Hurricane Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hurricane Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Fetching the data and cleaning:\n",
    "\n",
    "First, the data of the category 4 and category 5 hurricane present in the tabular form in Wikipedia is extracted, cleaned and stored in the data frame format. <br/>\n",
    "\n",
    "Category 4 - https://en.wikipedia.org/wiki/List_of_Category_4_Atlantic_hurricanes\n",
    "\n",
    "Category 5 - https://en.wikipedia.org/wiki/List_of_Category_5_Atlantic_hurricanes\n",
    "\n",
    "After few preliminary formatting and cleaning, data is now ready for some Analysis.<br/>\n",
    "\n",
    "Code for extracting the data, cleaning and formatting can be found below - \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: xml2\n",
      "\n",
      "Attaching package: 'dplyr'\n",
      "\n",
      "The following objects are masked from 'package:data.table':\n",
      "\n",
      "    between, first, last\n",
      "\n",
      "The following objects are masked from 'package:stats':\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "The following objects are masked from 'package:base':\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n",
      "Loading required package: MASS\n",
      "\n",
      "Attaching package: 'MASS'\n",
      "\n",
      "The following object is masked from 'package:dplyr':\n",
      "\n",
      "    select\n",
      "\n",
      "Loading required package: survival\n",
      "Loading required package: npsurv\n",
      "Loading required package: lsei\n",
      "-- Attaching packages --------------------------------------- tidyverse 1.2.1 --\n",
      "v ggplot2 3.0.0     v readr   1.1.1\n",
      "v tibble  1.4.2     v purrr   0.2.5\n",
      "v tidyr   0.8.1     v stringr 1.3.1\n",
      "v ggplot2 3.0.0     v forcats 0.3.0\n",
      "-- Conflicts ------------------------------------------ tidyverse_conflicts() --\n",
      "x dplyr::between()        masks data.table::between()\n",
      "x dplyr::filter()         masks stats::filter()\n",
      "x dplyr::first()          masks data.table::first()\n",
      "x readr::guess_encoding() masks rvest::guess_encoding()\n",
      "x dplyr::lag()            masks stats::lag()\n",
      "x dplyr::last()           masks data.table::last()\n",
      "x purrr::pluck()          masks rvest::pluck()\n",
      "x MASS::select()          masks dplyr::select()\n",
      "x purrr::transpose()      masks data.table::transpose()\n"
     ]
    }
   ],
   "source": [
    "# Loading the libraries\n",
    "library(rvest)\n",
    "library(data.table)\n",
    "library(dplyr)\n",
    "library(fitdistrplus)\n",
    "#library(plyr)\n",
    "library(tidyverse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"'html' is deprecated.\n",
      "Use 'read_html' instead.\n",
      "See help(\"Deprecated\")\"Warning message:\n",
      "\"'html' is deprecated.\n",
      "Use 'read_html' instead.\n",
      "See help(\"Deprecated\")\""
     ]
    }
   ],
   "source": [
    "#Fetching the Category 5\n",
    "scotusURL <- \"https://en.wikipedia.org/wiki/List_of_Category_5_Atlantic_hurricanes\"\n",
    "\n",
    "temp <- scotusURL %>% \n",
    "  html %>%\n",
    "  html_nodes(\"table\")\n",
    "\n",
    "Hurricane_Cat5 <- html_table(temp[2])[[1]] ## The table we're interested in\n",
    "\n",
    "\n",
    "#Fetching the Category 4\n",
    "scotusURL <- \"https://en.wikipedia.org/wiki/List_of_Category_4_Atlantic_hurricanes\"\n",
    "\n",
    "temp <- scotusURL %>% \n",
    "  html %>%\n",
    "  html_nodes(\"table\")\n",
    "\n",
    "Hurricane_Cat4_1 <- html_table(temp[2],fill = T)[[1]] ## The table we're interested\n",
    "Hurricane_Cat4_2 <- html_table(temp[3],fill = T)[[1]] ## The table we're interested\n",
    "Hurricane_Cat4_3 <- html_table(temp[4],fill = T)[[1]] ## The table we're interested\n",
    "Hurricane_Cat4_4 <- html_table(temp[5],fill = T)[[1]] ## The table we're interested\n",
    "Hurricane_Cat4_5 <- html_table(temp[6],fill = T)[[1]] ## The table we're interested"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cleaning and formating the data obtained for Category 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n<-dim(Hurricane_Cat4_1)[1]\n",
    "Hurricane_Cat4_1<-Hurricane_Cat4_1[2:(n-1),]\n",
    "\n",
    "n<-dim(Hurricane_Cat4_2)[1]\n",
    "Hurricane_Cat4_2<-Hurricane_Cat4_2[2:(n-1),]\n",
    "\n",
    "n<-dim(Hurricane_Cat4_3)[1]\n",
    "Hurricane_Cat4_3<-Hurricane_Cat4_3[2:(n-1),]\n",
    "\n",
    "n<-dim(Hurricane_Cat4_4)[1]\n",
    "Hurricane_Cat4_4<-Hurricane_Cat4_4[2:(n-1),]\n",
