poisson 95% confidence interval with scipy

gistfile1.txt

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# asking for 95% confidence interval for a parameter lambda of\n",
      "# a poisson distribution if 3 events detected"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import poisson\n",
      "import scipy.optimize as optimize\n",
      "\n",
      "threshold_lambda = optimize.bisect(lambda l: poisson.cdf(3, mu=l) - 0.05, 1, 10)\n",
      "print(threshold_lambda)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "7.75365652793\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# there is a backbround signal of lambda = 2.5, subtract it out\n",
      "print(\"95% confidence interval : {} to {}\".format(0, threshold_lambda-2.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "95% confidence interval : 0 to 5.25365652793\n"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
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