Distributions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Examples of Data Distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Uniform Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x154a7471710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "values = np.random.uniform(-10.0, 10.0, 100000)\n",
    "plt.hist(values, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Normal / Gaussian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Visualize the probability density function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x154a56e96d8>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Qv7xqFIVlNTzz5X6n4wQ8K/4AUFJdy2Mf53DZOfGkD+3jdBwToKYNi+Oyc/ry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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x154a1fadfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.arange(-3, 3, 0.001)\n",
    "plt.plot(x, norm.pdf(x))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Generate some random numbers with a normal distribution. \"mu\" is the desired mean, \"sigma\" is the standard deviation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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leeOoa+qVZFP3z/eRJJ9OcskY1PTxJCeSPNLTd0WSnUke7R4vH7P6xjJf+tVM0AM7gVdX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x154a56ae828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "mu = 5.0\n",
    "sigma = 2.0\n",
    "values = np.random.normal(mu, sigma, 10000)\n",
    "plt.hist(values, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Exponential PDF / \"Power Law\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x154a94c7eb8>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HVJpZE/Al4O+Bn5nZp0hcHfdDGd+uvqEqIhI+2TYtIyIiaVC5i4iEkMpdRCSE\nVO4iIiGkchcRCSGVu4hICKncRURCSOUuIhJC/x8rkmEmUPJOnwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x154a56ffa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import expon\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.arange(0, 10, 0.001)\n",
    "plt.plot(x, expon.pdf(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Binomial Probability Mass Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x154a9530e80>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/RzztSY8Z+ZgBHvvo0bynuwT/XuDUvuVVvXVd2jyyQ18AqmoLsAXmj/g71PUL/uyFT11O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\nSXs9077LAmQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x154a94ed978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n, p = 10, 0.5\n",
    "x = np.arange(0, 10, 0.001)\n",
    "plt.plot(x, binom.pmf(x, n, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Poisson Probability Mass Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Example: My website gets on average 500 visits per day. What's the odds of getting 550?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x154a9597940>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DZVi+8tBWWrs1wknG1hd+upE/XTiLr/7hxWGHIqhGIRl6pbKRa+95TUlCsqK6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x154a588fcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import poisson\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "mu = 500\n",
    "x = np.arange(400, 600, 0.5)\n",
    "plt.plot(x, poisson.pmf(x, mu))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Pop Quiz!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "What's the equivalent of a probability distribution function when using discrete instead of continuous data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}