{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "48d1d696-3b52-47c2-96c2-074a1b32f304",
   "metadata": {},
   "source": [
    "# Distributions - R"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "247cd557-3d56-4611-a332-9cc44f87d9ae",
   "metadata": {},
   "source": [
    "## Normal Distribution\n",
    "\n",
    "* **Parameterization:** mean (μ): `mean`, standard deviation (σ): `sd`\n",
    "* **Distribution Functions:** `_norm`: `dnorm`, `pnorm`, `qnorm`, `rnorm`\n",
    "* **Reporting:** \"Figure 2 shows the distributions of response Y for both levels of factor X. To test whether these distributions were normally distributed, a Kolmogorov-Smirnov test was run on Y for both levels of X. The test for level ‘a’ was statistically non-significant (D = .158, p = .404), as was the test for level ‘b’ (D = .104, p = .867), indicating non-detectable deviations from a normal distribution for both levels.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b2741c58-ca1f-4fc4-a031-220538fbd2e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>10.055297</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>b</td><td>11.462669</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>a</td><td>12.140244</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>14.025322</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td> 6.922079</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>b</td><td>16.523659</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>a</td><td> 7.350582</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>13.416170</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>11.279275</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>b</td><td>12.571377</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>a</td><td>12.216500</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>12.017293</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>10.485682</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>b</td><td>14.422881</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>a</td><td>12.127070</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>16.750440</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td> 8.874990</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>b</td><td>11.498568</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>a</td><td>11.509413</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>13.603714</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & S & X & Y\\\\\n",
       "  & <int> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & 10.055297\\\\\n",
       "\t2 &  2 & b & 11.462669\\\\\n",
       "\t3 &  3 & a & 12.140244\\\\\n",
       "\t4 &  4 & b & 14.025322\\\\\n",
       "\t5 &  5 & a &  6.922079\\\\\n",
       "\t6 &  6 & b & 16.523659\\\\\n",
       "\t7 &  7 & a &  7.350582\\\\\n",
       "\t8 &  8 & b & 13.416170\\\\\n",
       "\t9 &  9 & a & 11.279275\\\\\n",
       "\t10 & 10 & b & 12.571377\\\\\n",
       "\t11 & 11 & a & 12.216500\\\\\n",
       "\t12 & 12 & b & 12.017293\\\\\n",
       "\t13 & 13 & a & 10.485682\\\\\n",
       "\t14 & 14 & b & 14.422881\\\\\n",
       "\t15 & 15 & a & 12.127070\\\\\n",
       "\t16 & 16 & b & 16.750440\\\\\n",
       "\t17 & 17 & a &  8.874990\\\\\n",
       "\t18 & 18 & b & 11.498568\\\\\n",
       "\t19 & 19 & a & 11.509413\\\\\n",
       "\t20 & 20 & b & 13.603714\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 3\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 |  1 | a | 10.055297 |\n",
       "| 2 |  2 | b | 11.462669 |\n",
       "| 3 |  3 | a | 12.140244 |\n",
       "| 4 |  4 | b | 14.025322 |\n",
       "| 5 |  5 | a |  6.922079 |\n",
       "| 6 |  6 | b | 16.523659 |\n",
       "| 7 |  7 | a |  7.350582 |\n",
       "| 8 |  8 | b | 13.416170 |\n",
       "| 9 |  9 | a | 11.279275 |\n",
       "| 10 | 10 | b | 12.571377 |\n",
       "| 11 | 11 | a | 12.216500 |\n",
       "| 12 | 12 | b | 12.017293 |\n",
       "| 13 | 13 | a | 10.485682 |\n",
       "| 14 | 14 | b | 14.422881 |\n",
       "| 15 | 15 | a | 12.127070 |\n",
       "| 16 | 16 | b | 16.750440 |\n",
       "| 17 | 17 | a |  8.874990 |\n",
       "| 18 | 18 | b | 11.498568 |\n",
       "| 19 | 19 | a | 11.509413 |\n",
       "| 20 | 20 | b | 13.603714 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X Y        \n",
       "1   1 a 10.055297\n",
       "2   2 b 11.462669\n",
       "3   3 a 12.140244\n",
       "4   4 b 14.025322\n",
       "5   5 a  6.922079\n",
       "6   6 b 16.523659\n",
       "7   7 a  7.350582\n",
       "8   8 b 13.416170\n",
       "9   9 a 11.279275\n",
       "10 10 b 12.571377\n",
       "11 11 a 12.216500\n",
       "12 12 b 12.017293\n",
       "13 13 a 10.485682\n",
       "14 14 b 14.422881\n",
       "15 15 a 12.127070\n",
       "16 16 b 16.750440\n",
       "17 17 a  8.874990\n",
       "18 18 b 11.498568\n",
