00_FortCollinsPOSTCRASH.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Master's Thesis: Investigating Maximum Rainfall Trends in Colorado"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Institution:</b> University of Georgia <br>\n",
    "<b>Department:</b> Statistics <br>\n",
    "<b>Student:</b> Jeremy Mulcahey <br>\n",
    "<b>Advisor:</b> Dr. Lynne Seymour <br>\n",
    "<b>File:</b> 01_FortCollins<br>\n",
    "<b>Last Edit:</b> 7/4/2016"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Section 0: Preparing data <br>\n",
    "Section 1: Distribution of Max Precipitation and Trends<br>\n",
    "Section 2: Parameter Estimation, Distribution, and Trends"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Section 0: Preparing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "require(fitdistrplus); # required for parameter estimation\n",
    "require(caTools);      # required for smoothing\n",
    "require(repr);         # required for resizing plots in IRKernel\n",
    "require(\"IRdisplay\");  # graphic embedding\n",
    "require(MASS);         # testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# establish working directorys\n",
    "setwd(\"C:/Users/jerem/Desktop/UGA/Master'sThesis/\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data files for individual station names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = read.csv(file = \"data/FORT_MonMax_GHCN.csv\", head=T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adjust the data for later use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "11"
      ],
      "text/latex": [
       "11"
      ],
      "text/markdown": [
       "11"
      ],
      "text/plain": [
       "[1] 11"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an index as x - used as needed\n",
    "month = seq(1,nrow(data),by=1)\n",
    "data = cbind(data,month)\n",
    "\n",
    "# first year of the data (changes by station name)\n",
    "firstYear = data$YEAR[1]\n",
    "\n",
    "# station name for plotting\n",
    "stationName = as.character(data$STATION_NAME[1])\n",
    "\n",
    "# -999 messed with the plotting - change to NA\n",
    "data[data==-999] = NA\n",
    "\n",
    "sum(is.na(data)) #print number of missing values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check number of years in the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "118"
      ],
      "text/latex": [
       "118"
      ],
      "text/markdown": [
       "118"
      ],
      "text/plain": [
       "[1] 118"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data$YEAR[nrow(data)]-firstYear"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check that there are no missing rows. This is an issue in some of the datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "  1   2   3   4   5   6   7   8   9  10  11  12 \n",
       "119 119 119 119 119 119 119 119 119 119 119 119 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(data$MONTH)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a data frame of all the 10 year periods following the first year for data collected at the station."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#create the first decade (first year and the following 9 years)\n",
    "max_PRCP = data.frame(data[which(data$YEAR < (firstYear + 10)),6])\n",
    "\n",
    "# add all the subsequent decades to the data frame incrementing by 1 year at a time\n",
    "# i.e. 1896-1905, 1897-1906, etc\n",
    "for(year in c((data$YEAR[1] + 1):2005)){\n",