    "\n",
    "n<-dim(Hurricane_Cat4_5)[1]\n",
    "Hurricane_Cat4_5<-Hurricane_Cat4_5[2:(n-1),]\n",
    "\n",
    "#Getting the 5th one into format\n",
    "Hurricane_Cat4_5$`Maximumsustained winds` <- as.numeric(substr(\n",
    "    Hurricane_Cat4_5$`Maximumsustained winds`,1,3))\n",
    "\n",
    "Hurricane_Cat4_5$`Minimum pressure` <- as.numeric(substr(\n",
    "    Hurricane_Cat4_5$`Minimum pressure`,1,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating the Category 4 master table \n",
    "\n",
    "Huri_Cat4 <- rbindlist( list(Hurricane_Cat4_1[, c(1,2,3,6,7)],  \n",
    "                             Hurricane_Cat4_2[, c(1,2,3,6,7)], \n",
    "                             Hurricane_Cat4_3[, c(1,2,3,6,7)],\n",
    "                             Hurricane_Cat4_4[, c(1,2,3,6,7)],  \n",
    "                             Hurricane_Cat4_5[, c(1,3,4,5,6)]))\n",
    "\n",
    "Huri_Cat4$mon <- gsub(\"([A-Za-z]+).*\", \"\\\\1\", Huri_Cat4$Month)\n",
    "Huri_Cat4$Min_pressure <- gsub(\"([0-9]+)\", \"\\\\1\", Huri_Cat4$'Minimum pressure')\n",
    "Huri_Cat4$year <- as.numeric(Huri_Cat4$Season)\n",
    "\n",
    "colnames(Huri_Cat4)[c(4,7)] <- c('Max_Wind', 'Min_Pressure')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cleaning and formating the data obtained for Category 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Clearning and Prer the Category 5 Huricane table\n",
    "n<-dim(Hurricane_Cat5)[1]\n",
    "Hurricane_Cat5<-Hurricane_Cat5[1:(n-1),]\n",
    "\n",
    "Hurricane_Cat5$`Duration(hours)` <- substr(Hurricane_Cat5$`Duration(hours)`, 21,24)\n",
    "Hurricane_Cat5$`Sustainedwind speeds`<- substr(Hurricane_Cat5$`Sustainedwind speeds`,1,3)\n",
    "Hurricane_Cat5$Pressure<- substr(Hurricane_Cat5$Pressure,21,24)\n",
    "Hurricane_Cat5$Deaths<- substr(Hurricane_Cat5$Deaths,21,30)\n",
    "\n",
    "Hurricane_Cat5$mon <- gsub(\"([A-Za-z]+).*\", \"\\\\1\", Hurricane_Cat5$`Dates as aCategory 5`)\n",
    "Hurricane_Cat5$year <- gsub(\"[A-Za-z]+.+,\", \"\\\\1\", Hurricane_Cat5$`Dates as aCategory 5`)\n",
    "Hurricane_Cat5$year <- as.numeric(gsub(\"([0-9]+).*$\", \"\\\\1\", Hurricane_Cat5$year))\n",
    "\n",
    "colnames(Hurricane_Cat5)[c(4,5)] <- c('Max_Wind', 'Min_Pressure')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Creating the decade variable \n",
    "Huri_Cat4$Decade <- Huri_Cat4$year - Huri_Cat4$year %% 10\n",
    "Hurricane_Cat5$Decade <- Hurricane_Cat5$year - Hurricane_Cat5$year %% 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Counting the frequencies of Huricane Data and Plotting them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Decade</th><th scope=col>count</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1850</td><td> 2  </td></tr>\n",
       "\t<tr><td>1860</td><td> 1  </td></tr>\n",
       "\t<tr><td>1870</td><td> 1  </td></tr>\n",
       "\t<tr><td>1880</td><td> 4  </td></tr>\n",
       "\t<tr><td>1890</td><td> 4  </td></tr>\n",
       "\t<tr><td>1900</td><td> 2  </td></tr>\n",
       "\t<tr><td>1910</td><td> 6  </td></tr>\n",
       "\t<tr><td>1920</td><td> 6  </td></tr>\n",
       "\t<tr><td>1930</td><td>10  </td></tr>\n",
       "\t<tr><td>1940</td><td> 9  </td></tr>\n",
       "\t<tr><td>1950</td><td>14  </td></tr>\n",
       "\t<tr><td>1960</td><td>10  </td></tr>\n",
       "\t<tr><td>1970</td><td> 5  </td></tr>\n",
       "\t<tr><td>1980</td><td> 7  </td></tr>\n",
       "\t<tr><td>1990</td><td>12  </td></tr>\n",
       "\t<tr><td>2000</td><td>14  </td></tr>\n",
       "\t<tr><td>2010</td><td>13  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " Decade & count\\\\\n",
       "\\hline\n",
       "\t 1850 &  2  \\\\\n",
       "\t 1860 &  1  \\\\\n",
       "\t 1870 &  1  \\\\\n",
       "\t 1880 &  4  \\\\\n",
       "\t 1890 &  4  \\\\\n",
       "\t 1900 &  2  \\\\\n",
       "\t 1910 &  6  \\\\\n",
       "\t 1920 &  6  \\\\\n",
       "\t 1930 & 10  \\\\\n",
       "\t 1940 &  9  \\\\\n",
       "\t 1950 & 14  \\\\\n",
       "\t 1960 & 10  \\\\\n",
       "\t 1970 &  5  \\\\\n",
       "\t 1980 &  7  \\\\\n",
       "\t 1990 & 12  \\\\\n",
       "\t 2000 & 14  \\\\\n",
       "\t 2010 & 13  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Decade | count | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1850 |  2   | \n",
       "| 1860 |  1   | \n",
       "| 1870 |  1   | \n",
       "| 1880 |  4   | \n",
       "| 1890 |  4   | \n",
       "| 1900 |  2   | \n",
       "| 1910 |  6   | \n",
       "| 1920 |  6   | \n",
       "| 1930 | 10   | \n",
       "| 1940 |  9   | \n",
       "| 1950 | 14   | \n",