       "19 19 a 11.509413\n",
       "20 20 b 13.603714"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has one factor (X) w/two levels (a,b) and continuous response Y\n",
    "df <- read.csv(\"data/1F2LBs_normal.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e9cec899-737b-4860-9a32-e5882f1eeb67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df[df$X == \"a\", ]$Y\n",
       "D = 0.15752, p-value = 0.4042\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df[df$X == \"b\", ]$Y\n",
       "D = 0.10418, p-value = 0.8674\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(MASS) # for fitdistr\n",
    "fa = fitdistr(df[df$X == \"a\",]$Y, \"normal\")$estimate # create fit for X.a\n",
    "ks.test(df[df$X == \"a\",]$Y, \"pnorm\", mean=fa[1], sd=fa[2])\n",
    "fb = fitdistr(df[df$X == \"b\",]$Y, \"normal\")$estimate # create fit for X.b\n",
    "ks.test(df[df$X == \"b\",]$Y, \"pnorm\", mean=fb[1], sd=fb[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "62529cc0-637c-42ad-9597-5bf4357d5d24",
   "metadata": {},
   "outputs": [
    {
     "data": {
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7uld+5VFKU23nqcTmdGRoZctagR9SbYeTwej8dTcXk8HldVNRgMylUbiUQikUgw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8Sr4Zos0Znte2//EZAAAApbEhfsYOAABASwQ7AN/qa9oAAAJdSURBVAAATRDsAAAA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\nTtO5ibwv+wAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "\n",
    "# Histograms\n",
    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
    "ggplot(data=df, aes(x=Y, col=X, fill=X)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # create the histogram; the alpha value ensures overlaps can be seen\n",
    "  geom_histogram(color=\"darkgray\", binwidth=1, breaks=seq(4,18,by=1), alpha=0.25, position=\"identity\") + \n",
    "  # create stacked plots by X, one for each histogram\n",
    "  facet_grid(X ~ .) + \n",
    "  # determine the fill color values of each histogram\n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\")) + \n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Histograms of Y by X\", x=\"Y\", y=\"Count\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_continuous(breaks=seq(4,18,by=1), labels=seq(4,18,by=1), limits=c(4,18)) +\n",
    "  scale_y_continuous(breaks=seq(0,8,by=2), labels=seq(0,8,by=2), limits=c(0,8))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3026026b-f5f7-4d54-a63d-53ce7d1c352c",
   "metadata": {},
   "source": [
    "## Lognormal Distribution\n",
    "\n",
    "* **Parameterization:** mean (μ): `meanlog`, standard deviation (σ): `sdlog`\n",
    "* **Distribution Functions:** `_lnorm`: `dlnorm`, `plnorm`, `qlnorm`, `rlnorm`\n",
    "* **Reporting:** \"Figure 3 shows the distributions of response Y for both levels of factor X. To test whether these distributions were lognormally distributed, a Kolmogorov-Smirnov test was run on Y for both levels of X. The test for level ‘a’ was statistically non-significant (D = .096, p = .918), as was the test for level ‘b’ (D = .161, p = .375), indicating non-detectable deviations from a lognormal distribution for both levels.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6a49b78f-d79f-4269-84f8-c116d9f1ae00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>18.308269</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>b</td><td> 5.951342</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>a</td><td> 5.739954</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td> 5.932270</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>21.378222</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>b</td><td>25.155509</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>a</td><td>20.848274</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td> 6.533354</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td> 8.683973</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>b</td><td>11.213393</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>a</td><td> 6.517906</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>19.214861</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td> 1.084347</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>b</td><td>11.620167</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>a</td><td> 1.334683</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>12.304836</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>14.400186</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>b</td><td>18.914468</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>a</td><td> 3.369996</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td> 5.535679</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & S & X & Y\\\\\n",
       "  & <int> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & 18.308269\\\\\n",
       "\t2 &  2 & b &  5.951342\\\\\n",
       "\t3 &  3 & a &  5.739954\\\\\n",
