standard-normal-table.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2a7978c5-9a63-4d1b-b3c2-e24c810d17ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "using QuadGK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "df022625-6a43-4a07-9ee4-fd30121087f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "using DataFrames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3c5a1f0d-51e5-4f69-9f16-b3095c5d3bd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Float64}:\n",
       " 0.0\n",
       " 0.01\n",
       " 0.02\n",
       " 0.03\n",
       " 0.04\n",
       " 0.05\n",
       " 0.06\n",
       " 0.07\n",
       " 0.08\n",
       " 0.09"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "topnumbers = collect(0.00:0.01:0.09)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "efa9428a-6f4c-416b-838b-1b0e62dc17cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40-element Vector{Float64}:\n",
       " 0.0\n",
       " 0.1\n",
       " 0.2\n",
       " 0.3\n",
       " 0.4\n",
       " 0.5\n",
       " 0.6\n",
       " 0.7\n",
       " 0.8\n",
       " 0.9\n",
       " 1.0\n",
       " 1.1\n",
       " 1.2\n",
       " ⋮\n",
       " 2.8\n",
       " 2.9\n",
       " 3.0\n",
       " 3.1\n",
       " 3.2\n",
       " 3.3\n",
       " 3.4\n",
       " 3.5\n",
       " 3.6\n",
       " 3.7\n",
       " 3.8\n",
       " 3.9"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leftnumbers = collect(0.00:0.1:3.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a7b05334-b437-497b-b490-b2205fb8020f",
   "metadata": {},
   "outputs": [],
   "source": [
    "zvalues = zeros(length(leftnumbers), length(topnumbers));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3af875d0-aedd-415b-88b2-649cf63690f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "normal (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function normal(x::Float64)::Float64\n",
    "    return (1.0 / sqrt(2.0 * pi)) * exp(-0.5 * x * x)\n",
    "end "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0ebd200e-ae6a-426c-a808-d23d4dcf8f2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "i = 1\n",
    "for rowvals in leftnumbers\n",
    "    j = 1\n",
    "    for colvals in topnumbers\n",
    "        zvalues[i, j] = QuadGK.quadgk(normal, 0.0, rowvals + colvals) |> first\n",
    "        j += 1\n",
    "    end\n",
    "    i += 1\n",
    "end "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2f0505ab-0a41-4195-b5e5-e6f025a761d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40×10 Matrix{Float64}:\n",
       " 0.0        0.00398936  0.00797831  …  0.0279032  0.0318814  0.0358564\n",
       " 0.0398278  0.0437953   0.0477584      0.0674949  0.0714237  0.0753454\n",
       " 0.0792597  0.0831662   0.0870644      0.10642    0.110261   0.114092\n",
       " 0.117911   0.12172     0.125516       0.144309   0.148027   0.151732\n",
       " 0.155422   0.159097    0.162757       0.180822   0.184386   0.187933\n",
       " 0.191462   0.194974    0.198468    …  0.215661   0.219043   0.222405\n",
       " 0.225747   0.229069    0.232371       0.248571   0.251748   0.254903\n",
       " 0.258036   0.261148    0.264238       0.27935    0.282305   0.285236\n",
       " 0.288145   0.29103     0.293892       0.30785    0.31057    0.313267\n",
       " 0.31594    0.318589    0.321214       0.333977   0.336457   0.338913\n",
       " 0.341345   0.343752    0.346136    …  0.35769    0.359929   0.362143\n",
       " 0.364334   0.3665      0.368643       0.379      0.381      0.382977\n",
       " 0.38493    0.386861    0.388768       0.397958   0.399727   0.401475\n",
       " ⋮                                  ⋱                        \n",
       " 0.497445   0.497523    0.497599       0.497948   0.498012   0.498074\n",
       " 0.498134   0.498193    0.49825        0.498511   0.498559   0.498605\n",
       " 0.49865    0.498694    0.498736    …  0.49893    0.498965   0.498999\n",
       " 0.499032   0.499065    0.499096       0.499238   0.499264   0.499289\n",
