06_SimpleStockStatistics.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Simple Stock Statistics"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "library(quantmod)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message:\n",
            "\"package 'quantmod' was built under R version 3.5.3\"Loading required package: xts\n",
            "Warning message:\n",
            "\"package 'xts' was built under R version 3.5.3\"Loading required package: zoo\n",
            "Warning message:\n",
            "\"package 'zoo' was built under R version 3.5.3\"\n",
            "Attaching package: 'zoo'\n",
            "\n",
            "The following objects are masked from 'package:base':\n",
            "\n",
            "    as.Date, as.Date.numeric\n",
            "\n",
            "Loading required package: TTR\n",
            "Warning message:\n",
            "\"package 'TTR' was built under R version 3.5.3\"Version 0.4-0 included new data defaults. See ?getSymbols.\n"
          ]
        }
      ],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "getSymbols('AAPL', src = 'yahoo', from = as.Date('2016-01-01'), to = as.Date('2019-01-01'))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "'getSymbols' currently uses auto.assign=TRUE by default, but will\n",
            "use auto.assign=FALSE in 0.5-0. You will still be able to use\n",
            "'loadSymbols' to automatically load data. getOption(\"getSymbols.env\")\n",
            "and getOption(\"getSymbols.auto.assign\") will still be checked for\n",
            "alternate defaults.\n",
            "\n",
            "This message is shown once per session and may be disabled by setting \n",
            "options(\"getSymbols.warning4.0\"=FALSE). See ?getSymbols for details.\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "'AAPL'"
            ],
            "text/markdown": [
              "'AAPL'"
            ],
            "text/latex": [
              "'AAPL'"
            ],
            "text/plain": [
              "[1] \"AAPL\""
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 2,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "head(AAPL)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "           AAPL.Open AAPL.High AAPL.Low AAPL.Close AAPL.Volume AAPL.Adjusted\n",
              "2016-01-04    102.61    105.37   102.00     105.35    67649400      99.11741\n",
              "2016-01-05    105.75    105.85   102.41     102.71    55791000      96.63358\n",
              "2016-01-06    100.56    102.37    99.87     100.70    68457400      94.74249\n",
              "2016-01-07     98.68    100.13    96.43      96.45    81094400      90.74394\n",
              "2016-01-08     98.55     99.11    96.76      96.96    70798000      91.22377\n",
              "2016-01-11     98.97     99.06    97.34      98.53    49739400      92.70087"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 3,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "AD <- AAPL$AAPL.Adjusted"
      ],
      "outputs": [],
      "execution_count": 4,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Average\n",
        "mean(AD)\n",
        "\n",
        "# Find mean dropping NA values.\n",
        "mean(AD,na.rm = TRUE)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "143.945670116711"
            ],
            "text/markdown": [
              "143.945670116711"
            ],
            "text/latex": [
              "143.945670116711"
            ],
            "text/plain": [
              "[1] 143.9457"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "143.945670116711"
            ],
            "text/markdown": [
              "143.945670116711"
            ],
            "text/latex": [
              "143.945670116711"
            ],
            "text/plain": [
              "[1] 143.9457"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 5,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "median(AD, na.rm = FALSE)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "147.849899"
            ],
            "text/markdown": [
              "147.849899"
            ],
            "text/latex": [
              "147.849899"
            ],
            "text/plain": [
              "[1] 147.8499"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 6,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create the function.\n",
        "mode <- function(x) {\n",
        "   mode_x <- unique(x)\n",
        "   mode_x[which.max(tabulate(match(x, mode_x)))]\n",
        "}"
      ],
      "outputs": [],
      "execution_count": 7,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mode(AD)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "100.24173"
            ],
            "text/markdown": [
              "100.24173"
            ],
            "text/latex": [
              "100.24173"
            ],
            "text/plain": [
              "[1] 100.2417"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 8,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Standard Deviation\n",
        "sd(AD)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "38.6134108841945"
            ],
            "text/markdown": [
              "38.6134108841945"
            ],
            "text/latex": [
              "38.6134108841945"
            ],
            "text/plain": [
              "[1] 38.61341"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 9,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Variance\n",
        "var(AD)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table>\n",
              "<caption>A matrix: 1 × 1 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>AAPL.Adjusted</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>AAPL.Adjusted</th><td>1490.996</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": [
              "\n",
              "A matrix: 1 × 1 of type dbl\n",
              "\n",
              "| <!--/--> | AAPL.Adjusted |\n",
              "|---|---|\n",
              "| AAPL.Adjusted | 1490.996 |\n",
              "\n"
            ],
            "text/latex": [
              "A matrix: 1 × 1 of type dbl\n",
              "\\begin{tabular}{r|l}\n",
              "  & AAPL.Adjusted\\\\\n",
              "\\hline\n",
              "\tAAPL.Adjusted & 1490.996\\\\\n",
              "\\end{tabular}\n"
            ],
            "text/plain": [
              "              AAPL.Adjusted\n",
              "AAPL.Adjusted 1490.996     "
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "min(AD)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "85.976913"
            ],
            "text/markdown": [
              "85.976913"
            ],
            "text/latex": [
              "85.976913"
            ],
            "text/plain": [
              "[1] 85.97691"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "max(AD)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "229.39209"
            ],
            "text/markdown": [
              "229.39209"
            ],
            "text/latex": [
              "229.39209"
            ],
            "text/plain": [
              "[1] 229.3921"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 12,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Range\n",
        "max(AD) - min(AD)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "143.415177"
            ],
            "text/markdown": [
              "143.415177"
            ],
            "text/latex": [
              "143.415177"
            ],
            "text/plain": [
              "[1] 143.4152"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 13,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Interquartile Range\n",
        "IQR(AD)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "64.8796405"
            ],
            "text/markdown": [
              "64.8796405"
            ],
            "text/latex": [
              "64.8796405"
            ],
            "text/plain": [
              "[1] 64.87964"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 14,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Percentile\n",
        "quantile(AD, c(.10, .25, .50, .75, .99)) "
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<dl class=dl-horizontal>\n",
              "\t<dt>10%</dt>\n",
              "\t\t<dd>93.1774983</dd>\n",
              "\t<dt>25%</dt>\n",
              "\t\t<dd>106.07757775</dd>\n",
              "\t<dt>50%</dt>\n",
              "\t\t<dd>147.849899</dd>\n",
              "\t<dt>75%</dt>\n",
              "\t\t<dd>170.95721825</dd>\n",
              "\t<dt>99%</dt>\n",
              "\t\t<dd>224.01110907</dd>\n",
              "</dl>\n"
            ],
            "text/markdown": [
              "10%\n",
              ":   93.177498325%\n",
              ":   106.0775777550%\n",
              ":   147.84989975%\n",
              ":   170.9572182599%\n",
              ":   224.01110907\n",
              "\n"
            ],
            "text/latex": [
              "\\begin{description*}\n",
              "\\item[10\\textbackslash{}\\%] 93.1774983\n",
              "\\item[25\\textbackslash{}\\%] 106.07757775\n",
              "\\item[50\\textbackslash{}\\%] 147.849899\n",
              "\\item[75\\textbackslash{}\\%] 170.95721825\n",
              "\\item[99\\textbackslash{}\\%] 224.01110907\n",
              "\\end{description*}\n"
            ],
            "text/plain": [
