{
 "metadata": {
  "name": "simulation"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Simulation Basics -- equivalent in Python"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy.stats as s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# normal distribution\n",
      "# normal(mean, stdev, size)\n",
      "heights = np.random.normal(188, 3, 10)\n",
      "print heights"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 182.67139438  192.17804988  190.09008635  186.57278872  194.03622068\n",
        "  191.88272193  183.61975607  186.97670622  187.82621993  189.9658577 ]\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# binomial distribution\n",
      "# binomial(n, p, size)\n",
      "coinFlips = np.random.binomial(10, 0.5, 10)\n",
      "print coinFlips"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[4 6 5 6 7 3 4 6 5 6]\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# normal density\n",
      "x = np.linspace(-5, 5, num=10)\n",
      "normalDensity = s.norm.pdf(x, 0, 1)\n",
      "print np.around(normalDensity, decimals=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.    0.    0.01  0.1   0.34  0.34  0.1   0.01  0.    0.  ]\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# binomial density\n",
      "x = np.arange(0, 11, 1) # note that it's (0, 11, 1) instead of (0, 10, 1)\n",
      "binomialDensity = s.binom.pmf(x, 10, 0.5)\n",
      "print np.around(binomialDensity, decimals=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.    0.01  0.04  0.12  0.21  0.25  0.21  0.12  0.04  0.01  0.  ]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 'sample' draws a random sample with and without replacement --> numpy.random.choice in numpy 1.7\n",
      "heights = np.random.normal(188, 3, 10)\n",
      "\n",
      "# with replacement\n",
      "print 'random sampling with replacement:'\n",
      "print np.random.choice(heights, size=10, replace=True, p=None)\n",
      "\n",
      "# without replacement\n",
      "print '\\nrandom sampling without replacement'\n",
      "print np.random.choice(heights, size=10, replace=False, p=None)\n",
      "\n",
      "# sample according to a set of probability\n",
      "probs = [0.4, 0.3, 0.2, 0.1, 0, 0, 0, 0, 0, 0]\n",
      "print '\\nrandom sampling with replacement according to a set of probability:'\n",
      "print probs\n",
      "print '\\nsum of probabilities:'\n",
      "print sum(probs)\n",
      "print '\\nsampled:'\n",
      "print np.random.choice(heights, size=10, replace=True, p=probs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "random sampling with replacement:\n",
        "[ 188.51730245  187.57465384  187.7094007   187.34057076  189.44858637\n",
        "  187.57465384  188.51730245  184.62068782  187.57465384  189.4947812 ]\n",
        "\n",
        "random sampling without replacement\n",
        "[ 187.57465384  187.7094007   189.92494462  186.40851384  188.8397573\n",
        "  189.44858637  188.51730245  187.34057076  189.4947812   184.62068782]\n",
        "\n",
        "random sampling with replacement according to a set of probability:\n",
        "[0.4, 0.3, 0.2, 0.1, 0, 0, 0, 0, 0, 0]\n",
        "\n",
        "sum of probabilities:\n",
        "1.0\n",
        "\n",
        "sampled:\n",
        "[ 189.44858637  189.44858637  184.62068782  189.44858637  189.44858637\n",
        "  184.62068782  189.44858637  186.40851384  189.44858637  189.44858637]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# setting a seed\n",
      "np.random.seed(12345)\n",
      "print np.random.normal(0, 1, 5)\n",
      "print '-------------------------------------------------------------'\n",
      "\n",
      "np.random.seed(12345)\n",
      "print np.random.normal(0, 1, 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-0.20470766  0.47894334 -0.51943872 -0.5557303   1.96578057]\n",
        "-------------------------------------------------------------\n",
        "[-0.20470766  0.47894334 -0.51943872 -0.5557303   1.96578057]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}