       "| 1960 | 10   | \n",
       "| 1970 |  5   | \n",
       "| 1980 |  7   | \n",
       "| 1990 | 12   | \n",
       "| 2000 | 14   | \n",
       "| 2010 | 13   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   Decade count\n",
       "1  1850    2   \n",
       "2  1860    1   \n",
       "3  1870    1   \n",
       "4  1880    4   \n",
       "5  1890    4   \n",
       "6  1900    2   \n",
       "7  1910    6   \n",
       "8  1920    6   \n",
       "9  1930   10   \n",
       "10 1940    9   \n",
       "11 1950   14   \n",
       "12 1960   10   \n",
       "13 1970    5   \n",
       "14 1980    7   \n",
       "15 1990   12   \n",
       "16 2000   14   \n",
       "17 2010   13   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count_4 <- group_by(Huri_Cat4, Decade)\n",
    "count_4 <- summarize(count_4, count = n())\n",
    "count_4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAOVBMVEUAAAAzMzNNTU1mzapo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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(Huri_Cat4, aes(x=Decade)) + \n",
    "geom_histogram(binwidth=5, color = \"black\", fill = \"aquamarine3\" )+\n",
    "#geom_smooth(method = \"loess\", se = FALSE)+\n",
    "labs(x = \"Decades\", y = \"Number of Hurricanes\", \n",
    "     title = \"Count of Category - 4 Hurricanes over the Decades\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Decade</th><th scope=col>count</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1920</td><td>2   </td></tr>\n",
       "\t<tr><td>1930</td><td>6   </td></tr>\n",
       "\t<tr><td>1950</td><td>2   </td></tr>\n",
       "\t<tr><td>1960</td><td>4   </td></tr>\n",
       "\t<tr><td>1970</td><td>3   </td></tr>\n",
       "\t<tr><td>1980</td><td>3   </td></tr>\n",
       "\t<tr><td>1990</td><td>2   </td></tr>\n",
       "\t<tr><td>2000</td><td>8   </td></tr>\n",
       "\t<tr><td>2010</td><td>3   </td></tr>\n",
       "\t<tr><td>1940</td><td>0   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " Decade & count\\\\\n",
       "\\hline\n",
       "\t 1920 & 2   \\\\\n",
       "\t 1930 & 6   \\\\\n",
       "\t 1950 & 2   \\\\\n",
       "\t 1960 & 4   \\\\\n",
       "\t 1970 & 3   \\\\\n",
       "\t 1980 & 3   \\\\\n",
       "\t 1990 & 2   \\\\\n",
       "\t 2000 & 8   \\\\\n",
       "\t 2010 & 3   \\\\\n",
       "\t 1940 & 0   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Decade | count | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1920 | 2    | \n",
       "| 1930 | 6    | \n",
       "| 1950 | 2    | \n",
       "| 1960 | 4    | \n",
       "| 1970 | 3    | \n",
       "| 1980 | 3    | \n",
       "| 1990 | 2    | \n",
       "| 2000 | 8    | \n",
       "| 2010 | 3    | \n",
       "| 1940 | 0    | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   Decade count\n",
       "1  1920   2    \n",
       "2  1930   6    \n",
       "3  1950   2    \n",
       "4  1960   4    \n",
       "5  1970   3    \n",
       "6  1980   3    \n",
       "7  1990   2    \n",
       "8  2000   8    \n",
       "9  2010   3    \n",
       "10 1940   0    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count_5 <- group_by(Hurricane_Cat5, Decade)\n",
    "count_5 <- summarize(count_5, count = n())\n",
    "count_5 <- rbind(count_5,c(1940,0))\n",
    "count_5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decade - 1940 has not seen any category 5 Hurricanes, so we have added the one row 1940 with 0 into count_5 table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAOVBMVEUAAAAzMzNNTU1mzapo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\nf+ghEMQVT5TFAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(Hurricane_Cat5, aes(x=Decade)) + \n",
    "geom_histogram(binwidth=5, color = \"black\", fill = \"aquamarine3\" )+\n",
    "#geom_smooth(method = \"loess\", se = FALSE)+\n",
    "labs(x = \"Decades\", y = \"Number of Hurricanes\",\n",
    "     title = \"Count of Category - 5 Hurricanes over the Decades\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Combine Cat4 and Cat5 at name and year, max speed, minimun pressure\n",
    "Master <- rbind(Huri_Cat4[,c(1,9,4,7)], Hurricane_Cat5[,c(1,12,4,5)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Decade</th><th scope=col>count</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1850</td><td> 2  </td></tr>\n",
       "\t<tr><td>1860</td><td> 1  </td></tr>\n",
       "\t<tr><td>1870</td><td> 1  </td></tr>\n",
       "\t<tr><td>1880</td><td> 4  </td></tr>\n",
       "\t<tr><td>1890</td><td> 4  </td></tr>\n",
       "\t<tr><td>1900</td><td> 2  </td></tr>\n",