              "     10%      25%      50%      75%      99% \n",
              " 93.1775 106.0776 147.8499 170.9572 224.0111 "
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 15,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "ADm <- mean(AD)\n",
        "ADsd <- sd(AD)"
      ],
      "outputs": [],
      "execution_count": 16,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# probability distribution \n",
        "dnorm(AD, ADm, ADsd)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "           AAPL.Adjusted\n",
              "2016-01-04  0.0052662261\n",
              "2016-01-05  0.0048771762\n",
              "2016-01-06  0.0045876093\n",
              "2016-01-07  0.0039990010\n",
              "2016-01-08  0.0040677443\n",
              "2016-01-11  0.0042827160\n",
              "2016-01-12  0.0044826810\n",
              "2016-01-13  0.0041261270\n",
              "2016-01-14  0.0044207502\n",
              "2016-01-15  0.0040907800\n",
              "2016-01-19  0.0040272398\n",
              "2016-01-20  0.0040447690\n",
              "2016-01-21  0.0039788860\n",
              "2016-01-22  0.0046905998\n",
              "2016-01-25  0.0044095318\n",
              "2016-01-26  0.0044869180\n",
              "2016-01-27  0.0036023931\n",
              "2016-01-28  0.0036882913\n",
              "2016-01-29  0.0041193143\n",
              "2016-02-01  0.0039963169\n",
              "2016-02-02  0.0037387712\n",
              "2016-02-03  0.0039855842\n",
              "2016-02-04  0.0040899878\n",
              "2016-02-05  0.0037452918\n",
              "2016-02-08  0.0038758159\n",
              "2016-02-09  0.0038731557\n",
              "2016-02-10  0.0037780411\n",
              "2016-02-11  0.0037035851\n",
              "2016-02-12  0.0037413722\n",
              "2016-02-16  0.0040954485\n",
              "2016-02-17  0.0042996868\n",
              "2016-02-18  0.0040437336\n",
              "2016-02-19  0.0040139331\n",
              "2016-02-22  0.0041282635\n",
              "2016-02-23  0.0038333812\n",
              "2016-02-24  0.0040220509\n",
              "2016-02-25  0.0041118404\n",
              "2016-02-26  0.0041323734\n",
              "2016-02-29  0.0041022728\n",
              "2016-03-01  0.0046412164\n",
              "2016-03-02  0.0046729005\n",
              "2016-03-03  0.0047815095\n",
              "2016-03-04  0.0050027653\n",
              "2016-03-07  0.0048354161\n",
              "2016-03-08  0.0047133420\n",
              "2016-03-09  0.0047263708\n",
              "2016-03-10  0.0047336103\n",
              "2016-03-11  0.0048924570\n",
              "2016-03-14  0.0049306102\n",
              "2016-03-15  0.0052360789\n",
              "2016-03-16  0.0054449791\n",
              "2016-03-17  0.0054193262\n",
              "2016-03-18  0.0054374281\n",
              "2016-03-21  0.0054359225\n",
              "2016-03-22  0.0055584576\n",
              "2016-03-23  0.0054691456\n",
              "2016-03-24  0.0053997261\n",
              "2016-03-28  0.0053275095\n",
              "2016-03-29  0.0057043571\n",
              "2016-03-30  0.0059916554\n",
              "2016-03-31  0.0059043784\n",
              "2016-04-01  0.0060575701\n",
              "2016-04-04  0.0062309685\n",
              "2016-04-05  0.0060299689\n",
              "2016-04-06  0.0062064049\n",
              "2016-04-07  0.0058355672\n",
              "2016-04-08  0.0058539068\n",
              "2016-04-11  0.0059089633\n",
              "2016-04-12  0.0061266007\n",
              "2016-04-13  0.0063721924\n",
              "2016-04-14  0.0063813965\n",
              "2016-04-15  0.0060361055\n",
              "2016-04-18  0.0056739068\n",
              "2016-04-19  0.0055872791\n",
              "2016-04-20  0.0056206865\n",
              "2016-04-21  0.0054449791\n",
              "2016-04-22  0.0054012345\n",
              "2016-04-25  0.0053109931\n",
              "2016-04-26  0.0052017099\n",
              "2016-04-27  0.0042579309\n",
              "2016-04-28  0.0038519199\n",
              "2016-04-29  0.0037087861\n",
              "2016-05-02  0.0036957918\n",
              "2016-05-03  0.0038984504\n",
              "2016-05-04  0.0037675468\n",
              "2016-05-05  0.0037175932\n",
              "2016-05-06  0.0036497917\n",
              "2016-05-09  0.0036588826\n",
              "2016-05-10  0.0037412111\n",
              "2016-05-11  0.0036225936\n",
              "2016-05-12  0.0033478782\n",
              "2016-05-13  0.0033702168\n",
              "2016-05-16  0.0038019200\n",
              "2016-05-17  0.0037504181\n",
              "2016-05-18  0.0038925485\n",
              "2016-05-19  0.0038444345\n",
              "2016-05-20  0.0039815081\n",
              "2016-05-23  0.0041470642\n",
              "2016-05-24  0.0043522728\n",
              "2016-05-25  0.0045976426\n",
              "2016-05-26  0.0047120925\n",
              "2016-05-27  0.0047033596\n",
              "2016-05-31  0.0046322970\n",
              "2016-06-01  0.0044315621\n",
              "2016-06-02  0.0043269175\n",
              "2016-06-03  0.0043550967\n",
              "2016-06-06  0.0044557485\n",
              "2016-06-07  0.0045128675\n",
              "2016-06-08  0.0044999890\n",
              "2016-06-09  0.0046019681\n",
              "2016-06-10  0.0044842721\n",
              "2016-06-13  0.0042735902\n",
              "2016-06-14  0.0042903980\n",
              "2016-06-15  0.0042456402\n",
              "2016-06-16  0.0043030249\n",
              "2016-06-17  0.0039964290\n",
              "2016-06-20  0.0039652618\n",
              "2016-06-21  0.0040755326\n",
              "2016-06-22  0.0040263497\n",
              "2016-06-23  0.0041016053\n",
              "2016-06-24  0.0037385860\n",
              "2016-06-27  0.0035621047\n",
              "2016-06-28  0.0037635912\n",
              "2016-06-29  0.0038711309\n",
              "2016-06-30  0.0040331642\n",
              "2016-07-01  0.0040727937\n",
              "2016-07-05  0.0039503977\n",
              "2016-07-06  0.0040236241\n",
              "2016-07-07  0.0040796459\n",
              "2016-07-08  0.0041816549\n",
              "2016-07-11  0.0042233343\n",
              "2016-07-12  0.0042847926\n",
              "2016-07-13  0.0042080314\n",
              "2016-07-14  0.0044785612\n",
              "2016-07-15  0.0044771357\n",
              "2016-07-18  0.0046279619\n",
              "2016-07-19  0.0046337462\n",
              "2016-07-20  0.0046467677\n",
              "2016-07-21  0.0045702757\n",
              "2016-07-22  0.0044600231\n",
              "2016-07-25  0.0042735902\n",
              "2016-07-26  0.0041802693\n",
              "2016-07-27  0.0050866414\n",
              "2016-07-28  0.0052952759\n",
              "2016-07-29  0.0052756686\n",
              "2016-08-01  0.0055547697\n",
              "2016-08-02  0.0053164160\n",
              "2016-08-03  0.0055151426\n",
              "2016-08-04  0.0056148541\n",
              "2016-08-05  0.0058631064\n",
              "2016-08-08  0.0060009196\n",
              "2016-08-09  0.0060691497\n",
              "2016-08-10  0.0059435893\n",
              "2016-08-11  0.0059327463\n",
              "2016-08-12  0.0059714726\n",
              "2016-08-15  0.0061731368\n",
              "2016-08-16  0.0061576107\n",
              "2016-08-17  0.0061327750\n",
              "2016-08-18  0.0061110482\n",
              "2016-08-19  0.0061545063\n",
              "2016-08-22  0.0060226237\n",
              "2016-08-23  0.0060753569\n",
              "2016-08-24  0.0059482351\n",
              "2016-08-25  0.0058770253\n",
              "2016-08-26  0.0057796633\n",
              "2016-08-29  0.0057611431\n",
              "2016-08-30  0.0056348370\n",
              "2016-08-31  0.0056502128\n",
              "2016-09-01  0.0057472615\n",
              "2016-09-02  0.0059017831\n",
              "2016-09-06  0.0058971408\n",
              "2016-09-07  0.0059993684\n",
              "2016-09-08  0.0055611175\n",
              "2016-09-09  0.0051972301\n",
              "2016-09-12  0.0055488512\n",
              "2016-09-13  0.0059358430\n",
              "2016-09-14  0.0065285821\n",
              "2016-09-15  0.0071134044\n",
              "2016-09-16  0.0070141905\n",
              "2016-09-19  0.0068084159\n",
              "2016-09-20  0.0068068727\n",
              "2016-09-21  0.0068037923\n",
              "2016-09-22  0.0069682536\n",
              "2016-09-23  0.0066741206\n",
              "2016-09-26  0.0067003963\n",
              "2016-09-27  0.0067328342\n",
              "2016-09-28  0.0068653799\n",
              "2016-09-29  0.0065921079\n",
              "2016-09-30  0.0067266584\n",
              "2016-10-03  0.0066447340\n",
              "2016-10-04  0.0067189349\n",
              "2016-10-05  0.0067266584\n",
              "2016-10-06  0.0068561483\n",
              "2016-10-07  0.0068822964\n",
              "2016-10-10  0.0071863793\n",
              "2016-10-11  0.0072242771\n",
              "2016-10-12  0.0073810429\n",
              "2016-10-13  0.0073269466\n",
              "2016-10-14  0.0074244810\n",
              "2016-10-17  0.0074125137\n",
              "2016-10-18  0.0074005342\n",
              "2016-10-19  0.0073480094\n",
              "2016-10-20  0.0073389837\n",