    "    max_PRCP = cbind(max_PRCP,data[which(data$YEAR >= year & data$YEAR < year+10),6])\n",
    "}\n",
    "\n",
    "# name the columns as the first year of the observed 10 year periods\n",
    "colnames(max_PRCP) = as.character(c(firstYear:2005))\n",
    "\n",
    "# set the missing values to NA\n",
    "max_PRCP[max_PRCP==-999] = NA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Subsetting out the event year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data2012 = data[which(data$YEAR<2013),]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 1: Distribution of Max Precipitation and Trends"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options(repr.plot.width=5, repr.plot.height=5) #reduces the plot sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAMAAACJuGjuAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nxAIREAtE+B8pXtHReS9kQAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"FORT COLLINS CO US \n",
       "Observed 24 Hour Max Rainfall \n",
       "from 1896 to 2014\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data$Max.PRCP, xlab = sprintf(\"Observed 24 hour Maximum Rainfall (tenths of mm)\",\n",
    "                                   firstYear), main=sprintf(\"%s \\nObserved 24 Hour Max Rainfall \\nfrom %i to 2014\",\n",
    "                                   stationName,firstYear),col=\"lightblue\")        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAMAAACJuGjuAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nERALREAsEAGxQIT/ARqr1G/ay8w7AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"FORT COLLINS CO US \n",
       "Observed 24 Hour Max Rainfall \n",
       "from 1896 to 2013\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data2012$Max.PRCP, xlab = sprintf(\"Observed 24 hour Maximum Rainfall (tenths of mm)\",\n",
    "                                   firstYear), main=sprintf(\"%s \\nObserved 24 Hour Max Rainfall \\nfrom %i to 2013\",\n",
    "                                   stationName,firstYear),col=\"lightblue\")        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum Rainfall Trends"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create for maximum rainfall\n",
    "maxTS = ts(data$Max.PRCP, start=firstYear, freq=12)\n",
    "\n",
    "# create regression line\n",
    "reg = lm(Max.PRCP. ~ month, data=data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Slope of the regression line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>month:</strong> 0.014"
      ],
      "text/latex": [
       "\\textbf{month:} 0.014"
      ],
      "text/markdown": [
       "**month:** 0.014"
      ],
      "text/plain": [
       "month \n",
       "0.014 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "round(reg$coefficients[2],3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>month:</strong> 19.992"
      ],
      "text/latex": [
       "\\textbf{month:} 19.992"
      ],
      "text/markdown": [
       "**month:** 19.992"
      ],
      "text/plain": [
       " month \n",
       "19.992 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(data$MONTH)*round(reg$coefficients[2],3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although month isn't very predictive of maximum observed rainfall, there does appear to be an increase over the time data was collected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAMAAACJuGjuAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nABYURQALiiKABUURwIKi6D/ORHYwYEnAwwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"FORT COLLINS CO US \n",
