PoissonDistribution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Poisson Distribution\n",
    "\n",
    "probability density function: \n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\lambda^k e^{-\\lambda}}{k!}\n",
    "\\end{equation}\n",
    "\n",
    "mean:\n",
    "\\begin{equation}\n",
    "\\lambda\n",
    "\\end{equation}\n",
    "\n",
    "variance:\n",
    "\\begin{equation}\n",
    "\\lambda\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discrete pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 16 artists>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hhr4kNcTQl6SGGPqS1BBDX5IaYuhLUkMMfUlqiKEvSQ0x9CWpIYa+JDXE0Jekhhj6ktQQ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\ndGdWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1127c9320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = range(16)\n",
    "lambda1 = 1.5\n",
    "\n",
    "plt.bar(a, stats.poisson.pmf(a, lambda1), color=\"#348ABD\",\n",
    "        label=\"$\\lambda = %.1f$\" % lambda1, alpha=0.60,\n",
    "        edgecolor=\"#348ABD\", lw=\"3\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Continuous pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x112752e48>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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09vG3P9rPxa/CV3/9ZlbXVwZak4hIJjPD3W0yrxm3W8bd48CDwGbgdWCTu+82swfM7COp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\nu4hIAVK4i4gUIIW7iEgBUriLiBSg/w8ReQZ4gAYWLgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11263d748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.linspace(0, 16, 100)\n",
    "lambda1 = 0.5\n",
    "plt.plot(a, stats.expon.pdf(a, scale=1/lambda1), lw=3,\n",
    "             color=\"#348ABD\", label=\"$\\lambda = %.1f$\" % lambda1)\n",
    "plt.fill_between(a, stats.expon.pdf(a, scale=1/lambda1), color=\"#348ABD\", alpha=.33)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def poisson(lamb, k):\n",
    "    return (lamb**k * math.e**(-1*k)) / math.factorial(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02800522595692347"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson(1.5, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x113ce79e8>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2QF4wzPiBVB/33xu3+ViD69wLHFwvvwz4AVWQA6xp2McPgQOoAmIzMLsePwhY17Dm3cA/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\nIS5JBTPEJalghrgkFcwQl6SC/T+HcqrQCNdRMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1139b2588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = range(16)\n",
    "prob = [poisson(1.5, i) for i in x]\n",
    "\n",
    "pd.Series(prob, index=x).plot(kind='bar', lw=3,\n",
    "             color=\"#348ABD\", alpha=0.60,\n",
    "        edgecolor=\"#348ABD\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": 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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}