              "2016-10-21  0.0072696467\n",
              "2016-10-24  0.0074274741\n",
              "2016-10-25  0.0075169055\n",
              "2016-10-26  0.0071164509\n",
              "2016-10-27  0.0069467908\n",
              "2016-10-28  0.0068299819\n",
              "2016-10-31  0.0068022514\n",
              "2016-11-01  0.0064851655\n",
              "2016-11-02  0.0065006739\n",
              "2016-11-03  0.0063150443\n",
              "2016-11-04  0.0061605305\n",
              "2016-11-07  0.0064055516\n",
              "2016-11-08  0.0065069100\n",
              "2016-11-09  0.0064788509\n",
              "2016-11-10  0.0059967953\n",
              "2016-11-11  0.0060965689\n",
              "2016-11-14  0.0056737177\n",
              "2016-11-15  0.0058909408\n",
              "2016-11-16  0.0063400143\n",
              "2016-11-17  0.0063337699\n",
              "2016-11-18  0.0063509394\n",
              "2016-11-21  0.0066112520\n",
              "2016-11-22  0.0066221426\n",
              "2016-11-23  0.0065333985\n",
              "2016-11-25  0.0066205865\n",
              "2016-11-28  0.0065863499\n",
              "2016-11-29  0.0065692222\n",
              "2016-11-30  0.0064227090\n",
              "2016-12-01  0.0062619753\n",
              "2016-12-02  0.0063259678\n",
              "2016-12-05  0.0062026660\n",
              "2016-12-06  0.0063337699\n",
              "2016-12-07  0.0065022318\n",
              "2016-12-08  0.0066718991\n",
              "2016-12-09  0.0069552304\n",
              "2016-12-12  0.0068548712\n",
              "2016-12-13  0.0071455798\n",
              "2016-12-14  0.0071455798\n",
              "2016-12-15  0.0072416270\n",
              "2016-12-16  0.0072644252\n",
              "2016-12-19  0.0073658645\n",
              "2016-12-20  0.0074125769\n",
              "2016-12-21  0.0074291194\n",
              "2016-12-22  0.0073129523\n",
              "2016-12-23  0.0073477422\n",
              "2016-12-27  0.0074591458\n",
              "2016-12-28  0.0073839644\n",
              "2016-12-29  0.0073794412\n",
              "2016-12-30  0.0072416270\n",
              "2017-01-03  0.0072917392\n",
              "2017-01-04  0.0072720131\n",
              "2017-01-05  0.0073613347\n",
              "2017-01-06  0.0075562742\n",
              "2017-01-09  0.0077159864\n",
              "2017-01-10  0.0077335936\n",
              "2017-01-11  0.0078270015\n",
              "2017-01-12  0.0077540995\n",
              "2017-01-13  0.0077233264\n",
              "2017-01-17  0.0078632523\n",
              "2017-01-18  0.0078618023\n",
              "2017-01-19  0.0078313589\n",
              "2017-01-20  0.0078632523\n",
              "2017-01-23  0.0078748222\n",
              "2017-01-24  0.0078589094\n",
              "2017-01-25  0.0081311799\n",
              "2017-01-26  0.0081395860\n",
              "2017-01-27  0.0081409853\n",
              "2017-01-30  0.0080960533\n",
              "2017-01-31  0.0080565228\n",
              "2017-02-01  0.0090204793\n",
              "2017-02-02  0.0089946288\n",
              "2017-02-03  0.0090588858\n",
              "2017-02-06  0.0091957935\n",
              "2017-02-07  0.0093294469\n",
              "2017-02-08  0.0093823808\n",
              "2017-02-09  0.0094781122\n",
              "2017-02-10  0.0094483536\n",
              "2017-02-13  0.0095619007\n",
              "2017-02-14  0.0097170380\n",
              "2017-02-15  0.0097581119\n",
              "2017-02-16  0.0097448415\n",
              "2017-02-17  0.0097753187\n",
              "2017-02-21  0.0098524224\n",
              "2017-02-22  0.0098830982\n",
              "2017-02-23  0.0098394287\n",
              "2017-02-24  0.0098493796\n",
              "2017-02-27  0.0098697467\n",
              "2017-02-28  0.0098742171\n",
              "2017-03-01  0.0100598732\n",
              "2017-03-02  0.0100096006\n",
              "2017-03-03  0.0100592937\n",
              "2017-03-06  0.0100331225\n",
              "2017-03-07  0.0100439679\n",
              "2017-03-08  0.0100121156\n",
              "2017-03-09  0.0099917232\n",
              "2017-03-10  0.0100208486\n",
              "2017-03-13  0.0100245545\n",
              "2017-03-14  0.0100114875\n",
              "2017-03-15  0.0100974678\n",
              "2017-03-16  0.0101097503\n",
              "2017-03-17  0.0100713803\n",
              "2017-03-20  0.0101485332\n",
              "2017-03-21  0.0100627731\n",
              "2017-03-22  0.0101466076\n",
              "2017-03-23  0.0101217119\n",
              "2017-03-24  0.0101071068\n",
              "2017-03-27  0.0101196547\n",
              "2017-03-28  0.0102439560\n",
              "2017-03-29  0.0102543437\n",
              "2017-03-30  0.0102482535\n",
              "2017-03-31  0.0102392078\n",
              "2017-04-03  0.0102405767\n",
              "2017-04-04  0.0102734468\n",
              "2017-04-05  0.0102511668\n",
              "2017-04-06  0.0102392078\n",
              "2017-04-07  0.0102278937\n",
              "2017-04-10  0.0102216221\n",
              "2017-04-11  0.0101566088\n",
              "2017-04-12  0.0101645055\n",
              "2017-04-13  0.0101283323\n",
              "2017-04-17  0.0101658791\n",
              "2017-04-18  0.0101358423\n",
              "2017-04-19  0.0101092222\n",
              "2017-04-20  0.0101926382\n",
              "2017-04-21  0.0101854117\n",
              "2017-04-24  0.0102385201\n",
              "2017-04-25  0.0102667060\n",
              "2017-04-26  0.0102398941\n",
              "2017-04-27  0.0102436205\n",
              "2017-04-28  0.0102388640\n",
              "2017-05-01  0.0103124579\n",
              "2017-05-02  0.0103243243\n",
              "2017-05-03  0.0103192782\n",
              "2017-05-04  0.0103116620\n",
              "2017-05-05  0.0103316906\n",
              "2017-05-08  0.0102803923\n",
              "2017-05-09  0.0102521928\n",
              "2017-05-10  0.0102737783\n",
              "2017-05-11  0.0102320928\n",
              "2017-05-12  0.0101406615\n",
              "2017-05-15  0.0101598546\n",
              "2017-05-16  0.0101704419\n",
              "2017-05-17  0.0103206550\n",
              "2017-05-18  0.0102762157\n",
              "2017-05-19  0.0102614194\n",
              "2017-05-22  0.0102306565\n",
              "2017-05-23  0.0102373876\n",
              "2017-05-24  0.0102527367\n",
              "2017-05-25  0.0102349352\n",
              "2017-05-26  0.0102438909\n",
              "2017-05-30  0.0102418622\n",
              "2017-05-31  0.0102701664\n",
              "2017-06-01  0.0102577598\n",
              "2017-06-02  0.0101713468\n",
              "2017-06-05  0.0102328086\n",
              "2017-06-06  0.0102134151\n",
              "2017-06-07  0.0101749412\n",
              "2017-06-08  0.0101914753\n",
              "2017-06-09  0.0103306381\n",
              "2017-06-12  0.0103026331\n",
              "2017-06-13  0.0103209293\n",
              "2017-06-14  0.0102973640\n",
              "2017-06-15  0.0102765633\n",
              "2017-06-16  0.0102096108\n",
              "2017-06-19  0.0103177661\n",
              "2017-06-20  0.0102941255\n",
              "2017-06-21  0.0103107204\n",
              "2017-06-22  0.0103065708\n",
              "2017-06-23  0.0103169467\n",
              "2017-06-26  0.0103098869\n",
              "2017-06-27  0.0102606045\n",
              "2017-06-28  0.0103100545\n",
              "2017-06-29  0.0102590818\n",
              "2017-06-30  0.0102691196\n",
              "2017-07-03  0.0102534699\n",
              "2017-07-05  0.0102710946\n",
              "2017-07-06  0.0102271342\n",
              "2017-07-07  0.0102735871\n",
              "2017-07-10  0.0102952213\n",
              "2017-07-11  0.0103047312\n",
              "2017-07-12  0.0103085191\n",
              "2017-07-13  0.0103303739\n",
              "2017-07-14  0.0103304028\n",
              "2017-07-17  0.0103273816\n",
              "2017-07-18  0.0103225998\n",
              "2017-07-19  0.0103094965\n",
              "2017-07-20  0.0103195499\n",
              "2017-07-21  0.0103204137\n",
              "2017-07-24  0.0102876193\n",
              "2017-07-25  0.0102707290\n",
              "2017-07-26  0.0102488615\n",
              "2017-07-27  0.0103166254\n",
              "2017-07-28  0.0103278199\n",
              "2017-07-31  0.0103313658\n",
              "2017-08-01  0.0103229234\n",
              "2017-08-02  0.0100861679\n",
              "2017-08-03  0.0101658791\n",
              "2017-08-04  0.0101261325\n",
              "2017-08-07  0.0099850079\n",
              "2017-08-08  0.0098970917\n",
              "2017-08-09  0.0098229447\n",
              "2017-08-10  0.0101489432\n",
              "2017-08-11  0.0100301445\n",
              "2017-08-14  0.0098676528\n",
              "2017-08-15  0.0097270350\n",
              "2017-08-16  0.0097812538\n",
              "2017-08-17  0.0100063173\n",
              "2017-08-18  0.0100289114\n",
              "2017-08-21  0.0100465470\n",
              "2017-08-22  0.0098729184\n",
              "2017-08-23  0.0098577975\n",
              "2017-08-24  0.0099104453\n",
              "2017-08-25  0.0098668983\n",
              "2017-08-28  0.0097380637\n",