       "\t<tr><td>1910</td><td> 6  </td></tr>\n",
       "\t<tr><td>1920</td><td> 8  </td></tr>\n",
       "\t<tr><td>1930</td><td>16  </td></tr>\n",
       "\t<tr><td>1940</td><td> 9  </td></tr>\n",
       "\t<tr><td>1950</td><td>16  </td></tr>\n",
       "\t<tr><td>1960</td><td>14  </td></tr>\n",
       "\t<tr><td>1970</td><td> 8  </td></tr>\n",
       "\t<tr><td>1980</td><td>10  </td></tr>\n",
       "\t<tr><td>1990</td><td>14  </td></tr>\n",
       "\t<tr><td>2000</td><td>22  </td></tr>\n",
       "\t<tr><td>2010</td><td>16  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " Decade & count\\\\\n",
       "\\hline\n",
       "\t 1850 &  2  \\\\\n",
       "\t 1860 &  1  \\\\\n",
       "\t 1870 &  1  \\\\\n",
       "\t 1880 &  4  \\\\\n",
       "\t 1890 &  4  \\\\\n",
       "\t 1900 &  2  \\\\\n",
       "\t 1910 &  6  \\\\\n",
       "\t 1920 &  8  \\\\\n",
       "\t 1930 & 16  \\\\\n",
       "\t 1940 &  9  \\\\\n",
       "\t 1950 & 16  \\\\\n",
       "\t 1960 & 14  \\\\\n",
       "\t 1970 &  8  \\\\\n",
       "\t 1980 & 10  \\\\\n",
       "\t 1990 & 14  \\\\\n",
       "\t 2000 & 22  \\\\\n",
       "\t 2010 & 16  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Decade | count | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1850 |  2   | \n",
       "| 1860 |  1   | \n",
       "| 1870 |  1   | \n",
       "| 1880 |  4   | \n",
       "| 1890 |  4   | \n",
       "| 1900 |  2   | \n",
       "| 1910 |  6   | \n",
       "| 1920 |  8   | \n",
       "| 1930 | 16   | \n",
       "| 1940 |  9   | \n",
       "| 1950 | 16   | \n",
       "| 1960 | 14   | \n",
       "| 1970 |  8   | \n",
       "| 1980 | 10   | \n",
       "| 1990 | 14   | \n",
       "| 2000 | 22   | \n",
       "| 2010 | 16   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   Decade count\n",
       "1  1850    2   \n",
       "2  1860    1   \n",
       "3  1870    1   \n",
       "4  1880    4   \n",
       "5  1890    4   \n",
       "6  1900    2   \n",
       "7  1910    6   \n",
       "8  1920    8   \n",
       "9  1930   16   \n",
       "10 1940    9   \n",
       "11 1950   16   \n",
       "12 1960   14   \n",
       "13 1970    8   \n",
       "14 1980   10   \n",
       "15 1990   14   \n",
       "16 2000   22   \n",
       "17 2010   16   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count <- group_by(Master, Decade)\n",
    "count <- summarize(count, count = n())\n",
    "count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAOVBMVEUAAAAzMzNFi3RNTU1o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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(Master, aes(x=Decade)) + \n",
    "geom_histogram(binwidth=5, color = \"black\", fill = \"aquamarine4\" )+\n",
    "#geom_smooth(method = \"loess\", se = FALSE)+\n",
    "labs(x = \"Decades\", y = \"Number of Hurricanes\", \n",
    "     title = \"Count of Category - 4 & 5 Hurricanes over the Decades\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Observation\n",
    "\n",
    "An interesting observation that can be seen here is the increase trend in the total number of hurricane per decade that we have seen since 1850."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating some Desciptive Statistics for the Category 4, Category 5 and master data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Category 4 Mean value -  7.05882352941176\"\n",
      "[1] \"Category 4 Varaince value -  20.4338235294118\"\n",
      "[1] \"Category 4 SD value -  4.52037869314195\"\n",
      "[1] \"Category 4 Median value -  6\"\n",
      "[1] \"Category 4 Max value -  14\"\n",
      "[1] \"Category 4 Min value -  1\"\n"
     ]
    }
   ],
   "source": [
    "# Calculating the parameters for category 4\n",
    "mean_4 = mean(count_4$count)\n",
    "var_4 = var(count_4$count)\n",
    "sd_4 = sd(count_4$count)\n",
    "med_4 = median(count_4$count)\n",
    "max_4 = max(count_4$count)\n",
    "min_4 = min(count_4$count)\n",
    "\n",
    "print(paste(\"Category 4 Mean value - \", mean_4))\n",
    "print(paste(\"Category 4 Varaince value - \", var_4))\n",
    "print(paste(\"Category 4 SD value - \", sd_4))\n",
    "print(paste(\"Category 4 Median value - \", med_4))\n",
    "print(paste(\"Category 4 Max value - \", max_4))\n",
    "print(paste(\"Category 4 Min value - \", min_4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Category 5 Mean value -  3.3\"\n",
      "[1] \"Category 5 Varaince value -  5.12222222222222\"\n",
      "[1] \"Category 5 SD value -  2.26323269290239\"\n",
      "[1] \"Category 5 Median value -  3\"\n",
