{
 "metadata": {
  "name": "",
  "signature": "sha256:3228696d7209af74c8987a359c5aca247f9b5dd596b9f33915a81987f32077d1"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Kolmogorov Smirnov Test\n",
      "\n",
      "- **Author:** [Chris Albon](http://www.chrisalbon.com/), [@ChrisAlbon](https://twitter.com/chrisalbon)\n",
      "- **Date:** -\n",
      "- **Repo:** [Python 3 code snippets for data science](https://github.com/chrisalbon/code_py)\n",
      "- **Note:**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Import required packages\n",
      "from scipy import stats\n",
      "import scipy as sp\n",
      "import numpy as np\n",
      "import math\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create x, which is uniformly distributed\n",
      "x = np.random.uniform(size=1000)\n",
      "\n",
      "# Plot x to double check its distribution\n",
      "plt.hist(x)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fA3w2yeeq6sGxVjZ5g7TFO4C7q2ouyXOB+SQvrqpvj7m2WbSu3BxXyA9yU9TKbTZ361oz\n0A1i3Zet1wJbqmqtX9cOZ4O0xU8CH17Kd44Hzkuyv6pumUyJEzNIWzwMfL2qvgN8J8k/Ai8GWgv5\nQdriFcDvA1TVV5L8O/B84M6JVDg71p2b4xquuRN4XpJTkxwNXAys/JDeAvwqQJKXAd+sqsUx1TNN\nh2yLJM8BPgZcWlUPTaHGSTlkW1TVj1XVaVV1Gkvj8r/RYMDDYJ+RjwM/neSoJMew9EXb/ROucxIG\naYtdwLkA3Rj084F/m2iVs2HduTmWnnw9w01RSX69e/0vqmpHkvOTPAT8D/DGcdQybYO0BfBO4EeB\nD3Q92P1Vdc60ah6XAdviiDDgZ2RXkk8AXwKeBK6tquZCfsD3xbuB65Pcw1Ln9Heq6vGpFT0mSW4E\nXg0cn+Rh4CqWhu1656Y3Q0lSw/zzf5LUMENekhpmyEtSwwx5SWqYIS9JDTPkJalhhrwkNcyQl6SG\n/T979rsnMlBdqAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107b94a90>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create y, which is NOT uniformly distributed\n",
      "y = x**4\n",
      "\n",
      "# Plot y to double check its distribution\n",
      "plt.hist(y)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x107dd0450>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Run kstest on x. We want the second returned value to be \n",
      "# not statistically significant, meaning that both come from \n",
      "# the same distribution.\n",
      "stats.kstest(x, 'uniform', args=(min(x),max(x)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "(0.043685470092267642, 0.042698030459771275)"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Run kstest on y. We want the second returned value to be \n",
      "# statistically significant, meaning that likely do not both \n",
      "# come from the same distribution.\n",
      "stats.kstest(y, 'uniform', args=(min(y),max(y)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "(0.48969825580402526, 0.0)"
       ]
      }
     ],
     "prompt_number": 19
    }
   ],
   "metadata": {}
  }
 ]
}