              "2017-08-29  0.0096108294\n",
              "2017-08-30  0.0095697666\n",
              "2017-08-31  0.0095072880\n",
              "2017-09-01  0.0095023910\n",
              "2017-09-05  0.0096855204\n",
              "2017-09-06  0.0097003678\n",
              "2017-09-07  0.0097556853\n",
              "2017-09-08  0.0099554070\n",
              "2017-09-11  0.0097355274\n",
              "2017-09-12  0.0097885755\n",
              "2017-09-13  0.0098826266\n",
              "2017-09-14  0.0099789833\n",
              "2017-09-15  0.0098653876\n",
              "2017-09-18  0.0099526664\n",
              "2017-09-19  0.0099485395\n",
              "2017-09-20  0.0101109327\n",
              "2017-09-21  0.0102305720\n",
              "2017-09-22  0.0102776398\n",
              "2017-09-25  0.0103073903\n",
              "2017-09-26  0.0102394192\n",
              "2017-09-27  0.0101979330\n",
              "2017-09-28  0.0102345141\n",
              "2017-09-29  0.0102024613\n",
              "2017-10-02  0.0102148124\n",
              "2017-10-03  0.0101873568\n",
              "2017-10-04  0.0102272896\n",
              "2017-10-05  0.0101455448\n",
              "2017-10-06  0.0101499088\n",
              "2017-10-09  0.0101229607\n",
              "2017-10-10  0.0101198548\n",
              "2017-10-11  0.0100847883\n",
              "2017-10-12  0.0101146280\n",
              "2017-10-13  0.0100595876\n",
              "2017-10-16  0.0098653876\n",
              "2017-10-17  0.0098197897\n",
              "2017-10-18  0.0098744189\n",
              "2017-10-19  0.0101156795\n",
              "2017-10-20  0.0101012963\n",
              "2017-10-23  0.0101056053\n",
              "2017-10-24  0.0100531043\n",
              "2017-10-25  0.0100925612\n",
              "2017-10-26  0.0100344393\n",
              "2017-10-27  0.0095978749\n",
              "2017-10-30  0.0092232995\n",
              "2017-10-31  0.0089544365\n",
              "2017-11-01  0.0092043976\n",
              "2017-11-02  0.0090649852\n",
              "2017-11-03  0.0085136385\n",
              "2017-11-06  0.0082750010\n",
              "2017-11-07  0.0081966846\n",
              "2017-11-08  0.0079928110\n",
              "2017-11-09  0.0080446418\n",
              "2017-11-10  0.0081277340\n",
              "2017-11-13  0.0082268026\n",
              "2017-11-14  0.0085858165\n",
              "2017-11-15  0.0088753444\n",
              "2017-11-16  0.0086174436\n",
              "2017-11-17  0.0087406321\n",
              "2017-11-20  0.0087623275\n",
              "2017-11-21  0.0083424427\n",
              "2017-11-22  0.0080863001\n",
              "2017-11-24  0.0080848660\n",
              "2017-11-27  0.0082099201\n",
              "2017-11-28  0.0083520986\n",
              "2017-11-29  0.0088255007\n",
              "2017-11-30  0.0085179424\n",
              "2017-12-01  0.0086240095\n",
              "2017-12-04  0.0087851799\n",
              "2017-12-05  0.0088053893\n",
              "2017-12-06  0.0088840021\n",
              "2017-12-07  0.0088455110\n",
              "2017-12-08  0.0088392701\n",
              "2017-12-11  0.0084069976\n",
              "2017-12-12  0.0085379976\n",
              "2017-12-13  0.0084613905\n",
              "2017-12-14  0.0084681527\n",
              "2017-12-15  0.0082268026\n",
              "2017-12-18  0.0078744298\n",
              "2017-12-19  0.0081462358\n",
              "2017-12-20  0.0081731916\n",
              "2017-12-21  0.0080791316\n",
              "2017-12-22  0.0080791316\n",
              "2017-12-26  0.0086865733\n",
              "2017-12-27  0.0086826860\n",
              "2017-12-28  0.0086200727\n",
              "2017-12-29  0.0088567260\n",
              "2018-01-02  0.0084627449\n",
              "2018-01-03  0.0084668018\n",
              "2018-01-04  0.0083576134\n",
              "2018-01-05  0.0080805667\n",
              "2018-01-08  0.0081731916\n",
              "2018-01-09  0.0081760213\n",
              "2018-01-10  0.0081816843\n",
              "2018-01-11  0.0080403161\n",
              "2018-01-12  0.0077755171\n",
              "2018-01-16  0.0079081501\n",
              "2018-01-17  0.0074732640\n",
              "2018-01-18  0.0074488870\n",
              "2018-01-19  0.0075703289\n",
              "2018-01-22  0.0077888596\n",
              "2018-01-23  0.0077829325\n",
              "2018-01-24  0.0081915785\n",
              "2018-01-25  0.0086161347\n",
              "2018-01-26  0.0085632877\n",
              "2018-01-29  0.0090114925\n",
              "2018-01-30  0.0091274687\n",
              "2018-01-31  0.0090741055\n",
              "2018-02-01  0.0090328924\n",
              "2018-02-02  0.0097708439\n",
              "2018-02-05  0.0100559102\n",
              "2018-02-06  0.0095444530\n",
              "2018-02-07  0.0098475762\n",
              "2018-02-08  0.0101297273\n",
              "2018-02-09  0.0100219487\n",
              "2018-02-12  0.0095111238\n",
              "2018-02-13  0.0093441771\n",
              "2018-02-14  0.0090004584\n",
              "2018-02-15  0.0082653004\n",
              "2018-02-16  0.0083434063\n",
              "2018-02-20  0.0084232812\n",
              "2018-02-21  0.0085289846\n",
              "2018-02-22  0.0083336938\n",
              "2018-02-23  0.0079044133\n",
              "2018-02-26  0.0073816811\n",
              "2018-02-27  0.0074706255\n",
              "2018-02-28  0.0075118401\n",
              "2018-03-01  0.0079776148\n",
              "2018-03-02  0.0077994597\n",
              "2018-03-05  0.0077083988\n",
              "2018-03-06  0.0077308623\n",
              "2018-03-07  0.0079732360\n",
              "2018-03-08  0.0076903945\n",
              "2018-03-09  0.0072255712\n",
              "2018-03-12  0.0069535745\n",
              "2018-03-13  0.0072271190\n",
              "2018-03-14  0.0074629827\n",
              "2018-03-15  0.0074308249\n",
              "2018-03-16  0.0075270708\n",
              "2018-03-19  0.0079337653\n",
              "2018-03-20  0.0079425514\n",
              "2018-03-21  0.0085020738\n",
              "2018-03-22  0.0088181698\n",
              "2018-03-23  0.0092794514\n",
              "2018-03-26  0.0082960951\n",
              "2018-03-27  0.0088819818\n",
              "2018-03-28  0.0091056823\n",
              "2018-03-29  0.0089508536\n",
              "2018-04-02  0.0090823343\n",
              "2018-04-03  0.0088757698\n",
              "2018-04-04  0.0084560184\n",
              "2018-04-05  0.0082919065\n",
              "2018-04-06  0.0088770125\n",
              "2018-04-09  0.0086640800\n",
              "2018-04-10  0.0082287160\n",
              "2018-04-11  0.0083420201\n",
              "2018-04-12  0.0081020416\n",
              "2018-04-13  0.0080168821\n",
              "2018-04-16  0.0078572504\n",
              "2018-04-17  0.0074935378\n",
              "2018-04-18  0.0075544457\n",
              "2018-04-19  0.0082919065\n",
              "2018-04-20  0.0091927899\n",
              "2018-04-23  0.0092464515\n",
              "2018-04-24  0.0094883752\n",
              "2018-04-25  0.0094164604\n",
              "2018-04-26  0.0093569136\n",
              "2018-04-27  0.0095490811\n",
              "2018-04-30  0.0092442403\n",
              "2018-05-01  0.0087865161\n",
              "2018-05-02  0.0077458141\n",
              "2018-05-03  0.0076978976\n",
              "2018-05-04  0.0066200531\n",
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              "2018-11-12  0.0046711231\n",
              "2018-11-13  0.0049676710\n",
              "2018-11-14  0.0058242275\n",
              "2018-11-15  0.0050948005\n",
              "2018-11-16  0.0047682519\n",
              "2018-11-19  0.0059750291\n",
              "2018-11-20  0.0073912796\n",
              "2018-11-21  0.0074223234\n",
              "2018-11-23  0.0080982344\n",
              "2018-11-26  0.0077530000\n",
              "2018-11-27  0.0078101918\n",
              "2018-11-28  0.0067657364\n",
              "2018-11-29  0.0069872660\n",
              "2018-11-30  0.0071407474\n",
              "2018-12-03  0.0061422512\n",
              "2018-12-04  0.0074362739\n",
              "2018-12-06  0.0077378932\n",
              "2018-12-07  0.0086280004\n",
              "2018-12-10  0.0084781144\n",
              "2018-12-11  0.0086093363\n",
              "2018-12-12  0.0085461652\n",
              "2018-12-13  0.0082902394\n",
              "2018-12-14  0.0090109691\n",
              "2018-12-17  0.0091921578\n",
              "2018-12-18  0.0089387966\n",
              "2018-12-19  0.0095177650\n",
              "2018-12-20  0.0098746619\n",
              "2018-12-21  0.0102249637\n",
              "2018-12-24  0.0103217366\n",
              "2018-12-26  0.0098483764\n",
              "2018-12-27  0.0099251721\n",
              "2018-12-28  0.0099193739\n",
              "2018-12-31  0.0098027877"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y <- dnorm(AD, ADm, ADsd)\n",
        "plot(y)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
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              "EBKAAEICEPB/GPQKCgMGoYMAAAAASUVORK5CYII="