      "[1] \"Category 5 Max value -  8\"\n",
      "[1] \"Category 5 Min value -  0\"\n"
     ]
    }
   ],
   "source": [
    "# Calculating the parameters for category 5\n",
    "mean_5 = mean(count_5$count)\n",
    "var_5 = var(count_5$count)\n",
    "sd_5 = sd(count_5$count)\n",
    "med_5 = median(count_5$count)\n",
    "max_5 = max(count_5$count)\n",
    "min_5 = min(count_5$count)\n",
    "\n",
    "print(paste(\"Category 5 Mean value - \", mean_5))\n",
    "print(paste(\"Category 5 Varaince value - \", var_5))\n",
    "print(paste(\"Category 5 SD value - \", sd_5))\n",
    "print(paste(\"Category 5 Median value - \", med_5))\n",
    "print(paste(\"Category 5 Max value - \", max_5))\n",
    "print(paste(\"Category 5 Min value - \", min_5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Category 4 & 5 Mean value -  9\"\n",
      "[1] \"Category 4 & 5 Varaince value -  40.875\"\n",
      "[1] \"Category 4 & 5 SD value -  6.39335592627221\"\n",
      "[1] \"Category 4 & 5 Median value -  8\"\n",
      "[1] \"Category 4 & 5 Max value -  22\"\n",
      "[1] \"Category 4 & 5 Min value -  1\"\n"
     ]
    }
   ],
   "source": [
    "# Calculating the parameters for category 4 and 5 clubbed together\n",
    "mean_all = mean(count$count)\n",
    "var_all = var(count$count)\n",
    "sd_all = sd(count$count)\n",
    "med_all = median(count$count)\n",
    "max_all = max(count$count)\n",
    "min_all = min(count$count)\n",
    "\n",
    "print(paste(\"Category 4 & 5 Mean value - \", mean_all))\n",
    "print(paste(\"Category 4 & 5 Varaince value - \", var_all))\n",
    "print(paste(\"Category 4 & 5 SD value - \", sd_all))\n",
    "print(paste(\"Category 4 & 5 Median value - \", med_all))\n",
    "print(paste(\"Category 4 & 5 Max value - \", max_all))\n",
    "print(paste(\"Category 4 & 5 Min value - \", min_all))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poisson distribution is popular for modelling the number of times an event occurs in an interval of time or space, let us consider modelling the data into Poisson Distribution. We can also consider negative binomial distribution as that can also be a good fit for the problem at hand."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each storm is considered as a point event in time, occurring independently. If λ is a measure of the historically based number of events per decade, then P(X = x | λ) defines the probability of having x events per year, which is given by the Poisson probability distribution function (PDF) –\n",
    "$$ P(x) = \\frac{\\lambda^x}{x!}\\ e^{-\\lambda} $$\n",
    "\n",
    "The parameter of the Poisson distribution λ can be estimated from data –\n",
    "$$ λ =  \\frac{\\sum_{i=1}^{N}x_i}{N} $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Parameters Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameter for Poisson distribution is estimated and results are presented below - "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"lamba value for category 4 hurricanes -  7.05882352941176\"\n"
     ]
    }
   ],
   "source": [
    "lambda_4 <- mean_4\n",
    "print(paste(\"lamba value for category 4 hurricanes - \",lambda_4 ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"lamba value for category 4 hurricanes -  3.3\"\n"
     ]
    }
   ],
   "source": [
    "lambda_5 <- mean_5\n",
    "print(paste(\"lamba value for category 4 hurricanes - \",lambda_5 ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"lambda value for category 4 & 5 hurricanes -  9\"\n"
     ]
    }
   ],
   "source": [
    "lambda <- mean_all\n",
    "print(paste(\"lambda value for category 4 & 5 hurricanes - \",lambda ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Density Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the calculated values of the lambda following density plots are obtained for the category 4, category 5 and combined hurricane distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAAAAAP9NTU1mzapo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\npQN4WWn0NawAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the poisson distribution for category 4\n",
    "plot(0:20, dpois( x=0:20, lambda=lambda_4 ), \n",
    "     xlim=c(-2,22),col = 'blue', lwd= 3, \n",
    "     xlab=\"No of Estimated Hurricanes\", ylab=\"Probability\")\n",
    "\n",
    "lines(0:20,dpois( x=0:20, lambda=lambda_4 ), \n",
    "      xlim=c(-2,22), col=\"aquamarine3\",lwd = 3 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAAAAAP9NTU1mzapo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\n8QAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the poisson distribution for category 5\n",
