R/CLT.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "set.seed(124)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## A function to randomly sample 'sampling.size' points from \n",
    "## 'sampling.distribution' 'replicates' number of times\n",
    "## and store the means.\n",
    "\n",
    "sampler <- function(replicates, sampling.size, sampling.distribtution){\n",
    "    sample.means <- vector()   \n",
    "    N <- length(sampling.distribtution)\n",
    "    for(i in 1:replicates) \n",
    "    {\n",
    "        s <- sample(seq(1, N), sampling.size)\n",
    "        sample <- sampling.distribtution[s]\n",
    "        sample.means <- c(sample.means, mean(sample))\n",
    "\n",
    "    }\n",
    "    return(sample.means)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.98301435580402"
      ],
      "text/latex": [
       "1.98301435580402"
      ],
      "text/markdown": [
       "1.98301435580402"
      ],
      "text/plain": [
       "[1] 1.983014"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "4.06623608977553"
      ],
      "text/latex": [
       "4.06623608977553"
      ],
      "text/markdown": [
       "4.06623608977553"
      ],
      "text/plain": [
       "[1] 4.066236"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "<path style=\"fill:none;stroke-width:0.75;stroke-linecap:round;stroke-linejoin:round;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 381.601562 416.800781 L 400.800781 416.800781 L 400.800781 416.453125 L 381.601562 416.453125 Z M 381.601562 416.800781 \"/>\n",
       "<path style=\"fill:none;stroke-width:0.75;stroke-linecap:round;stroke-linejoin:round;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 400.800781 416.800781 L 420 416.800781 Z M 400.800781 416.800781 \"/>\n",
       "<path style=\"fill:none;stroke-width:0.75;stroke-linecap:round;stroke-linejoin:round;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 420 416.800781 L 439.199219 416.800781 L 439.199219 416.625 L 420 416.625 Z M 420 416.800781 \"/>\n",
       "<path style=\"fill:none;stroke-width:0.75;stroke-linecap:round;stroke-linejoin:round;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 439.199219 416.800781 L 458.398438 416.800781 L 458.398438 416.625 L 439.199219 416.625 Z M 439.199219 416.800781 \"/>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title “Histogram of x.gamma”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x.gamma <-rgamma(n=5000,shape=1,scale=2)\n",
    "hist(x.gamma)\n",
    "mean(x.gamma)\n",
    "var(x.gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $x \\sim \\Gamma(a,b)$:\n",
    "\n",
    "$$EX = ab$$\n",
    "\n",
    "Hence the mean in our case should be 2.\n",
    "\n",
    "$$ Var = ab^2=4$$\n",
    "\n",
    "\n",
    "And hence the sampling distribution of the mean should have\n",
    "$$\n",
    "Var(\\bar{X}) = ab^2/n\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.9144273721788"
      ],
      "text/latex": [
       "1.9144273721788"
      ],
      "text/markdown": [
       "1.9144273721788"
      ],
      "text/plain": [
       "[1] 1.914427"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "0.370371464421344"
      ],
      "text/latex": [
       "0.370371464421344"
      ],
      "text/markdown": [
       "0.370371464421344"
      ],
      "text/plain": [
       "[1] 0.3703715"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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403.480469 L 495.292969 403.945312 L 496.585938 404.390625 L 497.882812 404.832031 L 499.175781 405.257812 L 500.472656 405.675781 L 501.765625 406.085938 L 503.0625 406.480469 L 504 406.765625 \"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title “Sampling distribution of the mean with 10 samples”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s.10 <- sampler(10,20,x.gamma)\n",
    "hist(s.10, main=\"Sampling distribution of the mean with 10 samples\", xlab = \"Sample mean\", ylab=\"Probability\", prob=T)\n",
    "lines(density(s.10)) \n",
    "lines(density(s.10, adjust=2), lty=\"dotted\")  \n",
    "mean(s.10)\n",
    "var(s.10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.91777240446569"
      ],
      "text/latex": [
       "1.91777240446569"
      ],
      "text/markdown": [
       "1.91777240446569"
      ],
      "text/plain": [
       "[1] 1.917772"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "0.154173668232302"
      ],
      "text/latex": [
       "0.154173668232302"
      ],
      "text/markdown": [
       "0.154173668232302"
      ],
      "text/plain": [
       "[1] 0.1541737"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title “Sampling distribution of the mean with 100 samples”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s.100 <- sampler(100,20,x.gamma)\n",
    "hist(s.100, main=\"Sampling distribution of the mean with 100 samples\", xlab = \"Sample mean\", ylab=\"Probability\", prob=T)\n",
    "lines(density(s.100)) \n",
    "lines(density(s.100, adjust=2), lty=\"dotted\") \n",
    "mean(s.100)\n",
    "var(s.100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.94581638392367"
      ],
      "text/latex": [
       "1.94581638392367"
      ],
      "text/markdown": [
       "1.94581638392367"
      ],
      "text/plain": [
       "[1] 1.945816"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "0.202825893452269"
      ],
      "text/latex": [
       "0.202825893452269"
      ],
      "text/markdown": [
       "0.202825893452269"
      ],
      "text/plain": [
       "[1] 0.2028259"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title “Sampling distribution of the mean with 1000 samples”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s.1000 <- sampler(1000,20,x.gamma)\n",
    "hist(s.1000, main=\"Sampling distribution of the mean with 1000 samples\", xlab = \"Sample mean\", ylab=\"Probability\", prob=T)\n",
    "lines(density(s.1000)) \n",
    "lines(density(s.1000, adjust=2), lty=\"dotted\") \n",
    "mean(s.1000)\n",
    "var(s.1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.96405148426902"
      ],
      "text/latex": [
       "1.96405148426902"
      ],
      "text/markdown": [
       "1.96405148426902"
      ],
      "text/plain": [
       "[1] 1.964051"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "0.199093917595788"
      ],
      "text/latex": [
       "0.199093917595788"
      ],
      "text/markdown": [
       "0.199093917595788"
      ],
      "text/plain": [
       "[1] 0.1990939"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title “Sampling distribution of the mean with 2000 samples”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s.2000 <- sampler(2000,20,x.gamma)\n",
    "hist(s.2000, main=\"Sampling distribution of the mean with 2000 samples\", xlab = \"Sample mean\", ylab=\"Probability\", prob=T)\n",
    "lines(density(s.2000)) \n",
    "lines(density(s.2000, adjust=2), lty=\"dotted\") \n",
    "mean(s.2000)\n",
    "var(s.2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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