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 18,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "hist(y, main='Probability Distribution ')"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title \"Probability Distribution \""
            ],
            "image/png": [
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              "d3rx6jbDiX/Kzuu+v9pQ7dU7//8QkXKIdKlkDgQWdg7HHelF6i82bPWfHd7/xeiROV1BpOJF\n",
              "6iqRA7vlR1n9Nej0IvXnSBeZ68ILO/f9od1NXpGnJER6nnOGiU9M30xX2lNLveiwrHM7HEeK\n",
              "facXPlDRHWxh5yb0p2SdjLxznaO/Zfei5aTou19IuXy/3nJ5XeP5fjNd6e2vTS31cv+yTuFf\n",
              "bL94dYc7ZUoXdorKO9c5apHdi5aTQqTd8E/w8fVa4OgT0zfTld7+FDquW9wpLNJHq3uRebQL\n",
              "O+/PDkKvXc119nwtp+xetJwUIpX8zgahPeujzgGxY4/FD3TT9ecrh4Sdbejf89bqv5ui52tB\n",
              "Pb+z4Xas3DPssfeHO/rE9M1kpVvRZ4eFD/R1f8LSneTqLuysU3VeXwsquxctJolI9zcB3/vC\n",
              "t09M30xWKnuYtfCBvu5PWXqs5VZ3aafkd3Su8/paUNm9aDGpL24AuASRAARAJAABEAlAAOyQ\n",
              "NlcAAAGASURBVEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlA\n",
              "AEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARA\n",
              "JAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRLNKFzdvfkB1EMkkTTv1fh7DLvSVwB5FMcgzb\n",
              "/q9tuOTeEriDSDbZhO72J0d2xYBINtn3B3UnjuyKAZFs0oXqet1xZFcMiGSUNhyvG47sigGR\n",
              "jHIO9Zkju3JAJKtsQsWRXTkgklWOgWt2BYFIVukCR3YFgUhWuT0jcWRXDohklTrsc28CvEAk\n",
              "m4QQ6tzbACMQySZVaHJvAoxBJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlA\n",
              "AEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARA\n",
              "JAABEAlAAEQCEOAfipz0aV2jVdQAAAAASUVORK5CYII="
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 19,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "length(min(dnorm(AD, ADm, ADsd)))\n",
        "length(max(dnorm(AD, ADm, ADsd)))"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "1"
            ],
            "text/markdown": [
              "1"
            ],
            "text/latex": [
              "1"
            ],
            "text/plain": [
              "[1] 1"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "1"
            ],
            "text/markdown": [
              "1"
            ],
            "text/latex": [
              "1"
            ],
            "text/plain": [
              "[1] 1"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 20,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "min(dnorm(AD, ADm, ADsd))\n",
        "max(dnorm(AD, ADm, ADsd))"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.000892992135035721"
            ],
            "text/markdown": [
              "0.000892992135035721"
            ],
            "text/latex": [
              "0.000892992135035721"
            ],
            "text/plain": [
              "[1] 0.0008929921"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.0103316906312139"
            ],
            "text/markdown": [
              "0.0103316906312139"
            ],
            "text/latex": [
              "0.0103316906312139"
            ],
            "text/plain": [
              "[1] 0.01033169"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 21,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# probability of a normally distributed\n",
        "pnorm(AD, ADm, ADsd)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "           AAPL.Adjusted\n",
              "2016-01-04    0.12283100\n",
              "2016-01-05    0.11023562\n",
              "2016-01-06    0.10128720\n",
              "2016-01-07    0.08413184\n",
              "2016-01-08    0.08606714\n",
              "2016-01-11    0.09223375\n",
              "2016-01-12    0.09812983\n",
              "2016-01-13    0.08772460\n",
              "2016-01-14    0.09628696\n",
              "2016-01-15    0.08671959\n",
              "2016-01-19    0.08492472\n",
              "2016-01-20    0.08541838\n",
              "2016-01-21    0.08356886\n",
              "2016-01-22    0.10442982\n",
              "2016-01-25    0.09595476\n",
              "2016-01-26    0.09825647\n",
              "2016-01-27    0.07330188\n",
              "2016-01-28    0.07559975\n",
              "2016-01-29    0.08753053\n",
              "2016-02-01    0.08405663\n",
              "2016-02-02    0.07696230\n",
              "2016-02-03    0.08375616\n",
              "2016-02-04    0.08669712\n",
              "2016-02-05    0.07713897\n",
              "2016-02-08    0.08070738\n",
              "2016-02-09    0.08063404\n",
              "2016-02-10    0.07802856\n",
              "2016-02-11    0.07601160\n",
              "2016-02-12    0.07703276\n",
              "2016-02-16    0.08685206\n",
              "2016-02-17    0.09272808\n",
              "2016-02-18    0.08538919\n",
              "2016-02-19    0.08455073\n",
              "2016-02-22    0.08778550\n",
              "2016-02-23    0.07954053\n",
              "2016-02-24    0.08477880\n",
              "2016-02-25    0.08731783\n",
              "2016-02-26    0.08790269\n",
              "2016-02-29    0.08704585\n",
              "2016-03-01    0.10291751\n",
              "2016-03-02    0.10388664\n",
              "2016-03-03    0.10724034\n",
              "2016-03-04    0.11422768\n",
              "2016-03-07    0.10892333\n",
              "2016-03-08    0.10512967\n",
              "2016-03-09    0.10553157\n",
              "2016-03-10    0.10575520\n",
              "2016-03-11    0.11071768\n",
              "2016-03-14    0.11192570\n",
              "2016-03-15    0.12183043\n",
              "2016-03-16    0.12885229\n",
              "2016-03-17    0.12797872\n",
              "2016-03-18    0.12859482\n",
              "2016-03-21    0.12854351\n",
              "2016-03-22    0.13275549\n",
              "2016-03-23    0.12967818\n",
              "2016-03-24    0.12731343\n",
              "2016-03-28    0.12487814\n",
              "2016-03-29    0.13786934\n",
              "2016-03-30    0.14826898\n",
              "2016-03-31    0.14506200\n",
              "2016-04-01    0.15071956\n",
              "2016-04-04    0.15728735\n",
              "2016-04-05    0.14969038\n",
              "2016-04-06    0.15634605\n",
              "2016-04-07    0.14256326\n",
              "2016-04-08    0.14322670\n",
              "2016-04-11    0.14522942\n",
              "2016-04-12    0.15331290\n",
              "2016-04-13    0.16277143\n",
              "2016-04-14    0.16313320\n",
              "2016-04-15    0.14991882\n",
              "2016-04-18    0.13679299\n",
              "2016-04-19    0.13375708\n",
              "2016-04-20    0.13492331\n",
              "2016-04-21    0.12885229\n",
              "2016-04-22    0.12736457\n",
              "2016-04-25    0.12432467\n",
              "2016-04-26    0.12069489\n",
              "2016-04-27    0.09151380\n",
              "2016-04-28    0.08004950\n",
              "2016-04-29    0.07615185\n",
              "2016-05-02    0.07580163\n",
              "2016-05-03    0.08133245\n",
              "2016-05-04    0.07774308\n",
              "2016-05-05    0.07638956\n",
              "2016-05-06    0.07456663\n",
              "2016-05-09    0.07481011\n",
              "2016-05-10    0.07702839\n",
              "2016-05-11    0.07383993\n",
              "2016-05-12    0.06664420\n",
              "2016-05-13    0.06721962\n",
              "2016-05-16    0.07867961\n",
              "2016-05-17    0.07727797\n",
              "2016-05-18    0.08116929\n",
              "2016-05-19    0.07984384\n",
              "2016-05-20    0.08364216\n",
              "2016-05-23    0.08832212\n",
              "2016-05-24    0.09426691\n",
              "2016-05-25    0.10159145\n",
              "2016-05-26    0.10509116\n",
              "2016-05-27    0.10482221\n",
              "2016-05-31    0.10264544\n",
              "2016-06-01    0.09660760\n",
              "2016-06-02    0.09352360\n",
              "2016-06-03    0.09434985\n",
              "2016-06-06    0.09732653\n",
              "2016-06-07    0.09903363\n",
              "2016-06-08    0.09864759\n",
              "2016-06-09    0.10172273\n",
              "2016-06-10    0.09817738\n",
              "2016-06-13    0.09196839\n",
              "2016-06-14    0.09245738\n",
              "2016-06-15    0.09115766\n",
              "2016-06-16    0.09282545\n",
              "2016-06-17    0.08405977\n",
              "2016-06-20    0.08318838\n",
              "2016-06-21    0.08628751\n",
              "2016-06-22    0.08489968\n",
              "2016-06-23    0.08702689\n",
              "2016-06-24    0.07695729\n",
              "2016-06-27    0.07223305\n",
              "2016-06-28    0.07763557\n",
              "2016-06-29    0.08057824\n",
              "2016-06-30    0.08509143\n",
              "2016-07-01    0.08620999\n",
              "2016-07-05    0.08277407\n",
              "2016-07-06    0.08482303\n",
              "2016-07-07    0.08640399\n",
              "2016-07-08    0.08931292\n",
              "2016-07-11    0.09051279\n",
              "2016-07-12    0.09229418\n",
              "2016-07-13    0.09007148\n",
              "2016-07-14    0.09800677\n",
              "2016-07-15    0.09796420\n",
              "2016-07-18    0.10251332\n",
              "2016-07-19    0.10268962\n",
              "2016-07-20    0.10308702\n",
              "2016-07-21    0.10076256\n",