    "plot(0:15, dpois( x=0:15, lambda=lambda_5 ), \n",
    "     xlim=c(-2,17), col = 'blue', lwd= 3, \n",
    "     xlab=\"No of Estimated Hurricanes\", ylab=\"Probability\")\n",
    "\n",
    "lines(0:15,dpois( x=0:15, lambda=lambda_5 ), \n",
    "      xlim=c(-2,17), col=\"aquamarine3\", lwd = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAAAAAP9Fi3RNTU1o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\nEiCAkAABhAQI+A/IAwTNwZe9JQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the poisson distribution for category 4 & 5 together\n",
    "plot(0:30, dpois( x=0:30, lambda=lambda ), \n",
    "     xlim=c(-2,33), col = 'blue', lwd= 3, \n",
    "     xlab=\"No of Estimated Hurricanes\", ylab=\"Probability\")\n",
    "\n",
    "lines(0:30,dpois( x=0:30, lambda=lambda ), \n",
    "      xlim=c(-2,33), col=\"aquamarine4\", lwd = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nSUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Q-Q plot\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqcomp(fitdist(count$count, \"pois\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Q-Q plot does seem to be good fit, but for a Poisson Distribution, we have mean = variance, but does not seem to be the case with your distribution,\n",
    "\n",
    "For Category 4 and 5 together, we have \n",
    "\n",
    "    mean < variance \n",
    "    (9 < 40.875)\n",
    "    \n",
    "This could be a case of **OverDispered Poisson.**\n",
    "\n",
    "The negative binomial distribution, can be used as an alternative to the Poisson distribution. It is especially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such cases, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. Hence a Poisson distribution is not an appropriate model. Since the negative binomial distribution has one more parameter than the Poisson, the second parameter can be used to adjust the variance independently of the mean.\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Negative Binomial Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now look at the negative binomial distribution Q-Q plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nrkJggg==",
      "text/plain": [
       "Plot with title \"Q-Q plot\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqcomp(fitdist(count$count, \"nbinom\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Parameter Estimation\n",
    "\n",
    "Looks like the Negative binomial is better fit than the poisson distribution. Let us estimate the parameters for the negative binomical distribution NB(r,p). We need to calculate the r and p\n",
    "\n",
    "$$ r = \\frac{\\mu^{2}}{\\sigma^{2} - \\mu} $$\n",
    "\n",
    "\n",
    "$$ p = \\frac{\\sigma^{2} - \\mu}{\\sigma^{2}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 2.541176\n"
     ]
    }
   ],
   "source": [
    "r = mean_all*mean_all / (var_all - mean_all)\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 0.7798165\n"
     ]
    }
   ],
   "source": [
    "p = (var_all-mean_all )/ var_all \n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAAAAAP9Fi3RNTU1o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\nSICA/00fGNVFa+RfAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the poisson distribution for category 4 & 5 together\n",
    "plot(0:45, dnbinom( x=0:45, mu = mean_all, size = r), \n",
    "     xlim=c(-2,48), col = 'blue', lwd= 3, \n",
    "     xlab=\"No of Estimated Hurricanes\", ylab=\"Probability\")\n",
    "\n",
    "lines(0:45,dnbinom( x=0:45, mu = mean_all, size = r),\n",
    "      xlim=c(-2,48), col=\"aquamarine4\", lwd =3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non-homogenous Poisson Distribution\n",
    "\n",
    "As mentioned earlier, we have noticed an increase in hurricanes over time, we now try to look at some other approach that addresses this effect.\n",
    "\n",
    "Earlier we observed that the Hurricane data was not fitting a Poisson distribution as the parameter ${\\lambda}$ was constant. Now we try to implement poisson distribution with varying ${\\lambda}$ and make observations.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"Unknown or uninitialised column: 'lambda_curr'.\""
     ]
    }
   ],
   "source": [
    "#Caluclating lambda with respect to past hurricanes with that particular decade\n",
    "sum = 0\n",
    "for (i in c(1:nrow(count))){\n",
    "    sum = sum + count$count[i]\n",