       "Observed 24 Hour Max Rainfall \n",
       "from 1896 to 2014 by Monthly Max\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(maxTS, xlab = \"Time (months)\", col = \"black\", lwd=2, ylab = \"Observed Max Precipitation\", \n",
    "     main=sprintf(\"%s \\nObserved 24 Hour Max Rainfall \\nfrom %i to 2014 by Monthly Max\", stationName,firstYear))\n",
    "abline(reg, col=\"red\", lwd=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the time series plot, we also see that the peaks are gradually increasing over time, which is of specific interest to people working with maximum rainfall estimation. These increasing peaks have been wreaking havoc on Texas and the Eastern US this year. (Template statement - change as needed for individual stations)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce smoothed plots to get a better understanding of the trends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title \"Smoothed 24 hour max rainfall from 1896 to 2014\""
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rollSmall = runmean(data$Max.PRCP., 300)\n",
    "rollLarge = runmean(data$Max.PRCP., 900)\n",
    "plot(rollSmall, type=\"l\", ylim = c(120,160), xlab = \"Time (months)\", \n",
    "    ylab = \"Rolling Average\", col = 2, main=\"Smoothed 24 hour max rainfall from 1896 to 2014\")\n",
    "    points(rollLarge, type=\"l\", col=4)\n",
    "    legend(0,160, c(\"300 window\",\"\", \"900 window\"), col=c(2,0,4), lty=c(1,0,1), bty=\"n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rollSmall = runmean(data$Max.PRCP., 300)\n",
    "rollLarge = runmean(data$Max.PRCP., 900)\n",
    "plot(rollSmall, type=\"l\", ylim = c(120,160), xlab = \"Time (months)\", \n",
    "    ylab = \"Rolling Average\", col = 2, main=\"Smoothed 24 hour max rainfall from 1896 to 2014\")\n",
    "    points(rollLarge, type=\"l\", col=4)\n",
    "    legend(0,160, c(\"300 window\",\"\", \"900 window\"), col=c(2,0,4), lty=c(1,0,1), bty=\"n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the data shows a slight decrease in average rainfall at the tail end of our data (2014), the long term trend shows that average rainfall has been increasing. Empirically, we have had a wet year in 2016 that we would expect to match/exceed the long term observed increase in average maximum rainfall.(Template statement - change as needed for individual stations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 2: Parameter Estimation, Distribution, and Trends"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mle = data.frame(alpha = double(),\n",
    "                 theta = double(),\n",
    "                 KS = double(),\n",
    "                 KStest = character(),\n",
    "                 CvM = double(),\n",
    "                 CvMtest = character(),\n",
    "                 AD = double(),\n",
    "                 ADtest = character(),\n",
    "                 stringsAsFactors = FALSE)\n",
    "                \n",
    "for (i in 1:length(max_PRCP)) {\n",
    "\n",
    "    testDist = na.omit(max_PRCP[,i])\n",
    "        \n",
    "        for(j in 1:length(testDist)){\n",
    "            if(testDist[j] < .1){\n",
    "            testDist[j]=.0001\n",
    "            }\n",
    "        }\n",
    "\n",
    "   gamma1 = fitdist(as.vector(testDist),\"gamma\",method = \"mle\")\n",
    "   mle[i,1] = gamma1$estimate[1]\n",
    "   mle[i,2] = gamma1$estimate[2]\n",
    "   \n",
    "   gof = gofstat(gamma1)\n",