       "\t4 &  4 & b &  5.932270\\\\\n",
       "\t5 &  5 & a & 21.378222\\\\\n",
       "\t6 &  6 & b & 25.155509\\\\\n",
       "\t7 &  7 & a & 20.848274\\\\\n",
       "\t8 &  8 & b &  6.533354\\\\\n",
       "\t9 &  9 & a &  8.683973\\\\\n",
       "\t10 & 10 & b & 11.213393\\\\\n",
       "\t11 & 11 & a &  6.517906\\\\\n",
       "\t12 & 12 & b & 19.214861\\\\\n",
       "\t13 & 13 & a &  1.084347\\\\\n",
       "\t14 & 14 & b & 11.620167\\\\\n",
       "\t15 & 15 & a &  1.334683\\\\\n",
       "\t16 & 16 & b & 12.304836\\\\\n",
       "\t17 & 17 & a & 14.400186\\\\\n",
       "\t18 & 18 & b & 18.914468\\\\\n",
       "\t19 & 19 & a &  3.369996\\\\\n",
       "\t20 & 20 & b &  5.535679\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 3\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 |  1 | a | 18.308269 |\n",
       "| 2 |  2 | b |  5.951342 |\n",
       "| 3 |  3 | a |  5.739954 |\n",
       "| 4 |  4 | b |  5.932270 |\n",
       "| 5 |  5 | a | 21.378222 |\n",
       "| 6 |  6 | b | 25.155509 |\n",
       "| 7 |  7 | a | 20.848274 |\n",
       "| 8 |  8 | b |  6.533354 |\n",
       "| 9 |  9 | a |  8.683973 |\n",
       "| 10 | 10 | b | 11.213393 |\n",
       "| 11 | 11 | a |  6.517906 |\n",
       "| 12 | 12 | b | 19.214861 |\n",
       "| 13 | 13 | a |  1.084347 |\n",
       "| 14 | 14 | b | 11.620167 |\n",
       "| 15 | 15 | a |  1.334683 |\n",
       "| 16 | 16 | b | 12.304836 |\n",
       "| 17 | 17 | a | 14.400186 |\n",
       "| 18 | 18 | b | 18.914468 |\n",
       "| 19 | 19 | a |  3.369996 |\n",
       "| 20 | 20 | b |  5.535679 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X Y        \n",
       "1   1 a 18.308269\n",
       "2   2 b  5.951342\n",
       "3   3 a  5.739954\n",
       "4   4 b  5.932270\n",
       "5   5 a 21.378222\n",
       "6   6 b 25.155509\n",
       "7   7 a 20.848274\n",
       "8   8 b  6.533354\n",
       "9   9 a  8.683973\n",
       "10 10 b 11.213393\n",
       "11 11 a  6.517906\n",
       "12 12 b 19.214861\n",
       "13 13 a  1.084347\n",
       "14 14 b 11.620167\n",
       "15 15 a  1.334683\n",
       "16 16 b 12.304836\n",
       "17 17 a 14.400186\n",
       "18 18 b 18.914468\n",
       "19 19 a  3.369996\n",
       "20 20 b  5.535679"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has one factor (X) w/two levels (a,b) and continuous response Y\n",
    "df <- read.csv(\"data/1F2LBs_lognormal.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d61a16eb-1473-43dd-9eb5-2b75524dcfe5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df[df$X == \"a\", ]$Y\n",
       "D = 0.0964, p-value = 0.918\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df[df$X == \"b\", ]$Y\n",
       "D = 0.16135, p-value = 0.3752\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(MASS) # for fitdistr\n",
    "fa = fitdistr(df[df$X == \"a\",]$Y, \"lognormal\")$estimate # create fit for X.a\n",
    "ks.test(df[df$X == \"a\",]$Y, \"plnorm\", meanlog=fa[1], sdlog=fa[2])\n",
    "fb = fitdistr(df[df$X == \"b\",]$Y, \"lognormal\")$estimate # create fit for X.b\n",
    "ks.test(df[df$X == \"b\",]$Y, \"plnorm\", meanlog=fb[1], sdlog=fb[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4c4ad290-4a8b-4da1-843a-16d90674b5e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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M6zqCKYZsrnvJc4NVl6cbFLbLyqm2EYKrMS/1UTl6gjarKSVMZZddESPzU1TSvR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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "\n",
    "# Plot lognormal histograms\n",
    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
    "ggplot(data=df, aes(x=Y, col=X, fill=X)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # create the histogram; the alpha value ensures overlaps can be seen\n",
    "  geom_histogram(color=\"darkgray\", binwidth=10, breaks=seq(0,80,by=10), alpha=0.25, position=\"identity\") + \n",
    "  # create stacked plots by X, one for each histogram\n",
    "  facet_grid(X ~ .) + \n",
    "  # determine the fill color values of each histogram\n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\")) + \n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Histograms of Y by X\", x=\"Y\", y=\"Count\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_continuous(breaks=seq(0,80,by=10), labels=seq(0,80,by=10), limits=c(0,80)) +\n",
    "  scale_y_continuous(breaks=seq(0,20,by=4), labels=seq(0,20,by=4), limits=c(0,20))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7650df17-1788-4a45-97d2-61d9c9664e69",
   "metadata": {},
   "source": [
    "## Poisson Distribution\n",
    "\n",
    "* **Parameterization:** lambda (λ): `lambda`\n",
    "* **Distribution Functions:** `_pois`: `dpois`, `ppois`, `qpois`, `rpois`\n",