    "    count$lambda_curr[i] <- sum/i\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAAAAAP9Fi3RNTU1o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\nIICQIICQIICQIICQIICQIICQIMB/zYHbb53Rlf4AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plotting the lambda value\n",
    "plot(count$Decade,count$lambda_curr,  col = 'blue', \n",
    "     lwd= 3, xlab=\"Value of Lambda vs Time\", ylab=\"Lambda\")\n",
    "\n",
    "lines(count$Decade,count$lambda_curr, col=\"aquamarine4\", lwd =3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Decade</th><th scope=col>count</th><th scope=col>lambda_curr</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1850    </td><td> 2      </td><td>2.000000</td></tr>\n",
       "\t<tr><td>1860    </td><td> 1      </td><td>1.500000</td></tr>\n",
       "\t<tr><td>1870    </td><td> 1      </td><td>1.333333</td></tr>\n",
       "\t<tr><td>1880    </td><td> 4      </td><td>2.000000</td></tr>\n",
       "\t<tr><td>1890    </td><td> 4      </td><td>2.400000</td></tr>\n",
       "\t<tr><td>1900    </td><td> 2      </td><td>2.333333</td></tr>\n",
       "\t<tr><td>1910    </td><td> 6      </td><td>2.857143</td></tr>\n",
       "\t<tr><td>1920    </td><td> 8      </td><td>3.500000</td></tr>\n",
       "\t<tr><td>1930    </td><td>16      </td><td>4.888889</td></tr>\n",
       "\t<tr><td>1940    </td><td> 9      </td><td>5.300000</td></tr>\n",
       "\t<tr><td>1950    </td><td>16      </td><td>6.272727</td></tr>\n",
       "\t<tr><td>1960    </td><td>14      </td><td>6.916667</td></tr>\n",
       "\t<tr><td>1970    </td><td> 8      </td><td>7.000000</td></tr>\n",
       "\t<tr><td>1980    </td><td>10      </td><td>7.214286</td></tr>\n",
       "\t<tr><td>1990    </td><td>14      </td><td>7.666667</td></tr>\n",
       "\t<tr><td>2000    </td><td>22      </td><td>8.562500</td></tr>\n",
       "\t<tr><td>2010    </td><td>16      </td><td>9.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " Decade & count & lambda\\_curr\\\\\n",
       "\\hline\n",
       "\t 1850     &  2       & 2.000000\\\\\n",
       "\t 1860     &  1       & 1.500000\\\\\n",
       "\t 1870     &  1       & 1.333333\\\\\n",
       "\t 1880     &  4       & 2.000000\\\\\n",
       "\t 1890     &  4       & 2.400000\\\\\n",
       "\t 1900     &  2       & 2.333333\\\\\n",
       "\t 1910     &  6       & 2.857143\\\\\n",
       "\t 1920     &  8       & 3.500000\\\\\n",
       "\t 1930     & 16       & 4.888889\\\\\n",
       "\t 1940     &  9       & 5.300000\\\\\n",
       "\t 1950     & 16       & 6.272727\\\\\n",
       "\t 1960     & 14       & 6.916667\\\\\n",
       "\t 1970     &  8       & 7.000000\\\\\n",
       "\t 1980     & 10       & 7.214286\\\\\n",
       "\t 1990     & 14       & 7.666667\\\\\n",
       "\t 2000     & 22       & 8.562500\\\\\n",
       "\t 2010     & 16       & 9.000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Decade | count | lambda_curr | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1850     |  2       | 2.000000 | \n",
       "| 1860     |  1       | 1.500000 | \n",
       "| 1870     |  1       | 1.333333 | \n",
       "| 1880     |  4       | 2.000000 | \n",
       "| 1890     |  4       | 2.400000 | \n",
       "| 1900     |  2       | 2.333333 | \n",
       "| 1910     |  6       | 2.857143 | \n",
       "| 1920     |  8       | 3.500000 | \n",
       "| 1930     | 16       | 4.888889 | \n",
       "| 1940     |  9       | 5.300000 | \n",
       "| 1950     | 16       | 6.272727 | \n",
       "| 1960     | 14       | 6.916667 | \n",
       "| 1970     |  8       | 7.000000 | \n",
       "| 1980     | 10       | 7.214286 | \n",
       "| 1990     | 14       | 7.666667 | \n",
       "| 2000     | 22       | 8.562500 | \n",
       "| 2010     | 16       | 9.000000 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   Decade count lambda_curr\n",
       "1  1850    2    2.000000   \n",
       "2  1860    1    1.500000   \n",
       "3  1870    1    1.333333   \n",
       "4  1880    4    2.000000   \n",
       "5  1890    4    2.400000   \n",
       "6  1900    2    2.333333   \n",
       "7  1910    6    2.857143   \n",
       "8  1920    8    3.500000   \n",
       "9  1930   16    4.888889   \n",
       "10 1940    9    5.300000   \n",
       "11 1950   16    6.272727   \n",
       "12 1960   14    6.916667   \n",
       "13 1970    8    7.000000   \n",
       "14 1980   10    7.214286   \n",
       "15 1990   14    7.666667   \n",
       "16 2000   22    8.562500   \n",