       " 0.499313   0.499336    0.499359       0.499462   0.499481   0.499499\n",
       " 0.499517   0.499534    0.49955        0.499624   0.499638   0.499651\n",
       " 0.499663   0.499675    0.499687       0.49974    0.499749   0.499758\n",
       " 0.499767   0.499776    0.499784    …  0.499822   0.499828   0.499835\n",
       " 0.499841   0.499847    0.499853       0.499879   0.499883   0.499888\n",
       " 0.499892   0.499896    0.4999         0.499918   0.499922   0.499925\n",
       " 0.499928   0.499931    0.499933       0.499946   0.499948   0.49995\n",
       " 0.499952   0.499954    0.499956       0.499964   0.499966   0.499967"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c75fed88-0f93-4855-a179-d4ed3b1a4061",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = DataFrame(hcat(leftnumbers, zvalues), map(x->string(x), vcat(\"\", topnumbers)));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2acac50-cc09-431d-8f06-847de112e9f7",
   "metadata": {},
   "source": [
    "### How to interprete the table?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a801612a-605c-45d6-a426-6f522fb0362a",
   "metadata": {},
   "source": [
    "Calculates the standard normal quantiles using the integral"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7d8bc6e-d92d-47d2-8478-afdf3a49fc90",
   "metadata": {},
   "source": [
    "$$\n",
    "\\int_0^{\\text{row  + col}} \\frac{1}{\\sqrt{2  \\pi}} e^{-\\frac{1}{2}x^2} \\text{dx}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cef00cdd-22c6-4455-9c3e-71649e0fe808",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m40×11 DataFrame\u001b[0m\n",
      "\u001b[1m Row \u001b[0m│\u001b[1m         \u001b[0m\u001b[1m 0.0       \u001b[0m\u001b[1m 0.01       \u001b[0m\u001b[1m 0.02       \u001b[0m\u001b[1m 0.03      \u001b[0m\u001b[1m 0.04      \u001b[0m\u001b[1m 0.05      \u001b[0m\u001b[1m 0.06      \u001b[0m\u001b[1m 0.07      \u001b[0m\u001b[1m 0.08      \u001b[0m\u001b[1m 0.09      \u001b[0m\n",
      "\u001b[1m     \u001b[0m│\u001b[90m Float64 \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\n",
      "─────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
      "   1 │     0.0  0.0        0.00398936  0.00797831  0.0119665  0.0159534  0.0199388  0.0239222  0.0279032  0.0318814  0.0358564\n",
      "   2 │     0.1  0.0398278  0.0437953   0.0477584   0.0517168  0.05567    0.0596177  0.0635595  0.0674949  0.0714237  0.0753454\n",
      "   3 │     0.2  0.0792597  0.0831662   0.0870644   0.0909541  0.0948349  0.0987063  0.102568   0.10642    0.110261   0.114092\n",
      "   4 │     0.3  0.117911   0.12172     0.125516    0.1293     0.133072   0.136831   0.140576   0.144309   0.148027   0.151732\n",
      "   5 │     0.4  0.155422   0.159097    0.162757    0.166402   0.170031   0.173645   0.177242   0.180822   0.184386   0.187933\n",
      "   6 │     0.5  0.191462   0.194974    0.198468    0.201944   0.205401   0.20884    0.21226    0.215661   0.219043   0.222405\n",
      "   7 │     0.6  0.225747   0.229069    0.232371    0.235653   0.238914   0.242154   0.245373   0.248571   0.251748   0.254903\n",
      "   8 │     0.7  0.258036   0.261148    0.264238    0.267305   0.27035    0.273373   0.276373   0.27935    0.282305   0.285236\n",
      "   9 │     0.8  0.288145   0.29103     0.293892    0.296731   0.299546   0.302337   0.305105   0.30785    0.31057    0.313267\n",
      "  10 │     0.9  0.31594    0.318589    0.321214    0.323814   0.326391   0.328944   0.331472   0.333977   0.336457   0.338913\n",
      "  11 │     1.0  0.341345   0.343752    0.346136    0.348495   0.35083    0.353141   0.355428   0.35769    0.359929   0.362143\n",
      "  12 │     1.1  0.364334   0.3665      0.368643    0.370762   0.372857   0.374928   0.376976   0.379      0.381      0.382977\n",
      "  13 │     1.2  0.38493    0.386861    0.388768    0.390651   0.392512   0.39435    0.396165   0.397958   0.399727   0.401475\n",