    "* **Reporting:** \"Figure 4 shows the distributions of response Y for both levels of factor X. To test whether these distributionswere Poisson distributed, a Chi-Squared goodness-of-fit test was run on Y for both levels of X. The test for level ‘a’ was statistically non-significant (χ2(3, N=30) = 2.62, p = .454), as was the test for level ‘b’ (χ2(4, N=30) = 2.79, p = .593), indicating non-detectable deviations from a Poisson distribution for both levels.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b5d2a7c2-2f44-44a3-9cab-676b36727446",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>b</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>a</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>b</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>a</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>7</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>b</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>a</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>b</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>a</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>6</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>b</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>a</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & S & X & Y\\\\\n",
       "  & <int> & <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & 5\\\\\n",
       "\t2 &  2 & b & 6\\\\\n",
       "\t3 &  3 & a & 3\\\\\n",
       "\t4 &  4 & b & 3\\\\\n",
       "\t5 &  5 & a & 3\\\\\n",
       "\t6 &  6 & b & 5\\\\\n",
       "\t7 &  7 & a & 5\\\\\n",
       "\t8 &  8 & b & 7\\\\\n",
       "\t9 &  9 & a & 2\\\\\n",
       "\t10 & 10 & b & 4\\\\\n",
       "\t11 & 11 & a & 2\\\\\n",
       "\t12 & 12 & b & 5\\\\\n",
       "\t13 & 13 & a & 0\\\\\n",
       "\t14 & 14 & b & 5\\\\\n",
       "\t15 & 15 & a & 0\\\\\n",
       "\t16 & 16 & b & 6\\\\\n",
       "\t17 & 17 & a & 2\\\\\n",
       "\t18 & 18 & b & 3\\\\\n",
       "\t19 & 19 & a & 4\\\\\n",
       "\t20 & 20 & b & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 3\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X &lt;chr&gt; | Y &lt;int&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 |  1 | a | 5 |\n",
       "| 2 |  2 | b | 6 |\n",
       "| 3 |  3 | a | 3 |\n",
       "| 4 |  4 | b | 3 |\n",
       "| 5 |  5 | a | 3 |\n",
       "| 6 |  6 | b | 5 |\n",
       "| 7 |  7 | a | 5 |\n",
       "| 8 |  8 | b | 7 |\n",
       "| 9 |  9 | a | 2 |\n",
       "| 10 | 10 | b | 4 |\n",
       "| 11 | 11 | a | 2 |\n",
       "| 12 | 12 | b | 5 |\n",
       "| 13 | 13 | a | 0 |\n",
       "| 14 | 14 | b | 5 |\n",
       "| 15 | 15 | a | 0 |\n",
       "| 16 | 16 | b | 6 |\n",
       "| 17 | 17 | a | 2 |\n",
       "| 18 | 18 | b | 3 |\n",
       "| 19 | 19 | a | 4 |\n",
       "| 20 | 20 | b | 6 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X Y\n",
       "1   1 a 5\n",
       "2   2 b 6\n",
       "3   3 a 3\n",
       "4   4 b 3\n",
       "5   5 a 3\n",
       "6   6 b 5\n",
       "7   7 a 5\n",
       "8   8 b 7\n",
       "9   9 a 2\n",
       "10 10 b 4\n",
       "11 11 a 2\n",
       "12 12 b 5\n",
       "13 13 a 0\n",
       "14 14 b 5\n",
       "15 15 a 0\n",
       "16 16 b 6\n",
       "17 17 a 2\n",
       "18 18 b 3\n",
       "19 19 a 4\n",
       "20 20 b 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has one factor (X) w/two levels (a,b) and nonnegative integer response Y\n",
    "df <- read.csv(\"data/1F2LBs_poisson.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6154d21e-ba9a-4be4-b607-35b2b318c21c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: survival\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Chi-squared statistic:  2.619401 \n",
       "Degree of freedom of the Chi-squared distribution:  3 \n",
       "Chi-squared p-value:  0.4540985 \n",
       "   the p-value may be wrong with some theoretical counts < 5  \n",
       "Chi-squared table:\n",
       "     obscounts theocounts\n",
       "<= 1  5.000000   7.280252\n",
       "<= 2 10.000000   7.284586\n",
       "<= 3  5.000000   6.637067\n",
       "<= 4  6.000000   4.535329\n",
       "> 4   4.000000   4.262765\n",
       "\n",
       "Goodness-of-fit criteria\n",
       "                               1-mle-pois\n",
       "Akaike's Information Criterion   112.8951\n",
       "Bayesian Information Criterion   114.2962"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Chi-squared statistic:  2.794443 \n",
       "Degree of freedom of the Chi-squared distribution:  4 \n",
       "Chi-squared p-value:  0.5927924 \n",
       "   the p-value may be wrong with some theoretical counts < 5  \n",
       "Chi-squared table:\n",
       "     obscounts theocounts\n",
       "<= 2  4.000000   5.436500\n",
       "<= 3  6.000000   5.173554\n",
       "<= 4  5.000000   5.734022\n",
       "<= 5  6.000000   5.084166\n",
       "<= 6  6.000000   3.756634\n",
       "> 6   3.000000   4.815124\n",
