F4BX7O22u7Oj3dlPl01qWqoe\nWno5yz4IVcDE9nbb1f0HK2OIFcAyCVWwPoZYASyQUAWrVIdakxXAorybuwJTy7Khe8+uun7ZgDrU\nTZzKQvbQKCsA0tpdqBKb2JgYpGK0iv8rWgHMQvcfbEFnlJXeQIDpCVWwEe1RVkG0ApjcviaQWPuE\nGauu/6orH9ZW/06cqkO9rvpfW3X9V135oP6zWnXlw/rr/ygtVbBB161WoTb5AsC4djdQHfajPYY9\nem42dgDuoaUKNu6frVa/bKUy4gogOS1VsBftyULb/9BqBZCEUAW70+kWbDdZCVgAT9vasPyqqkII\nRVH0bn30MQTlE5ZfVGX2WT6E73s21F8P7ta3S7+vl3O8Czz5yq+l/KIqs8Pya7edo62q6nA4NF/m\neR4DVtvSPj27Kr+oyijfX+b2KKs3W7CWUP9lVkb5dZVfVGV2WH7tNjJQvUlU5/O5ruvj8Xi5XG61\nVwG94pD2gYHtzX8zVRBg0TYypqosy9Ba1y9+eTqdqqoSreA51wPbG3IVwLWNtFRdLpc8z9uvxFx1\n3QMIPKrdgnWzH7Dutmb1/jdtxQEmtZGWqnBjcLpQBcld56r709K/SprhHdicLYSqgeR0uVwmrAjs\n1J1rC76Uoh4KYY8mNuWVX2Zl1lx+n/OzbCFUPSTLHvu1rnzC8ouqjPKzl3/AHn85w7qN+AthwfYV\nqnb1YCcAzGaX99stDFSPo6l6OwE7o9cBAEayhVDVa3hqdQCAtDYy1WlRFJfLpX0s168AAIxnIy1V\nsV0qy7KqqqqqKsvyeuaquGmW6g14tFZvlp/yGJNXfmJjnPxVn//Zf0CzV+B+yas68YGv6FT3GuP8\nT3ZCVl35JBWYvcIjqrfifD63jyvP83s2zejRWh2Px+HynRB5PB7HqXhdj1D5RjyKsX9GyevfKTDq\nya9T17/zbhPU/9oTF2mzS1ycajLJqzrllVuPeaqXefHWb9V/yos3beXXeOXefy9Yqe2Eqls6n8j4\nE539B/lorWL5PM9vlW9fUWPfbJJX/vqdR/0BJa9/u8D5fI63lvHu9CN9eJoKx/pP+dv5iYu0/at5\nylCVvKpTXrnX3yLhqV7mxVu/Vf8pL96RPjwrunKbAu3yYUONO/UeQlX8nLVfiT/Iif+67Xi0Vtef\nvPY7xH0719J4v93SVr5TcoI/dpPXv7fAeB+wVX94ej16RPFX+fl8nv5aTlvV6U/+eKd6mRfvm/Wf\n8uJd+4fn2nj3gvXa1MH06v2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       "prompt_number": 6,
       "text": "<ROOT.TCanvas object (\"icanvas\") at 0x4d661d0>"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "canvas = rootnotes.default_canvas()\nframe = x.frame(20)\ndataset.plotOn(frame)\nscaled_poisson_pdf.plotOn(frame)\nframe.Draw()\ncanvas",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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IhCoAgAiEKgCACIQqAIAIhCoAgAiEKgCACIQqAIAIhCoAgAiEKgCACIQqAIAI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\n2gi+TpVvVGWUr6L82rbNu6d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       "prompt_number": 7,
       "text": "<ROOT.TCanvas object (\"icanvas\") at 0x4d661d0>"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}