      "  14 │     1.3  0.4032     0.404902    0.406582    0.408241   0.409877   0.411492   0.413085   0.414657   0.416207   0.417736\n",
      "  15 │     1.4  0.419243   0.42073     0.422196    0.423641   0.425066   0.426471   0.427855   0.429219   0.430563   0.431888\n",
      "  16 │     1.5  0.433193   0.434478    0.435745    0.436992   0.43822    0.439429   0.44062    0.441792   0.442947   0.444083\n",
      "  17 │     1.6  0.445201   0.446301    0.447384    0.448449   0.449497   0.450529   0.451543   0.45254    0.453521   0.454486\n",
      "  18 │     1.7  0.455435   0.456367    0.457284    0.458185   0.45907    0.459941   0.460796   0.461636   0.462462   0.463273\n",
      "  19 │     1.8  0.46407    0.464852    0.46562     0.466375   0.467116   0.467843   0.468557   0.469258   0.469946   0.470621\n",
      "  20 │     1.9  0.471283   0.471933    0.472571    0.473197   0.47381    0.474412   0.475002   0.475581   0.476148   0.476705\n",
      "  21 │     2.0  0.47725    0.477784    0.478308    0.478822   0.479325   0.479818   0.480301   0.480774   0.481237   0.481691\n",
      "  22 │     2.1  0.482136   0.482571    0.482997    0.483414   0.483823   0.484222   0.484614   0.484997   0.485371   0.485738\n",
      "  23 │     2.2  0.486097   0.486447    0.486791    0.487126   0.487455   0.487776   0.488089   0.488396   0.488696   0.488989\n",
      "  24 │     2.3  0.489276   0.489556    0.48983     0.490097   0.490358   0.490613   0.490863   0.491106   0.491344   0.491576\n",
      "  25 │     2.4  0.491802   0.492024    0.49224     0.492451   0.492656   0.492857   0.493053   0.493244   0.493431   0.493613\n",
      "  26 │     2.5  0.49379    0.493963    0.494132    0.494297   0.494457   0.494614   0.494766   0.494915   0.49506    0.495201\n",
      "  27 │     2.6  0.495339   0.495473    0.495604    0.495731   0.495855   0.495975   0.496093   0.496207   0.496319   0.496427\n",
      "  28 │     2.7  0.496533   0.496636    0.496736    0.496833   0.496928   0.49702    0.49711    0.497197   0.497282   0.497365\n",
      "  29 │     2.8  0.497445   0.497523    0.497599    0.497673   0.497744   0.497814   0.497882   0.497948   0.498012   0.498074\n",
      "  30 │     2.9  0.498134   0.498193    0.49825     0.498305   0.498359   0.498411   0.498462   0.498511   0.498559   0.498605\n",
      "  31 │     3.0  0.49865    0.498694    0.498736    0.498777   0.498817   0.498856   0.498893   0.49893    0.498965   0.498999\n",
      "  32 │     3.1  0.499032   0.499065    0.499096    0.499126   0.499155   0.499184   0.499211   0.499238   0.499264   0.499289\n",
      "  33 │     3.2  0.499313   0.499336    0.499359    0.499381   0.499402   0.499423   0.499443   0.499462   0.499481   0.499499\n",
      "  34 │     3.3  0.499517   0.499534    0.49955     0.499566   0.499581   0.499596   0.49961    0.499624   0.499638   0.499651\n",
      "  35 │     3.4  0.499663   0.499675    0.499687    0.499698   0.499709   0.49972    0.49973    0.49974    0.499749   0.499758\n",
      "  36 │     3.5  0.499767   0.499776    0.499784    0.499792   0.4998     0.499807   0.499815   0.499822   0.499828   0.499835\n",
      "  37 │     3.6  0.499841   0.499847    0.499853    0.499858   0.499864   0.499869   0.499874   0.499879   0.499883   0.499888\n",
      "  38 │     3.7  0.499892   0.499896    0.4999      0.499904   0.499908   0.499912   0.499915   0.499918   0.499922   0.499925\n",
      "  39 │     3.8  0.499928   0.499931    0.499933    0.499936   0.499938   0.499941   0.499943   0.499946   0.499948   0.49995\n",
      "  40 │     3.9  0.499952   0.499954    0.499956    0.499958   0.499959   0.499961   0.499963   0.499964   0.499966   0.499967"
     ]
    }
   ],
   "source": [
    "show(df, allcols = true, allrows = true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42e0f1c8-4f91-459f-aeda-2f8a2ba8686e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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