       "\n",
       "Goodness-of-fit criteria\n",
       "                               1-mle-pois\n",
       "Akaike's Information Criterion   121.0369\n",
       "Bayesian Information Criterion   122.4381"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(fitdistrplus) # for fitdist, gofstat\n",
    "fa = fitdist(df[df$X == \"a\",]$Y, \"pois\") # create fit for X.a\n",
    "gofstat(fa)\n",
    "fb = fitdist(df[df$X == \"b\",]$Y, \"pois\") # create fit for X.b\n",
    "gofstat(fb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2f5579d0-4503-41fc-9fe5-da172760fac6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mzPGPvrzz+X7LNsf8ghpdfl3tOuurxw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1qdscvPz8/6mMlksrKyMhKJhMPhrA++y3KO40SjUQW1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\nAAAAmiDYAQAAaOL/AZX+5FhDyoQ8AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "\n",
    "# Plot Poisson histograms\n",
    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
    "ggplot(data=df, aes(x=Y, col=X, fill=X)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # create the histogram; the alpha value ensures overlaps can be seen\n",
    "  geom_histogram(color=\"darkgray\", binwidth=1, breaks=seq(0,8,by=1), alpha=0.25, position=\"identity\") + \n",
    "  # create stacked plots by X, one for each histogram\n",
    "  facet_grid(X ~ .) + \n",
    "  # determine the fill color values of each histogram\n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\")) + \n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Histograms of Y by X\", x=\"Y\", y=\"Count\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_continuous(breaks=seq(0,8,by=1), labels=seq(0,8,by=1), limits=c(0,8)) +\n",
    "  scale_y_continuous(breaks=seq(0,10,by=2), labels=seq(0,10,by=2), limits=c(0,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e31eeb0c-f45c-4cd7-8d69-3efbb06eeb2e",
   "metadata": {},
   "source": [
    "## Negative Binomial Distribution\n",
    "\n",
    "* **Parameterization:** theta (θ): `theta`, mu (μ): `mu`\n",
    "* **Distribution Functions:** `_nbinom`: `dnbinom`, `pnbinom`, `qnbinom`, `rnbinom`\n",
    "* **Reporting:** \"Figure 5 shows the distributions of response Y for both levels of factor X. To test whether these distributions were negative binomially distributed, a Chi-Squared goodness-of-fit test was run on Y for both levels of X. The test for level ‘a’ was statistically non-significant (χ2(4, N=30) = 1.74, p = .783), as was the test for level ‘b’ (χ2(3, N=30) = 1.27, p = .737), indicating non-detectable deviations from a negative binomial distribution for both levels.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "401c2cb3-a662-476b-9621-935a1539961f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>22</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>b</td><td>11</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>a</td><td>16</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td> 9</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td> 8</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>b</td><td>16</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>a</td><td>13</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td> 4</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>18</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>b</td><td>10</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>a</td><td>15</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td> 6</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>27</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>b</td><td>19</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>a</td><td>15</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>14</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>22</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>b</td><td>20</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>a</td><td>36</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>10</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & S & X & Y\\\\\n",
       "  & <int> & <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & 22\\\\\n",
       "\t2 &  2 & b & 11\\\\\n",
       "\t3 &  3 & a & 16\\\\\n",
       "\t4 &  4 & b &  9\\\\\n",
       "\t5 &  5 & a &  8\\\\\n",
       "\t6 &  6 & b & 16\\\\\n",
       "\t7 &  7 & a & 13\\\\\n",
       "\t8 &  8 & b &  4\\\\\n",
       "\t9 &  9 & a & 18\\\\\n",
       "\t10 & 10 & b & 10\\\\\n",
       "\t11 & 11 & a & 15\\\\\n",
       "\t12 & 12 & b &  6\\\\\n",
       "\t13 & 13 & a & 27\\\\\n",
       "\t14 & 14 & b & 19\\\\\n",
       "\t15 & 15 & a & 15\\\\\n",
       "\t16 & 16 & b & 14\\\\\n",
       "\t17 & 17 & a & 22\\\\\n",
       "\t18 & 18 & b & 20\\\\\n",
       "\t19 & 19 & a & 36\\\\\n",