    "   mle[i,3] = gof$ks\n",
    "   mle[i,4] = gof$kstest\n",
    "   mle[i,5] = gof$cvm\n",
    "   mle[i,6] = gof$cvmtest\n",
    "   mle[i,7] = gof$ad\n",
    "   mle[i,8] = gof$adtest\n",
    "}\n",
    "\n",
    "mle[\"invTheta\"] = 1/(mle$theta)\n",
    "mle[\"mean\"] = mle$invTheta*mle$alpha\n",
    "mle[\"var\"] = mle$alpha*(mle$invTheta^2)\n",
    "mle[\"sd\"] = sqrt(mle$var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the estimated distributions over time and create a gif (done in R/windows)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display one pane of the gif - change per station\n",
    "display_png(file = \"plots/baseRSlideShowFortCollins/0098plot.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check distribution of estimated means - should be approximately normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  mle$mean\n",
       "W = 0.98722, p-value = 0.3832\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shapiro.test(mle$mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obtain values for histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "meanSum = summary(mle$mean)\n",
    "meanDist = fitdistr(mle$mean,\"normal\")\n",
    "x = seq(meanSum[1],meanSum[6],length = 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAMAAACJuGjuAAAAOVBMVEX9/v0AAAAAAP9MTUxnaGd7e3uLjIuZmpmmpqat2OaxsrG7vLvFxsXOz87X2Nff4N/n6Ofu7+79/v0UCEn/AAAAE3RSTlP///////////////////////8Asn3cCAAAAAlwSFlzAAASdAAAEnQB3mYfeAAAIABJREFUeJztneuiqioURg/LS+7KSt//YY/iDRDFwIlT+8aPvVuFOIGRIhr8VwNAwH9HBwCuCcQCJEAsQALEAiRALEACxAIkQCxAAsQCJEAsQALEAiRALEACxAIkQCxAAsQCJEAsQALEAiRALEACxAIkQCxAAsQCJEAsQALEAiRALEACxAIkQCxAAsQCJEAsQALEAiRALEACxAIkQCxAAsQCJEAsQALEAiRALEACxAIkQCxAAsQCJEAsQALEAiRALEACM7FET1Z8xjcsyW6zrZbTmlu5Uq1xT4SY9i0j7eL8yNfe+S7wTZbWYIwMhMqegVpgKlZDObwxS/RKxGyrpbTzrQLq9N7GZYj1lC+fPMQyg4FYA2rJX/0btkTWN9Zra/g0oE5TId5msJl8mfEQywwGYg30Ba7Kpg0TR6LN72/5dBPWdjJfHoQ1mHnA0eLhKVYtjw7l9EZ1b7+G+bMev3bdq08qCu2I9UhFcvtoecn/ta26PZS39sRWTjsum33c1EOSLZEebN5FWcpX3YdVkYhk6CI+27fT7i/7LowDqVJQrVzqhp8mpuxhRGMNBmINTEUvu95M98Yn6cXIDEXS4a1+48xyFl0Qq08q8iFR0f2tNbuaaHYKaf54dFHe5Cv50RDqS91c/mXfhS6WWlC1XOqGrz7FTKx5MBBrYCp61VgzvnGT/dKqqcuHroiQH0zV2JOoednFysfEub6tesWpJbKKlct9JSIf2nIwo327eS+r6rrQxDR2oYulFtRSrpu6h7lYs2Ag1oBSdFUD0V1Ja7J1R6hK2aptzuZcUCbd5ZHeZMafZdsQVXPmEeMpt932ptW9JZER7PvRHo2aY8jj3X3YuVR1gqT9AMBYiPkujLCsBdU3fHZ/PZNZPrNg1jrvW1vEl3OI1Vbi0NHR2kIbkxj+LscjhPGp8uetOybIw8lt2rbSqtySyAj2/RHi3g5DfPq2bI5xveu5WSrrLoywrAXVN+x7UnJQwREMxBpZEOvenwn0sS3RN6Kpjrbpgljjth9r4jEfa6Lp43ejQtocmZL6PSbp6S5qP88iEyu7MN61FnTm3qyuFoKBWCNTifWzQTG01qe2tJCfWPVKYjOaZbGao5q8zpiJJU9bqfLHFrGsBV2I3CKWEQz6WCNT0Uv97FM9uyusrF4VSz2CbT5iJbY865VE08fv9oyUth2qt3E8aWnPVunt8bbGY5R4paDbj1hGMBBrZCp6Nu8vl7eFFpqqUY7/TH2sVouXtXnyhe6TVvdLiaZg3/2NuU899bHGLtIwFrd2UDSjtBV0FvlSH8sMBmKNDEV/5dqYQTp2iYcDR1VbxWrNaq8K77X8ahfyFuFUydNWSxd8Wt27rwo/Mrb2pN13w9prtpf8bxpfWz1i6VHOCzrbcLgqFDOxZsFArBGhoHzZmxbOPrJr2zSCvHQqartYHUnbOrfp73q+1Th22Q0O2Vt9IdEUbN31ipR8x1Gml9y86ERfFkuPUi+oVazlcax5MGp1Gn9SK8ZXLO3CaOjTygHpm9D7Wko15sq23XlBDlrbthqk0R+mMWrcnmgKtu4Oa8rhrOy3aJu3HyMXidTMvgsjSq2gdrH6PcxH3ufBQKyBodRZUY1vyP9ltyPrejxtN0Pr8igN8GjvqfU36t7tPbXnmMzcqrwl89uAZo1bE9Xqn+3wknpirormfJSXYwTJrR1fyhd3YUSpFtQuVrdFab0IMIKBWOBrqpXnPxgAsc6G6K5935k2uM8OiHU2pgsKZWCDHxDrbIxP1sjrA7ZArNNR3dtr3+TG+XgFsQAREAuQALEACRALkACxAAkQC5AAsQAJEAuQALEACRALkACxAAkQC5AAsQAJEAuQALEACRALkACxAAkQC5AAsQAJEAuQALEACRALkACxAAkQC5AAsQAJEAuQALEACRALkACxAAkQC5AAsQAJEAuQALEACRALkACxAAkQC5AAsQAJEAuQALEACRALkACxAAkQC5AAsQAJEAuQALEACRALkACxAAkQC5AAsVwIN0eHyBGI5UL8cwGxLEAsFxDLC4jlAmJ5AbFcQCwvIJYLiOUFxHIBsbyAWC4glhcQywXE8gJiuYBYXkAsFxDLC4jlAmJ5AbFcQCwvIJYLiOUFxHIBsbyAWC4glhcQywXE8gJiuYBYXkAsFxDLC4jlAmJ5AbFcQCwvIJYLiOUFxHIBsbyAWC4glhcQywXE8gJiuYBYXkAsFxDLC4jlAmJ5AbFcQCwvIJYLiOUFxHIBsbyAWC4glhcQywXE8gJiuYBYXkAsFxDLC4jlAmJ5ES7W1afghFheQCwXEMsLX7F+Z95giOWFr1ivBGJBrBW8T4VVLrJP++LSVtUQy5OAPtZTiGcNsSCWlZDO+ycTeQWxIJaNsKvCu0hKiHXxCvAjcLjhnV67515DLE+Cx7FuEOviFeAHbum4gFhe+Iv1uudyCCsvXjvGww+I5YWvWFWqDI9mu4bEDIjlha9YhUieb/nqUyai2C8gdkAsL3zFSsR7fP0WyT7BsARieeF/E3rpj6sBsbzAEcsFxPIioI9VynvQ6GNBLBveww2ZclWYVuanF3qmBmJ5ETCOVchxrCS/O8axTl7vEMuLCCPvJ693iOUFxHIBsbyAWC4glhe7iLXePz95vUMsLyCWC4jlBU6FLiCWFxDLBcTyAmK5gFheRHjQ7+T1DrG8iPCg38nrHWJ5EeFBv5PXO8TyIsJjMyevd4jlRYQH/U5e7xDLCxyxXEAsLyI86HfyeodYXhA96Kdy8nqHWF7gQT8XEMsLjLy7gFheQCwXEMsLiOUCYnkBsVxALC8glguI5QXEcgGxvIBYLiCWFxDLBcTyAmK5gFheQCwXEMsLiOUCYnkBsVzYxfprgVjLQCwXc7H+VCCWHYjlQtilml5DLBsQy4WYa2W+c3SIHIFYLoRukf3EeHSQ/IBYLsSqVtNx7Og4mQGxXAiXV00fC2bNgFguhEOr/qoQaulALBfC5VV/VQizNCCWC9F5tajVNI4FsxQglguxfrhSxIJZChDLhXB5pQyQwqwRiOXCpZV2SwdmDUAsB26vtFs6MKsHYjlwe6XfK4RZHRBrnb+/b5/HglkSiLXK3/diwSwJxFqjdeT7J0hhVg2xVpGGeDyaDLMg1irSD59n3iEWxFqh08PrxxQwC2It8hck1q+bBbGWGNzw+/nXz5sFsRYYzfD8XeGvmwWxFhi98P3BKsSi5pRiTVp4/xL6t80KFeuRiPSxnuSMYv3tItYvm+Ut1jsXyaO+X3P1L9UJ/7kbftosX7He0qhC3Kr6k4vVY9b5xNKMCJgU5JfN8hXr1i5zUnSL6FQiXUt6OrF0H0Jmm4FYX9Mt+CVy5Y/FpJ67OAxdh6BpjH7XrDCxnt058FqrfxkyBIr1q2b5nwpvw8pM1e1Sq3+ZLoRNvAaxvqRKxvOfWD9gnUys2TEmcEa/XzXLfxyrGHRKVo9X5xPLeCNYrN80CyPvOnMNQucghVhU/LhYP2pWwEKYd7kQpsiLEy+EKQz+/sx3BMTywrvznipVf95bOqY1ll8Rhk/H/ZNmBSw2/uzWsT/1YuOGNbZfp0IsL3zFSsR7fP0+7wDpbEpkCrF+0qywkXfbH/OknruIgSmWTZs9xPo9s3DEcni1h1i/eMgK6GOVH/nqOn0sOrF+0Czv4YZMuSpMK/NT7Xo9LEJS9NUB7NpALB8CxrEKOY6V5Pczj2NFEuv3zPrxkXdt2YkFbSCWDxBr9IpUrJ8zC2I5DlgQy49dxLrAONbKuhP7iPVrZkEsiEUCToUOr/YRa+nJiZOMyngAseKItb6PjbmcCYjl8Go/sRxmca4mD379Qb/eK4i1N3jQz9Xi+4nl2A99aWOCB/2cRxKI5QMem4ko1npfjr60MVHFSu+fzdtd6EE/19UaxPJBFat9AGarWxc6YkUUa3VYg760MVHFqp63zW5d50E/1/JeEMsLs4/1uqfb3Fp/0E+Fc43FFmvt1hF9aWNi6by/k8YVx7yi9WUe9HOvnwqxfJiLVWYbxqa+gXONRRdr5fEc+tLGxBCrujeHq7SsGrvyvXbBucbEhoV59xZr6YFC+tLGRBPr1Xbei+5yb7+77ZxrbMuKz/uKtfwINH1pY6KNYzUHq8fQD3fMpvYFnGtsy4rPO4u1+KMN+tLGRBvHykuKXTCusQ1eQSw/tHEsml0wrrFDxFr6YSx9cWOij7z3L5LdToMy2z0z25UtK4mTiGWdI4K+vDGxifXZ9zFZtjW2aYl6ArEWJh+hL3BMBrFK7fHr1ZUmvoVtjW1aop5CLPs8XPQFjsl4xFIf3EsdY+nfwbbGIBYh1j7WvnCtsfb3WAeJZZ2Skr7EMfnhH1NALEoGsdqjFdFv3JjWmPwB6VFiWcxiWk2+QCyIRcLPngq7X7wfJtbcLJ7V5A3EglgkaGI90rr+pDuPNvAUq5+i4zixZmaxrCZ/VLHKtm/VPj4qrj+OBbGIUcXKxLN+i7R+7vj4aM1TrGFOoQPFMs3iWE0BmAOk7/YXN9e/KoRY1Jhi5aL8AbHGSdCOFMswi2E1haCfCt9l++Do9U+FEIsco/MuxL09YO36JCm/GptmbTxULN0sftUUhD7c0P2mOX3uugt+NQax6PnFAVJlmtljxdLMYldNYUAsiEUCxIJYJGhi3dNfeLpBnXD9YLFUs7hVUyCqWPffeGwGYsVAFSvZMMeMB8xqTFsh4mixFLOYVVMov/fMO8SKgipWLkh+C82rxvQlbQ4XazKLVzUFo4r1SbJ9n8Tq4FVjECsOxuS2l++8G2twHS/WaBaragoHYkEsEn5sgNRcNJCBWINZnKppByAWxCJBF6vM5cN+2xeo2AKjGputcspBrN4sRtW0B5pYWde9EskGs6qbEFn/3NZpljyBWNFQxXqIrGodeYibc7sq6RYrlH+cRaz5sswsxOrM4lNNu6Df0qk6RzZcFRbt7Z/qkciHmCGWi98Wq5u/od4kVtIl+STp5zRiWdaR5yGWNItNNe2DPh131f8EzD2j3+BSlWUQawM/LVbfxyq3POWQjvcV0+znxQrOpJ3ulk017YN2VZj3X68Nv/6aOvgfkZ1DLItXXMT6d3Gx5DiWyDf9SKcYbSodt4C41BhnsRqzuFTTTviPvL/HVZw+tzOIZfMKYpHxO7d0eIv1zxreiVHEKm/tbymyYu9nsniIZW84iEXFKNZnWos323Sv8HXv+vq5y0SItSnJxcwaxKqSdv3L5sXnmW5ZUa5SFxxYv4pkIdZCs0EsKgaxCsWOrJ0ZxEEhkme3YuY5VrHnL5a4llmDWKmYzn+fDQNZiXiPr9/rhzgOYi01GsSiQp3nfWTDvcIv0kOsbUkWgzwlvmKd64i12GQQiwpfsZo+VtmdPM/QxzqHWJcyy1esOlOuCtPZD121O/v7RBrAcoNBLComsb514VXIcawkv7MfxzqLWFcyy1+szRwu1kpzQSwqfuBe4d95xLqQWT8h1vJnEIuKXcRiPY612lbcxLqOWRALYpFw+VPhekuxE+syZkEsiEXC1cVytBM/sa5ilr9Y53jQD2IdhK9YJ3nQz9VKDMW6iFm+Yp3kQT+IdRS+Yp3ksRmIdRS+Yp3jQT9nG3EU6xpmXfuIBbEOI6CPxf9BP3cLsRTrEmZ5DzesP+inArEg1jfwf9BvQ/vwFOsKZl155B1iHciFxdrSOkzFuoBZEAtikXBdsTa1DVexzm8WxIJYJFxWrG0tw1as05sFsSAWCVcVa2O78BXr7GZdWSzXpP4tjMQy+PubR3tETXpyUbHk132nBo+TyTzJtMD9mOSAmvQFYoUngVgWrilW1z85uVhzsyCWBsSCWCTEr47+gursYs3MglgaEAtikRC9OoYRoNOLZZoFsTQgFsQiIXZ1jEPW5xfLMAtiaUCsELFUsyCWRuTqmO6xXUCsfxBrGYgVkkQ1C2JpxK0O5aEAiHUgECs8Ce1+FLMglkbU6lCfYrqKWKNZEEsDYoUlgVgLxKwO7bHLi4g1mQWxNCAWxCIhYnXoz4lfRazRLIilEa86/iAWG64klrka02XEGsyCWBoRxTJ2TN7gO2YCsb4mVnXMfoh3HbF6syCWRqTqmC9LCLEO5EpizXZM3+D7ZeJIIs2CWBpxqsPyi/RrifUHsQwg1h5JpFgbiFLZG7iKWLYpNC4lVmvWllxiVPYWIFZ4Eohl4SJiWef8uZZYjVkQSwNiQaztfNFljFBW+yRlFxPLMv2MJRf6yt6Gr1gPiLVvJpvEcpt1erHqd7K+ruoEfVkXZlW8mlhbDlnnF6t+r6/5NQGxdkviNusCYjVnw7c7UR1BrKVpYCHWgVzhqvB3xHKfDCHWfizOWw2xDuT8Ys0flxl3HKnBI4rlNOsCYr3uciFMkRfHLoS5PNH+NcVaN+v0YlWpMoq1PvBAW9aVBRyuKJbrkHV6sQqRPLuLwmMXG18+EV5ULIdZpxcrUcYa3iJZS0os1sqOIzV4bLHWzDq9WNpdnONu6ayuZHRNsdYPWacXi8cRa+1EeFmxVs06vVhNH6v8yFdH9rHWl167rljLZp1erDpTrgrTyvw0zmPYjiX9rirW2iHr/GLVr0KOYyX5/bBxrF8Va8WsC4i1GbKyutYghVgHArHCk8QXa9ksiBWOc9FkiHUgu4h1yDjW+lCD3HGkBj9ArEWzIFYobq8uLpbdrGuJtY5HWd2/JP+zLfJuEqnBjxBrySyItb6Jq4q3/GAlWoMfItZCFUCs9U0cNfy37cebkZIcFIrVrAuIRfmgn6OS/zbOYxApyVGh2Mw6vVi0D/o5xTquNQ/czyyJxazTi0X7oN96JXez25E0lVeS40K5oFi0j82sVvIfxBqZmXV6sWgf9HOIRdlUHkkOFcsw6/RiHXfEGuY8J2oqjyRHhnI5sWgf9Fup5D+IpWGYdXqxHA/6qewq1njsh1gdxsnw/GKRPui3JhZ5U32d5NhQdLMuINZm9hRLWW2Urqm+TXJwKBDri00WavYPYllgudD9qcRSj/pHt+YB+1kWi+FC92cSS+tNHN2aB+xnMQnHhe7PJVa0pvoqyfGhTGZBrPVN7LUXsam+ScIgFIi1cRNr3UGs5Y/YLRt9GrHMu2IcWpNRKOMNif3bz4+ziDW/20rdVNuTsAjlj9kirOcRK3pTbU7CI5Q/XouwnkQsyxNt9E21NQmTUCDWhk1mdQax3ElYre57CrGsvxqI0VTbknAJRf7GZP/28+MMYtl/5xSjqbYlYRNK+6u4/dvPjxOItfDLzChNtSkJn1A2zDsQiyPEcv82XuiVdWBTnUustrKYqHWIWN/U4OLsF3u0w+XE4mMWc7H+FidpYNSajEJpOu9MzOIt1rJXnFqTUSjtVSEPs1iLtTrv9D7tsEcSRqHI4QYWZnEWa3WuIkatySiUbhyLg1mMxXIsGrNPO+yRhFEo/QApA7P4iuWYW41RazIKZRh5P/7ikK1YzhUf92mHPZIwCmW8pXO4WVzFcs4Fyag1GYWi3Cs82CyeYq0MM+zcDnskYRSKehP6WLNYirXBK06tySgU7emGQ83iKBarKZFPLNahZvET64/XlMhnFutIs9iJ9cdsSuRTi3XgxSE3sdhNMHpusY4zi5dYQ6+dVVOx2Y+PWIepxUqs8WqQVVOx2Y+fWNKs+GrxEetPGWRg1VRs9uMp1jFqcRHrT/WKV1Ox2Y+3WEecD5mIZQyJsmoqNvsJECu+WizEmo20s2oqNvsJEiv2+fCI1b/M+pnfwWHVVGz2EyZWZLWOWP1Lrx/bjUFWTcVmP6FiRVXriNW/1Pr5s3nFq6nY7CdcrIhqHbGWzlQ/dq2YNRWb/ewhVjS1jlj9a6ifJa2YNRWb/ewjViS1jjpi/f0ta8WsqdjsZyexmk6xrPuVGQ48hDA5YvUv4dCKWVOx2c9eYrXpVuv/SLFCVv9al2rHSo6UhFEom8VaPWccKlbA6l+neqD9smKNas2b41ixNhM228wJkjAK5SuxWqxqQSweSRiF8rVYElOtg0+Fu93SIavkSEkYheInlnpW3Gvq5eNv6RBWcqQkjELxFUtTa5dBrqNv6ZBWcqQkjELxF2vgaLH2uaVDXMmRkjAKJVysjZk4OfKWDnklR0rCKJTzi4UjFstQzi9W2C2dSJUcKQmjUM4vluOWzuotzQ3zvIND8ZVCIcItHfCLRBh5B78IxAIkQCxAwi5i7dLbA5cCYgEScCoEJEAsQALEAiREeNAP/CIRHvQDv0iEB/3ALxLhsRnwi0R40M+yLeCNpxQqRxyxdhlO3WdM9mqh8ClQhAf9ZrAp/PVC4VOgCHM3zGBT+OuFwqdARzzox6bw1wuFT4GOGHlnU/jrhcKnQBCLSSaccoFYPHJhFAqfAkEsJplwygVi8ciFUSh8CgSxmGTCKReIxSMXRqHwKRDEYpIJp1zOKhb4ASAWIAFiARIgFiABYgESIBYgAWIBEiAWIAFiARIgFiABYgESIBYgAWIBEiAWIAFiARIgFiAhllgPMX9ZJCIpvvkR9bjlIx23/DqTMZfqJsTtHRpKw0t4ZjLmos7F4Z9L/W5L9PHLpc9Emxfk+1AmIon1nmYwGV92P9JPPTIp5JZJ5ZPJlEsiN32HhdJQJd1r/1DeSmMGFKgMqJYhk8GrxCsUhThivZOxIcaXL5G82782/0B/3PItblX7Fbt5ZDLlUrTbFyIPCqUl714HhPKWUdSBudRJs2mVtzO0hBWoVfTlE4pKFLEeIhvinl4Womz+fYr715nkw5fr+0yUXBJR9ZkEhCI3688b/qE8po0CcnnKSX+q9mATVKD2GJz7hKIRRaymxEPc08tctL0B5cu6PZP+DfF9JrNc5DE/JJTP0CYBoTzEY3gzIJfbNGVZYN3m8jv3dSgaUcR6T5P+TS/1/77KRFK1c+p+m4mZSyGbNCSUTHy61wGh5KK8Nd3kwFxSUd8T2UsIrNu38AtFI9ZVoRKep1hm2kd7pPYpvHYW863CIe1dPGtPsWpFLEkWlosQ+dDtDqvb7oD1q2J9ZD8gTKxHnsgehH8o8kQRLJZo7KwrefQMyqXtvN/aEgXV7bu9qql/VawqyTwz0RPfPFtzOP20F/fBYnVU7ZV9kFhtH+vjmcuUtuu0n1esJEisLPXNxGzNJCCUm2yD7nVwKPKvgFyU/4Lqtt/YK5SJ48TqLjo+31x0TJdiafbxzWTx2tIjFHUC68NCmSo0JJcxlPEy0CeUiePEustve/nNjMtDJuW4yIpHJtMRs+2iyjOHdyiqWDuEkgfl0m36aesmoG6nsQ+fUCaOE8tjYLff8jMt3uMzOtznIkfeq7ytRv9QlNdBoRSy814G5fJpZ69uOu/PsALlw3DYCUbea5tYdTpeY3+ZyU25Ufp9JuP+k2lT71DU1/6hVF0oRVguzSFmjwKlohpffR3KxIFiVfLmuUcm6h347zOZQmk2TR9hoaivA0KpQkKZYimzYdOAAk0l8whlAs9jARIgFiABYgESIBYgAWIBEiAWIAFiARIgFiABYgESIBYgAWIBEiAWIAFiARIgFiABYgESIBYgAWIBEiAWIAFiARIgFiABYgESIBYgAWIBEiAWIAFiARIgFiABYgESIBYgAWIBEiAWIAFiARIgFiABYgESqMVSp39VKLvP1rctl7IcXyb5o5s9+fPIE6/42kULp0nrqke7uEP+WNlgI0qxZbxqWfR9mmwpk9cU2X1AmTmnqJGZGd1YhO84RqxUnXJ/iXThY23WyX4VhZtp7lZakcblrcpkWK3v45WZgiGWVhZtn7YtnWUKEUuYs9UamZnRsRVr+7sbE2lipd2XOkk9xRJicqhsmrSt9Fcu/A5/Wr7Lf6r7tG0ZWqb1kArHdLVmdD8qViEnj343//uKNb1OxHDCuonQs+G6WOtbhpbJEZIjV/PjM4hVZs0pvuwPymPId5Hc5XK88sxeNodiOVXveP5sF4Du27lI9JX1hCilAg/x7N+dEo8Ztd/BXO5jpEmVPoZ9DNk9pzUYPsXLyEGPcjlqS7mbl+puxn0OQTTvVOm071mZxrwzeRJ7NWdKW80NSxpYotNDMnLtN+mraIjO/Lj+lphiPbqoH7pYcnbyMusnOu/mKm9fDfWfT7ONy0S51maVbJF8WDRwSjxl1KSSfafJrGxIpYmVG50PLQc9yuWoLeVeEGsMopZlKqbkepmmvD/yDJ0klbXmVLH0T/SQinn1KFXURzf7eFtrK0TrvNftqebdHhdSvRKyqjVO/pu0fz/lOoL1+M1qP6qy9iz17JdK0NpMdoubLbtrrymxlpHMfVw1e8jnWZsCGKGbOShRLkZtlLu2tIz8QwlC5rNYJiXvdonfe7eFLYalOjWb4m0WTqsic6cnEEuMfRi1El710GGcwlfE6lZllF/i7pBS6i4UzZvD2UFNrGX00nLP+0ViMu3d4eUU7zyHIcqVqI1y15aW6UMdg9Cv08wyqXln4iHy2h6Dq06HkLJ3reeqbmKpEbZiTa+bU37+fk/v6tUx/Psp75lSQsXMseXV3J/9t7jfRNFilpERk7UaNbGsOTiinpfbLpYShN5sZpnUvJuTo0WkuVhmdNNu02T4cmuFUxKbOz2BWO2Sxd0Y0UolZNo33S1Wu2JT1tT2TKx5RkZMplhqH2slB0fU83J/L5ZWJi3vQhgd6m/Feg2jCXrhZmLZPv6KyMMNZZGafawpVfvvrblSKj9WH+xitWuyjV0M5aOVjBbEevYDk45QHFHPy/29WFqZ1LzDj1jN1ye3VI8plvXjr4g/jrVeCfKV2pr52DHrX76MuroJuUCcfFdJPMto2mzo3uS1Ht80jlVZQ9kU9bzcdrGUIOZiqWVS886bPlZWr8Twcor1HjrvWuFMsawff0VMsdLuUkMesZa/d6/6PZzc20Ty6qmWfdbSdlXYXrsMF0pqYi0jPZKFq8L2siCXI0WF6I4X1hwcUc/L3SX4GJ+s7t8zAAABXUlEQVRpV4VmjallUvJ+NifC+7CItRlD2nxQZU6x+kOWUbi5WJaPvyLmvcJn9+IlV8JL7NVTCCNRf7aXd+/kKNXNqKv+9NC9OyVWMppV8TSEpFfZa7hXKE+KCzk4olYiU172ZVE/U8ex9BrTyzTlXSVyHKvvfJkxyFHC3C1WJQ9ZRuFMsawff0XUm9By5F0eE9Ilsdpbr9lLniG6RHKEWty6L/x9NvJetzWdjFkoiaeMZlVcP8blAY0qe+aNW9m925s9B0fUamTTy6Es6mdjEHOxtDKNed/6kffMHkNTOTf7J3pIhQxTL5wplvXjr8DzWIAEiAVIgFiABIgFSIBYgASIBUiAWIAEiAVIgFiABIgFSIBYgASIBUiAWIAEiAVIgFiABIgFSIBYgASIBUiAWIAEiAVIgFiABIgFSIBYgASIBUiAWIAEiAVIgFiABIgFSIBYgASIBUiAWICE/wGf5yFwrGCiNwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Distribution of Mean using MLE\""
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# distribution of mean parameter\n",
    "hist(mle$mean, freq = FALSE, col = \"light blue\", main = \"Distribution of Mean using MLE\", \n",
    "     xlab = \"Estimated Mean of Gamma Fit for Maximum Rainfall\")\n",
    "\n",
    "# normal fit using estimated parameters\n",
    "curve(dnorm(x,meanDist$estimate[1],meanDist$estimate[2]), col=\"blue\", lwd=2,add=TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the mean over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "time = seq(1896, 2005)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "meanTS = ts(mle$mean, start=c(firstYear))\n",
    "reg = lm(mle$mean ~ time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>time:</strong> 0.164"
      ],
      "text/latex": [
       "\\textbf{time:} 0.164"
      ],
      "text/markdown": [
       "**time:** 0.164"
      ],
      "text/plain": [
       " time \n",
       "0.164 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "round(reg$coefficients[2],3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>time:</strong> 18.04"