              "2016-07-22    0.09745383\n",
              "2016-07-25    0.09196839\n",
              "2016-07-26    0.08927314\n",
              "2016-07-27    0.11693252\n",
              "2016-07-28    0.12379919\n",
              "2016-07-29    0.12314527\n",
              "2016-08-01    0.13262763\n",
              "2016-08-02    0.12450625\n",
              "2016-08-03    0.13125808\n",
              "2016-08-04    0.13471929\n",
              "2016-08-05    0.14356018\n",
              "2016-08-08    0.14861191\n",
              "2016-08-09    0.15115265\n",
              "2016-08-10    0.14649753\n",
              "2016-08-11    0.14609971\n",
              "2016-08-12    0.14752357\n",
              "2016-08-15    0.15507699\n",
              "2016-08-16    0.15448699\n",
              "2016-08-17    0.15354621\n",
              "2016-08-18    0.15272619\n",
              "2016-08-19    0.15436920\n",
              "2016-08-22    0.14941723\n",
              "2016-08-23    0.15138512\n",
              "2016-08-24    0.14666819\n",
              "2016-08-25    0.14406563\n",
              "2016-08-26    0.14055214\n",
              "2016-08-29    0.13988957\n",
              "2016-08-30    0.13541900\n",
              "2016-08-31    0.13595880\n",
              "2016-09-01    0.13939415\n",
              "2016-09-02    0.14496729\n",
              "2016-09-06    0.14479796\n",
              "2016-09-07    0.14855446\n",
              "2016-09-08    0.13284775\n",
              "2016-09-09    0.12054728\n",
              "2016-09-12    0.13242258\n",
              "2016-09-13    0.14621326\n",
              "2016-09-14    0.16899314\n",
              "2016-09-15    0.19379771\n",
              "2016-09-16    0.18940448\n",
              "2016-09-19    0.18054263\n",
              "2016-09-20    0.18047739\n",
              "2016-09-21    0.18034723\n",
              "2016-09-22    0.18739750\n",
              "2016-09-23    0.17493077\n",
              "2016-09-26    0.17601851\n",
              "2016-09-27    0.17736817\n",
              "2016-09-28    0.18296318\n",
              "2016-09-29    0.17156689\n",
              "2016-09-30    0.17711063\n",
              "2016-10-03    0.17372003\n",
              "2016-10-04    0.17678893\n",
              "2016-10-05    0.17711063\n",
              "2016-10-06    0.18256924\n",
              "2016-10-07    0.18368674\n",
              "2016-10-10    0.19708176\n",
              "2016-10-11    0.19880542\n",
              "2016-10-12    0.20607255\n",
              "2016-10-13    0.20353933\n",
              "2016-10-14    0.20812673\n",
              "2016-10-17    0.20755899\n",
              "2016-10-18    0.20699205\n",
              "2016-10-19    0.20452240\n",
              "2016-10-20    0.20410064\n",
              "2016-10-21    0.20088559\n",
              "2016-10-24    0.20826894\n",
              "2016-10-25    0.21255873\n",
              "2016-10-26    0.19393391\n",
              "2016-10-27    0.18646555\n",
              "2016-10-28    0.18145616\n",
              "2016-10-31    0.18028214\n",
              "2016-11-01    0.16724976\n",
              "2016-11-02    0.16787106\n",
              "2016-11-03    0.16053723\n",
              "2016-11-04    0.15459784\n",
              "2016-11-07    0.16408520\n",
              "2016-11-08    0.16812133\n",
              "2016-11-09    0.16699725\n",
              "2016-11-10    0.14845919\n",
              "2016-11-11    0.15218125\n",
              "2016-11-14    0.13678633\n",
              "2016-11-15    0.14457200\n",
              "2016-11-16    0.16151089\n",
              "2016-11-17    0.16126704\n",
              "2016-11-18    0.16193813\n",
              "2016-11-21    0.17234793\n",
              "2016-11-22    0.17279337\n",
              "2016-11-23    0.16918732\n",
              "2016-11-25    0.17272968\n",
              "2016-11-28    0.17133247\n",
              "2016-11-29    0.17063651\n",
              "2016-11-30    0.16476370\n",
              "2016-12-01    0.15848082\n",
              "2016-12-02    0.16096269\n",
              "2016-12-05    0.15620309\n",
              "2016-12-06    0.16126704\n",
              "2016-12-07    0.16793355\n",
              "2016-12-08    0.17483903\n",
              "2016-12-09    0.18683158\n",
              "2016-12-12    0.18251480\n",
              "2016-12-13    0.19524008\n",
              "2016-12-14    0.19524008\n",
              "2016-12-15    0.19959873\n",
              "2016-12-16    0.20064525\n",
              "2016-12-19    0.20535900\n",
              "2016-12-20    0.20756199\n",
              "2016-12-21    0.20834715\n",
              "2016-12-22    0.20288844\n",
              "2016-12-23    0.20450990\n",
              "2016-12-27    0.20977910\n",
              "2016-12-28    0.20621014\n",
              "2016-12-29    0.20599715\n",
              "2016-12-30    0.19959873\n",
              "2017-01-03    0.20190522\n",
              "2017-01-04    0.20099460\n",
              "2017-01-05    0.20514648\n",
              "2017-01-06    0.21447260\n",
              "2017-01-09    0.22240447\n",
              "2017-01-10    0.22329599\n",
              "2017-01-11    0.22808511\n",
              "2017-01-12    0.22433870\n",
              "2017-01-13    0.22277569\n",
              "2017-01-17    0.22997145\n",
              "2017-01-18    0.22989570\n",
              "2017-01-19    0.22831102\n",
              "2017-01-20    0.22997145\n",
              "2017-01-23    0.23057686\n",
              "2017-01-24    0.22974463\n",
              "2017-01-25    0.24443280\n",
              "2017-01-26    0.24490228\n",
              "2017-01-27    0.24498054\n",
              "2017-01-30    0.24248184\n",
              "2017-01-31    0.24030693\n",
              "2017-02-01    0.30118397\n",
              "2017-02-02    0.29927810\n",
              "2017-02-03    0.30405309\n",
              "2017-02-06    0.31467550\n",
              "2017-02-07    0.32572268\n",
              "2017-02-08    0.33031174\n",
              "2017-02-09    0.33896566\n",
              "2017-02-10    0.33622347\n",
              "2017-02-13    0.34696625\n",
              "2017-02-14    0.36307690\n",
              "2017-02-15    0.36768587\n",
              "2017-02-16    0.36617871\n",
              "2017-02-17    0.36966706\n",
              "2017-02-21    0.37895752\n",
              "2017-02-22    0.38286560\n",
              "2017-02-23    0.37734083\n",
              "2017-02-24    0.37857693\n",
              "2017-02-27    0.38114834\n",
              "2017-02-28    0.38172045\n",
              "2017-03-01    0.40868762\n",
              "2017-03-02    0.40064269\n",
              "2017-03-03    0.40859076\n",
              "2017-03-06    0.40432090\n",
              "2017-03-07    0.40606635\n",
              "2017-03-08    0.40102931\n",
              "2017-03-09    0.39793757\n",
              "2017-03-10    0.40238393\n",
              "2017-03-13    0.40296461\n",
              "2017-03-14    0.40093260\n",
              "2017-03-15    0.41521085\n",
              "2017-03-16    0.41745556\n",
              "2017-03-17    0.41063283\n",
              "2017-03-20    0.42498958\n",
              "2017-03-21    0.40917383\n",
              "2017-03-22    0.42459752\n",
              "2017-03-23    0.41970280\n",
              "2017-03-24    0.41696723\n",
              "2017-03-27    0.41931179\n",
              "2017-03-28    0.44804272\n",
              "2017-03-29    0.45121087\n",
              "2017-03-30    0.44932926\n",
              "2017-03-31    0.44665750\n",
              "2017-04-03    0.44705312\n",
              "2017-04-04    0.45765477\n",
              "2017-04-05    0.45022042\n",
              "2017-04-06    0.44665750\n",
              "2017-04-07    0.44349432\n",
              "2017-04-10    0.44181542\n",
              "2017-04-11    0.42665694\n",
              "2017-04-12    0.42832531\n",
              "2017-04-13    0.42097445\n",
              "2017-04-17    0.42861955\n",
              "2017-04-18    0.42244257\n",
              "2017-04-19    0.41735776\n",
              "2017-04-20    0.43461793\n",
              "2017-04-21    0.43294458\n",
              "2017-04-24    0.44645986\n",
              "2017-04-25    0.45527435\n",
              "2017-04-26    0.44685546\n",
              "2017-04-27    0.44794361\n",
              "2017-04-28    0.44655860\n",
              "2017-05-01    0.47565400\n",
              "2017-05-02    0.48492374\n",
              "2017-05-03    0.48043704\n",
              "2017-05-04    0.47515582\n",
              "2017-05-05    0.49939093\n",
              "2017-05-08    0.53974308\n",
              "2017-05-09    0.54946189\n",
              "2017-05-10    0.54222470\n",
              "2017-05-11    0.55535292\n",
              "2017-05-12    0.57660034\n",
              "2017-05-15    0.57266200\n",
              "2017-05-16    0.57039416\n",
              "2017-05-17    0.51844746\n",
              "2017-05-18    0.54132759\n",
              "2017-05-19    0.54650704\n",
              "2017-05-22    0.55574993\n",
              "2017-05-23    0.55386399\n",
              "2017-05-24    0.54929263\n",
              "2017-05-25    0.55455873\n",
              "2017-05-26    0.55197653\n",
              "2017-05-30    0.55257263\n",