       "\t20 & 20 & b & 10\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 3\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X &lt;chr&gt; | Y &lt;int&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 |  1 | a | 22 |\n",
       "| 2 |  2 | b | 11 |\n",
       "| 3 |  3 | a | 16 |\n",
       "| 4 |  4 | b |  9 |\n",
       "| 5 |  5 | a |  8 |\n",
       "| 6 |  6 | b | 16 |\n",
       "| 7 |  7 | a | 13 |\n",
       "| 8 |  8 | b |  4 |\n",
       "| 9 |  9 | a | 18 |\n",
       "| 10 | 10 | b | 10 |\n",
       "| 11 | 11 | a | 15 |\n",
       "| 12 | 12 | b |  6 |\n",
       "| 13 | 13 | a | 27 |\n",
       "| 14 | 14 | b | 19 |\n",
       "| 15 | 15 | a | 15 |\n",
       "| 16 | 16 | b | 14 |\n",
       "| 17 | 17 | a | 22 |\n",
       "| 18 | 18 | b | 20 |\n",
       "| 19 | 19 | a | 36 |\n",
       "| 20 | 20 | b | 10 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X Y \n",
       "1   1 a 22\n",
       "2   2 b 11\n",
       "3   3 a 16\n",
       "4   4 b  9\n",
       "5   5 a  8\n",
       "6   6 b 16\n",
       "7   7 a 13\n",
       "8   8 b  4\n",
       "9   9 a 18\n",
       "10 10 b 10\n",
       "11 11 a 15\n",
       "12 12 b  6\n",
       "13 13 a 27\n",
       "14 14 b 19\n",
       "15 15 a 15\n",
       "16 16 b 14\n",
       "17 17 a 22\n",
       "18 18 b 20\n",
       "19 19 a 36\n",
       "20 20 b 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has one factor (X) w/two levels (a,b) and nonnegative integer response Y\n",
    "df <- read.csv(\"data/1F2LBs_negbin.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c8d056bb-1c5f-4f91-99be-e7f3286ec515",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Chi-squared statistic:  1.73975 \n",
       "Degree of freedom of the Chi-squared distribution:  4 \n",
       "Chi-squared p-value:  0.7834849 \n",
       "   the p-value may be wrong with some theoretical counts < 5  \n",
       "Chi-squared table:\n",
       "      obscounts theocounts\n",
       "<= 7   5.000000   3.498637\n",
       "<= 11  4.000000   5.021527\n",
       "<= 14  5.000000   4.274380\n",
       "<= 18  4.000000   5.293625\n",
       "<= 23  4.000000   5.056978\n",
       "<= 28  4.000000   3.214631\n",
       "> 28   4.000000   3.640223\n",
       "\n",
       "Goodness-of-fit criteria\n",
       "                               1-mle-nbinom\n",
       "Akaike's Information Criterion     217.6756\n",
       "Bayesian Information Criterion     220.4780"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Chi-squared statistic:  1.268287 \n",
       "Degree of freedom of the Chi-squared distribution:  3 \n",
       "Chi-squared p-value:  0.736677 \n",
       "   the p-value may be wrong with some theoretical counts < 5  \n",
       "Chi-squared table:\n",
       "      obscounts theocounts\n",
       "<= 5   4.000000   3.954289\n",
       "<= 8   6.000000   5.716970\n",
       "<= 10  4.000000   4.235641\n",
       "<= 13  4.000000   5.710654\n",
       "<= 16  6.000000   4.245423\n",
       "> 16   6.000000   6.137024\n",
       "\n",
       "Goodness-of-fit criteria\n",
       "                               1-mle-nbinom\n",
       "Akaike's Information Criterion     194.1103\n",
       "Bayesian Information Criterion     196.9126"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(fitdistrplus) # for fitdist, gofstat\n",
    "fa = fitdist(df[df$X == \"a\",]$Y, \"nbinom\") # create fit for X.a\n",
    "gofstat(fa)\n",
    "fb = fitdist(df[df$X == \"b\",]$Y, \"nbinom\") # create fit for X.b\n",
    "gofstat(fb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c7ec8f92-d9b9-40c0-ace3-3e321621d9a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACT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\nW6Scd22DSyvfXUtvc9AlFw29bfAhzVae1OqEfr2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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "\n",
    "# Plot negative binomial histograms\n",
    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
    "ggplot(data=df, aes(x=Y, col=X, fill=X)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # create the histogram; the alpha value ensures overlaps can be seen\n",
    "  geom_histogram(color=\"darkgray\", binwidth=5, breaks=seq(0,40,by=5), alpha=0.25, position=\"identity\") + \n",
    "  # create stacked plots by X, one for each histogram\n",
    "  facet_grid(X ~ .) + \n",
    "  # determine the fill color values of each histogram\n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\")) + \n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Histograms of Y by X\", x=\"Y\", y=\"Count\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_continuous(breaks=seq(0,40,by=5), labels=seq(0,40,by=5), limits=c(0,40)) +\n",
    "  scale_y_continuous(breaks=seq(0,10,by=2), labels=seq(0,10,by=2), limits=c(0,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4faff49-c154-4848-a0d7-849ca926098e",
   "metadata": {},
   "source": [