       "17 2010   16    9.000000   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly we can see an increase in Lambda values (Poisson) with respect to decade(time). We try to find the relationship between lambda and time by fitting a regression model as the trend observed is linear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Fitting a linear model to estimate the coefficient and intercept\n",
    "fit = lm(count$lambda_curr~count$Decade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = count$lambda_curr ~ count$Decade)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.87015 -0.28807  0.03485  0.20484  1.37360 \n",
       "\n",
       "Coefficients:\n",
       "               Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  -94.725725   5.549659  -17.07 3.09e-11 ***\n",
       "count$Decade   0.051542   0.002875   17.93 1.53e-11 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.5806 on 15 degrees of freedom\n",
       "Multiple R-squared:  0.9554,\tAdjusted R-squared:  0.9525 \n",
       "F-statistic: 321.5 on 1 and 15 DF,  p-value: 1.526e-11\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the obtained linear equation of lambda with respect to time from the regression model is  - \n",
    "\n",
    "$$ {\\hat\\lambda} = 0.051542 * Decade - 94.725725 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAAAAAP9Fi3RNTU1o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\ngu7GAOoAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Predicted vs Fitted Values for parameter lambda\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(count$Decade,count$lambda_curr,  col = 'blue',\n",
    "     ylim=c(-1,10),  lwd= 3, xlab=\"Time\", ylab=\"Lambda/Lambda(predicted)\")\n",
    "\n",
    "lines(count$Decade, (0.051542 * count$Decade - 94.725725), \n",
    "      ylim=c(-1,10), col=\"aquamarine4\", lwd =3)\n",
    "\n",
    "title (\"Predicted vs Fitted Values for parameter lambda\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets check the predicted value of lambda for the upcoming decade 2020"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "9.389115"
      ],
      "text/latex": [
       "9.389115"
      ],
      "text/markdown": [
       "9.389115"
      ],
      "text/plain": [
       "[1] 9.389115"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_2020 = 0.051542 * 2020 - 94.725725\n",
    "lambda_2020"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAANlBMVEUAAAAAAP9Fi3RNTU1o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\nACEBAggJEEBIgABCAgQQEiDgP0dM27V+l2kfAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the poisson distribution for category 4 & 5 together for decade 2020\n",
    "plot(0:30, dpois( x=0:30, lambda=lambda_2020 ), \n",
    "     xlim=c(-2,33), col = 'blue', lwd= 3, \n",
    "     xlab=\"No of Estimated Hurricanes in Decade - 2020\", \n",
    "     ylab=\"Probability\")\n",
    "\n",
    "lines(0:30,dpois( x=0:30, lambda=lambda_2020 ), \n",
    "      xlim=c(-2,33), col=\"aquamarine4\", lwd = 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Surely considering lambda as a factor of time might not be right way to look at the problem, but the idea of lambda being dependant on various factors should be considered. Various factors that influence the lambda value are discussed in next section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reasons for Increase in Hurricanes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recent increases in Hurricanes can be in partly, due to the higher sea temperatures in the region that Atlantic hurricanes form in and move through.\n",
    "Numerous factor influence the sea surface temperature -\n",
    "\n",
    "    -Natural variability\n",
    "    -Human-induced emissions of heat-trapping gases and Particulate pollution\n",
    "   \n",
    "Some studies suggest that natural variability, which includes the **Atlantic Multidecadal Oscillation (AMO)**, is the dominant cause of the warming trend in the Atlantic. Atlantic Multidecadal Oscillation (AMO) is a climate cycle that affects the sea surface temperature (SST) of the North Atlantic Ocean based on different modes on multidecadal timescales.\n",
    "\n",
    "\n",
    "Like we just considered the time for measuring lambda for poisson distribution, similarly taking the above factors into consideration and modelling the hurricane data based on new data will give us a better distribution fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### References : \n",
    "\n",
    "\n",
    "1) https://en.wikipedia.org/wiki/Atlantic_multidecadal_oscillation\n",
    "\n",
    "\n",
    "2) https://nca2014.globalchange.gov/report/our-changing-climate/changes-hurricanes#statement-16558\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}