              "2017-05-31    0.54351999\n",
              "2017-06-01    0.54770104\n",
              "2017-06-02    0.57019690\n",
              "2017-06-05    0.55515400\n",
              "2017-06-06    0.56031055\n",
              "2017-06-07    0.56940772\n",
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              "2017-06-15    0.45880195\n",
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              "2017-06-20    0.46598507\n",
              "2017-06-21    0.47457903\n",
              "2017-06-22    0.47217961\n",
              "2017-06-23    0.47868077\n",
              "2017-06-26    0.47407921\n",
              "2017-06-27    0.45322446\n",
              "2017-06-28    0.47417895\n",
              "2017-06-29    0.45272678\n",
              "2017-06-30    0.45611178\n",
              "2017-07-03    0.45093644\n",
              "2017-07-05    0.45680914\n",
              "2017-07-06    0.44328832\n",
              "2017-07-07    0.45770571\n",
              "2017-07-10    0.46648443\n",
              "2017-07-11    0.47117980\n",
              "2017-07-12    0.47327931\n",
              "2017-07-13    0.49360185\n",
              "2017-07-14    0.50632818\n",
              "2017-07-17    0.51153778\n",
              "2017-07-18    0.51674540\n",
              "2017-07-19    0.52615158\n",
              "2017-07-20    0.51934789\n",
              "2017-07-21    0.51864777\n",
              "2017-07-24    0.53684018\n",
              "2017-07-25    0.54332080\n",
              "2017-07-26    0.55048607\n",
              "2017-07-27    0.52155003\n",
              "2017-07-28    0.51093690\n",
              "2017-07-31    0.50322177\n",
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              "2017-08-02    0.58680227\n",
              "2017-08-03    0.57138047\n",
              "2017-08-04    0.57945037\n",
              "2017-08-07    0.60305982\n",
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              "2017-08-09    0.62467896\n",
              "2017-08-10    0.57492667\n",
              "2017-08-11    0.59615272\n",
              "2017-08-14    0.61911866\n",
              "2017-08-15    0.63581630\n",
              "2017-08-16    0.62964229\n",
              "2017-08-17    0.59985975\n",
              "2017-08-18    0.59634814\n",
              "2017-08-21    0.59351369\n",
              "2017-08-22    0.61844604\n",
              "2017-08-23    0.62036715\n",
              "2017-08-24    0.61353349\n",
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              "2017-08-28    0.63458428\n",
              "2017-08-29    0.64815085\n",
              "2017-08-30    0.65225987\n",
              "2017-08-31    0.65829696\n",
              "2017-09-01    0.65875990\n",
              "2017-09-05    0.64035298\n",
              "2017-09-06    0.63874824\n",
              "2017-09-07    0.63259106\n",
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              "2017-09-11    0.63486866\n",
              "2017-09-12    0.62878498\n",
              "2017-09-13    0.61719549\n",
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              "2017-09-15    0.61940681\n",
              "2017-09-18    0.60773109\n",
              "2017-09-19    0.60831231\n",
              "2017-09-20    0.58232509\n",
              "2017-09-21    0.55577319\n",
              "2017-09-22    0.54079426\n",
              "2017-09-25    0.52736322\n",
              "2017-09-26    0.55328159\n",
              "2017-09-27    0.56412805\n",
              "2017-09-28    0.55467712\n",
              "2017-09-29    0.56303560\n",
              "2017-10-02    0.55995396\n",
              "2017-10-03    0.56660920\n",
              "2017-10-04    0.55666957\n",
              "2017-10-05    0.57561800\n",
              "2017-10-06    0.57472905\n",
              "2017-10-09    0.58005890\n",
              "2017-10-10    0.58065025\n",
              "2017-10-11    0.58704480\n",
              "2017-10-12    0.58163564\n",
              "2017-10-13    0.59136013\n",
              "2017-10-16    0.61940681\n",
              "2017-10-17    0.62506171\n",
              "2017-10-18    0.61825364\n",
              "2017-10-19    0.58143838\n",
              "2017-10-20    0.58409601\n",
              "2017-10-23    0.58330884\n",
              "2017-10-24    0.59243719\n",
              "2017-10-25    0.58566918\n",
              "2017-10-26    0.59546891\n",
              "2017-10-27    0.64946000\n",
              "2017-10-30    0.68310961\n",
              "2017-10-31    0.70364630\n",
              "2017-11-01    0.68463475\n",
              "2017-11-02    0.69548703\n",
              "2017-11-03    0.73308492\n",
              "2017-11-06    0.74739042\n",
              "2017-11-07    0.75188149\n",
              "2017-11-08    0.76315369\n",
              "2017-11-09    0.76034255\n",
              "2017-11-10    0.75575936\n",
              "2017-11-13    0.75016549\n",
              "2017-11-14    0.72855536\n",
              "2017-11-15    0.70926989\n",
              "2017-11-16    0.72653817\n",
              "2017-11-17    0.71848038\n",
              "2017-11-20    0.71702643\n",
              "2017-11-21    0.74344559\n",
              "2017-11-22    0.75805678\n",
              "2017-11-24    0.75813587\n",
              "2017-11-27    0.75112907\n",
              "2017-11-28    0.74287472\n",
              "2017-11-29    0.71272954\n",
              "2017-11-30    0.73281764\n",
              "2017-12-01    0.72611684\n",
              "2017-12-04    0.71548309\n",
              "2017-12-05    0.71410789\n",
              "2017-12-06    0.70866247\n",
              "2017-12-07    0.71134817\n",
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              "2017-12-11    0.73959915\n",
              "2017-12-12    0.73156751\n",
              "2017-12-13    0.73630221\n",
              "2017-12-14    0.73588863\n",
              "2017-12-15    0.75016549\n",
              "2017-12-18    0.76944370\n",
              "2017-12-19    0.75472560\n",
              "2017-12-20    0.75321059\n",
              "2017-12-21    0.75845182\n",
              "2017-12-22    0.75845182\n",
              "2017-12-26    0.72205687\n",
              "2017-12-27    0.72231157\n",
              "2017-12-28    0.72636957\n",
              "2017-12-29    0.71056957\n",
              "2018-01-02    0.73621944\n",
              "2018-01-03    0.73597132\n",
              "2018-01-04    0.74254798\n",
              "2018-01-05    0.75837279\n",
              "2018-01-08    0.75321059\n",
              "2018-01-09    0.75305093\n",
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              "2018-01-11    0.76057854\n",
              "2018-01-12    0.77456708\n",
              "2018-01-16    0.76767004\n",
              "2018-01-17    0.78954454\n",
              "2018-01-18    0.79071113\n",
              "2018-01-19    0.78484028\n",
              "2018-01-22    0.77388274\n",
              "2018-01-23    0.77418699\n",
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              "2018-01-25    0.72662205\n",
              "2018-01-26    0.72998005\n",
              "2018-01-29    0.69948087\n",
              "2018-01-30    0.69070609\n",
              "2018-01-31    0.69479715\n",
              "2018-02-01    0.69789370\n",
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              "2018-02-05    0.59197263\n",
              "2018-02-06    0.65473578\n",
              "2018-02-07    0.62164805\n",
              "2018-02-08    0.57875494\n",
              "2018-02-09    0.59744406\n",
              "2018-02-12    0.65793334\n",
              "2018-02-13    0.67301336\n",
              "2018-02-14    0.70029384\n",
              "2018-02-15    0.74795185\n",
              "2018-02-16    0.74338869\n",
              "2018-02-20    0.73861762\n",
              "2018-02-21    0.73213028\n",
              "2018-02-22    0.74396151\n",
              "2018-02-23    0.76786728\n",
              "2018-02-26    0.79389740\n",
              "2018-02-27    0.78967109\n",
              "2018-02-28    0.78768638\n",
              "2018-03-01    0.76397115\n",
              "2018-03-02    0.77333757\n",
              "2018-03-05    0.77797865\n",
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              "2018-03-07    0.76420615\n",
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              "2018-03-09    0.80113550\n",
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              "2018-03-22    0.71323311\n",
              "2018-03-23    0.67849587\n",
              "2018-03-26    0.74616445\n",
              "2018-03-27    0.70880439\n",
              "2018-03-28    0.69238778\n",
              "2018-03-29    0.70390476\n",
              "2018-04-02    0.69417241\n",
              "2018-04-03    0.70924009\n",
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              "2018-04-05    0.74640845\n",
              "2018-04-06    0.70915300\n",
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              "2018-04-25    0.66666230\n",
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              "2018-04-27    0.65428624\n",
              "2018-04-30    0.68140378\n",
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              "2018-05-04    0.82729216\n",
              "2018-05-07    0.83579359\n",
              "2018-05-08    0.84132831\n",
              "2018-05-09    0.84924976\n",
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              "2018-05-11    0.86058622\n",
              "2018-05-14    0.85807990\n",
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              "2018-05-16    0.85825179\n",
              "2018-05-17    0.85132697\n",
              "2018-05-18    0.84727009\n",
              "2018-05-21    0.85507882\n",
              "2018-05-22    0.85232983\n",
              "2018-05-23    0.85927984\n",
              "2018-05-24    0.85807990\n",
              "2018-05-25    0.86052964\n",
              "2018-05-29    0.85664241\n",
              "2018-05-30    0.85432202\n",
              "2018-05-31    0.85061637\n",
              "2018-06-01    0.86971562\n",
              "2018-06-04    0.87811341\n",
              "2018-06-05    0.88558176\n",
              "2018-06-06    0.88885322\n",
              "2018-06-07    0.88632010\n",
              "2018-06-08    0.87744141\n",
              "2018-06-11    0.87499021\n",
              "2018-06-12    0.88041955\n",
              "2018-06-13    0.87218519\n",
              "2018-06-14    0.87271780\n",
              "2018-06-15    0.86199671\n",
              "2018-06-18    0.86143370\n",
              "2018-06-19    0.84350775\n",
              "2018-06-20    0.84841095\n",
              "2018-06-21    0.84209658\n",
              "2018-06-22    0.83875091\n",
              "2018-06-25    0.82100090\n",
              "2018-06-26    0.83567504\n",
              "2018-06-27    0.83396426\n",
              "2018-06-28    0.84234257\n",
              "2018-06-29    0.83993324\n",
              "2018-07-02    0.85244751\n",
              "2018-07-03    0.83243390\n",
              "2018-07-05    0.84172721\n",
              "2018-07-06    0.85704593\n",
              "2018-07-09    0.87154411\n",
              "2018-07-10    0.87030910\n",
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              "2018-07-12    0.87393680\n",
              "2018-07-13    0.87551456\n",
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              "2018-07-17    0.87614184\n",
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              "2018-07-20    0.87608961\n",
              "2018-07-23    0.87697456\n",
              "2018-07-24    0.88404510\n",
              "2018-07-25    0.89285974\n",
              "2018-07-26    0.88996092\n",
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              "2018-07-30    0.86792363\n",
              "2018-07-31    0.86998551\n",
              "2018-08-01    0.92106677\n",
              "2018-08-02    0.94091894\n",
              "2018-08-03    0.94269879\n",
              "2018-08-06    0.94579601\n",
              "2018-08-07    0.94007356\n",
              "2018-08-08    0.94049738\n",
              "2018-08-09    0.94526095\n",
              "2018-08-10    0.94347954\n",
              "2018-08-13    0.94727361\n",
              "2018-08-14    0.94965335\n",
              "2018-08-15    0.95094083\n",
              "2018-08-16    0.95844238\n",
              "2018-08-17    0.96725810\n",
              "2018-08-20    0.96308547\n",
              "2018-08-21    0.96220929\n",
              "2018-08-22    0.96223032\n",
              "2018-08-23    0.96314743\n",
              "2018-08-24    0.96450884\n",
              "2018-08-27    0.96792649\n",
              "2018-08-28    0.97103389\n",
              "2018-08-29    0.97615807\n",
              "2018-08-30    0.97895618\n",
              "2018-08-31    0.98210082\n",
              "2018-09-04    0.98290811\n",
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              "2018-09-06    0.97633008\n",
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              "2018-09-11    0.97738163\n",
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              "2018-09-14    0.97736784\n",
              "2018-09-17    0.96781590\n",
              "2018-09-18    0.96847483\n",
              "2018-09-19    0.96871004\n",
              "2018-09-20    0.97158773\n",
              "2018-09-21    0.96740763\n",
              "2018-09-24    0.97282978\n",
              "2018-09-25    0.97499930\n",
              "2018-09-26    0.97223088\n",
              "2018-09-27    0.97885245\n",
              "2018-09-28    0.97985817\n",
              "2018-10-01    0.98167935\n",
              "2018-10-02    0.98388105\n",
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              "2018-10-08    0.97727136\n",
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              "2018-10-10    0.96490715\n",
              "2018-10-11    0.96094985\n",
              "2018-10-12    0.97487937\n",
              "2018-10-15    0.96684401\n",
              "2018-10-16    0.97493937\n",
              "2018-10-17    0.97346515\n",
              "2018-10-18    0.96422783\n",
              "2018-10-19    0.97036781\n",
              "2018-10-22    0.97260445\n",
              "2018-10-23    0.97579633\n",
              "2018-10-24    0.96231445\n",
              "2018-10-25    0.97120267\n",
              "2018-10-26    0.96478807\n",
              "2018-10-29    0.95592546\n",
              "2018-10-30    0.95839684\n",
              "2018-10-31    0.96958351\n",
              "2018-11-01    0.97504416\n",
              "2018-11-02    0.94333391\n",
              "2018-11-05    0.92401601\n",
              "2018-11-06    0.93167996\n",
              "2018-11-07    0.95018203\n",
              "2018-11-08    0.94822369\n",
              "2018-11-09    0.93632084\n",
              "2018-11-12    0.89616783\n",
              "2018-11-13    0.88689479\n",
              "2018-11-14    0.85784604\n",
              "2018-11-15    0.88280268\n",
              "2018-11-16    0.89317169\n",
              "2018-11-19    0.85234524\n",
              "2018-11-20    0.79344499\n",
              "2018-11-21    0.79197574\n",
              "2018-11-23    0.75739753\n",
              "2018-11-26    0.77571733\n",
              "2018-11-27    0.77278427\n",
              "2018-11-28    0.82125508\n",
              "2018-11-29    0.81177389\n",
              "2018-11-30    0.80497711\n",
              "2018-12-03    0.84609526\n",
              "2018-12-04    0.79131245\n",
              "2018-12-06    0.77648578\n",
              "2018-12-07    0.72586031\n",
              "2018-12-10    0.73527786\n",
              "2018-12-11    0.72705719\n",
              "2018-12-12    0.73105618\n",
              "2018-12-13    0.74650549\n",
              "2018-12-14    0.69951951\n",
              "2018-12-17    0.68561513\n",
              "2018-12-18    0.70477186\n",
              "2018-12-19    0.65730166\n",
              "2018-12-20    0.61822246\n",
              "2018-12-21    0.55729621\n",
              "2018-12-24    0.51752127\n",
              "2018-12-26    0.62154828\n",
              "2018-12-27    0.61154481\n",
              "2018-12-28    0.61233210\n",
              "2018-12-31    0.62710374"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 22,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y <- pnorm(AD, ADm, ADsd)\n",
        "plot(y)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": [
              "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAAAzMzNxcXGGhoaW\n",
              "lpajo6Opqamurq64uLjCwsLKysrS0tLZ2dng4ODn5+ft7e3z8/P///887ktcAAAACXBIWXMA\n",
              "ABJ0AAASdAHeZh94AAAgAElEQVR4nO2di3abOBQAIW3TdPvk/392Y4NBAiEkdMWVxMzZbWOD\n",
              "NTjRFBtjpxsAIJlOewMAWoCQAAQgJAABCAlAAEICEICQAAQgJAABCAlAAEICEICQAAQgJAAB\n",
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              "ACEBCEBIAAIQEoAAhAQgACEBCPA/gyfLNATdaIYAAAAASUVORK5CYII="
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 23,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "hist(y, main = \"Normal Distribution\")"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title \"Normal Distribution\""
            ],
            "image/png": [
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        }
      ],
      "execution_count": 24,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "library(e1071)   "
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message:\n",
            "\"package 'e1071' was built under R version 3.5.3\""
          ]
        }
      ],
      "execution_count": 25,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "skewness(AD)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.226605345891108"
            ],
            "text/markdown": [
              "0.226605345891108"
            ],
            "text/latex": [
              "0.226605345891108"
            ],
            "text/plain": [
              "[1] 0.2266053"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 26,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "kurtosis(AD) "
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "-0.973029107413621"
            ],
            "text/markdown": [
              "-0.973029107413621"
            ],
            "text/latex": [
              "-0.973029107413621"
            ],
            "text/plain": [
              "[1] -0.9730291"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 27,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    }
  ],
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