      ],
      "text/latex": [
       "\\textbf{time:} 18.04"
      ],
      "text/markdown": [
       "**time:** 18.04"
      ],
      "text/plain": [
       " time \n",
       "18.04 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(mle$mean)*round(reg$coefficients[2],3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title \"Fitted Gamma Distribution Means over time\""
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(meanTS, type=\"l\", col=\"red\", lwd = 1.75,\n",
    "     xlab = \"Time (year)\", ylab = \"Estimated Mean of Gamma Fit\", \n",
    "     main = \"Fitted Gamma Distribution Means over time\")\n",
    "abline(reg, col=\"blue\", lwd=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameter estimation looks good since it matches the smoothed averages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repeat for the variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  mle$var\n",
       "W = 0.98731, p-value = 0.3887\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shapiro.test(mle$var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "varSum = summary(mle$var)\n",
    "varDist = fitdistr(mle$var,\"normal\")\n",
    "x = seq(varSum[1],varSum[6],length = 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title \"Distribution of Variance using MLE\""
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# distribution of mean parameter\n",
    "hist(mle$var, freq = FALSE, col = \"light blue\", main = \"Distribution of Variance using MLE\", \n",
    "     xlab = \"Estimated Variance of Gamma Fit for Maximum Rainfall\")\n",
    "\n",
    "# normal fit using estimated parameters\n",
    "curve(dnorm(x,varDist$estimate[1],varDist$estimate[2]), col=\"blue\", lwd=2,add=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "varTS = ts(mle$var, start=c(firstYear))\n",
    "reg = lm(mle$var ~ time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>time:</strong> -0.289"
      ],
      "text/latex": [
       "\\textbf{time:} -0.289"
      ],
      "text/markdown": [
       "**time:** -0.289"
      ],
      "text/plain": [
       "  time \n",
       "-0.289 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "round(reg$coefficients[2],3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>time:</strong> -31.79"
      ],
      "text/latex": [
       "\\textbf{time:} -31.79"
      ],
      "text/markdown": [
       "**time:** -31.79"
      ],
      "text/plain": [
       "  time \n",
       "-31.79 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(mle$var)*round(reg$coefficients[2],3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title \"Fitted Gamma Distribution Variances over time\""
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(varTS, type=\"l\", col=\"red\", lwd = 1.75,\n",
    "     xlab = \"Time (year)\", ylab = \"Estimated Variance of Gamma Fit\", \n",
    "     main = \"Fitted Gamma Distribution Variances over time\")\n",
    "abline(reg, col=\"blue\", lwd=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case the distributions aren't making sense, check the number of times the Gamma distribution fit passed the KS test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "not rejected     rejected \n",
       "          92           18 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table(mle$KStest)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.3.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}