    "## Exponential Distribution\n",
    "\n",
    "* **Parameterization:** rate (λ): `rate`\n",
    "* **Distribution Functions:** `_exp`: `dexp`, `pexp`, `qexp`, `rexp`\n",
    "* **Reporting:** \"Figure 6 shows the distributions of response Y for both levels of factor X. To test whether these distributions were exponentially distributed, a Kolmogorov-Smirnov test was run on Y for both levels of X. The test for level ‘a’ was statistically non-significant (D = .107, p = .849), as was the test for level ‘b’ (D = .119, p = .742), indicating non-detectable deviations from an exponential distribution for both levels.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f93f179a-80e6-47c7-bf76-55e8658dce76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>12.477962</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>b</td><td> 5.975198</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>a</td><td> 7.781088</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>16.940324</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>10.526902</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>b</td><td> 4.675437</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>a</td><td> 9.899636</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>23.608037</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td> 2.041000</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>b</td><td> 5.257079</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>a</td><td>43.238041</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>13.202714</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td> 8.352570</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>b</td><td> 5.377658</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>a</td><td>16.142961</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td> 1.901692</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td> 1.372129</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>b</td><td>12.738519</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>a</td><td> 2.903349</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>25.792198</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & S & X & Y\\\\\n",
       "  & <int> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & 12.477962\\\\\n",
       "\t2 &  2 & b &  5.975198\\\\\n",
       "\t3 &  3 & a &  7.781088\\\\\n",
       "\t4 &  4 & b & 16.940324\\\\\n",
       "\t5 &  5 & a & 10.526902\\\\\n",
       "\t6 &  6 & b &  4.675437\\\\\n",
       "\t7 &  7 & a &  9.899636\\\\\n",
       "\t8 &  8 & b & 23.608037\\\\\n",
       "\t9 &  9 & a &  2.041000\\\\\n",
       "\t10 & 10 & b &  5.257079\\\\\n",
       "\t11 & 11 & a & 43.238041\\\\\n",
       "\t12 & 12 & b & 13.202714\\\\\n",
       "\t13 & 13 & a &  8.352570\\\\\n",
       "\t14 & 14 & b &  5.377658\\\\\n",
       "\t15 & 15 & a & 16.142961\\\\\n",
       "\t16 & 16 & b &  1.901692\\\\\n",
       "\t17 & 17 & a &  1.372129\\\\\n",
       "\t18 & 18 & b & 12.738519\\\\\n",
       "\t19 & 19 & a &  2.903349\\\\\n",
       "\t20 & 20 & b & 25.792198\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 3\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 |  1 | a | 12.477962 |\n",
       "| 2 |  2 | b |  5.975198 |\n",
       "| 3 |  3 | a |  7.781088 |\n",
       "| 4 |  4 | b | 16.940324 |\n",
       "| 5 |  5 | a | 10.526902 |\n",
       "| 6 |  6 | b |  4.675437 |\n",
       "| 7 |  7 | a |  9.899636 |\n",
       "| 8 |  8 | b | 23.608037 |\n",
       "| 9 |  9 | a |  2.041000 |\n",
       "| 10 | 10 | b |  5.257079 |\n",
       "| 11 | 11 | a | 43.238041 |\n",
       "| 12 | 12 | b | 13.202714 |\n",
       "| 13 | 13 | a |  8.352570 |\n",
       "| 14 | 14 | b |  5.377658 |\n",
       "| 15 | 15 | a | 16.142961 |\n",
       "| 16 | 16 | b |  1.901692 |\n",
       "| 17 | 17 | a |  1.372129 |\n",
       "| 18 | 18 | b | 12.738519 |\n",
       "| 19 | 19 | a |  2.903349 |\n",
       "| 20 | 20 | b | 25.792198 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X Y        \n",
       "1   1 a 12.477962\n",
       "2   2 b  5.975198\n",
       "3   3 a  7.781088\n",
       "4   4 b 16.940324\n",
       "5   5 a 10.526902\n",
       "6   6 b  4.675437\n",
       "7   7 a  9.899636\n",
       "8   8 b 23.608037\n",
       "9   9 a  2.041000\n",
       "10 10 b  5.257079\n",
       "11 11 a 43.238041\n",
       "12 12 b 13.202714\n",
       "13 13 a  8.352570\n",
       "14 14 b  5.377658\n",
       "15 15 a 16.142961\n",
       "16 16 b  1.901692\n",
       "17 17 a  1.372129\n",
       "18 18 b 12.738519\n",
       "19 19 a  2.903349\n",
       "20 20 b 25.792198"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has one factor (X) w/two levels (a,b) and continuous response Y\n",
    "df <- read.csv(\"data/1F2LBs_exponential.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "da1a5ec7-8112-4956-b470-6c5ab3ce6dbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df[df$X == \"a\", ]$Y\n",
       "D = 0.10665, p-value = 0.8491\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df[df$X == \"b\", ]$Y\n",
       "D = 0.11942, p-value = 0.7415\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(MASS) # for fitdistr\n",
    "fa = fitdistr(df[df$X == \"a\",]$Y, \"exponential\")$estimate # create fit for X.a\n",
    "ks.test(df[df$X == \"a\",]$Y, \"pexp\", rate=fa[1])\n",
    "fb = fitdistr(df[df$X == \"b\",]$Y, \"exponential\")$estimate # create fit for X.b\n",
    "ks.test(df[df$X == \"b\",]$Y, \"pexp\", rate=fb[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e42f15c5-1518-4cd8-aec9-59a50c5d0a3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/aNsb//+mvRMcumxxxTfF/uP/+Ga/ce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XxXgNIxgOR/ROdkkulxGRcDisd6xSyrZt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\nih0AAIBP/H/fo5kwCVs2AwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "\n",
    "# Plot exponential histograms\n",
    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
    "ggplot(data=df, aes(x=Y, col=X, fill=X)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # create the histogram; the alpha value ensures overlaps can be seen\n",
    "  geom_histogram(color=\"darkgray\", binwidth=5, breaks=seq(0,50,by=5), alpha=0.25, position=\"identity\") + \n",
    "  # create stacked plots by X, one for each histogram\n",
    "  facet_grid(X ~ .) + \n",
    "  # determine the fill color values of each histogram\n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\")) + \n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Histograms of Y by X\", x=\"Y\", y=\"Count\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_continuous(breaks=seq(0,50,by=5), labels=seq(0,50,by=5), limits=c(0,50)) +\n",
    "  scale_y_continuous(breaks=seq(0,14,by=2), labels=seq(0,14,by=2), limits=c(0,14))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed8ca09-1784-4a5c-8ba1-f183a00adc69",
   "metadata": {},
   "source": [
    "## Gamma Distribution\n",
    "\n",
    "* **Parameterization:** shape (α): `shape`, rate (β): `rate`\n",
    "* **Distribution Functions:** `_gamma`: `dgamma`, `pgamma`, `qgamma`, `rgamma`\n",
    "* **Reporting:** \"Figure 7 shows the distributions of response Y for both levels of factor X. To test whether these distributions were Gamma distributed, a Kolmogorov-Smirnov test was run on Y for both levels of X. The test for level ‘a’ was statistically non-significant (D = .116, p = .773), as was the test for level ‘b’ (D = .143, p = .526), indicating non-detectable deviations from a Gamma distribution for both levels.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0ac34455-6d1a-4617-9c68-fecbdac2dca2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>10.345366</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>b</td><td> 1.409266</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>a</td><td> 6.433979</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td> 3.092545</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td> 3.943187</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>b</td><td> 2.696895</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>a</td><td> 4.507424</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td> 2.838128</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td> 5.451457</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>b</td><td>11.115251</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>a</td><td> 5.308393</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td> 2.263850</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td> 6.573330</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>b</td><td> 5.052664</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>a</td><td> 3.564134</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td> 3.250415</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>10.281266</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>b</td><td> 2.987387</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>a</td><td> 3.656736</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td> 2.773202</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & S & X & Y\\\\\n",
       "  & <int> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & 10.345366\\\\\n",
       "\t2 &  2 & b &  1.409266\\\\\n",
       "\t3 &  3 & a &  6.433979\\\\\n",
       "\t4 &  4 & b &  3.092545\\\\\n",
       "\t5 &  5 & a &  3.943187\\\\\n",
       "\t6 &  6 & b &  2.696895\\\\\n",
       "\t7 &  7 & a &  4.507424\\\\\n",
       "\t8 &  8 & b &  2.838128\\\\\n",
       "\t9 &  9 & a &  5.451457\\\\\n",
       "\t10 & 10 & b & 11.115251\\\\\n",
       "\t11 & 11 & a &  5.308393\\\\\n",
       "\t12 & 12 & b &  2.263850\\\\\n",
       "\t13 & 13 & a &  6.573330\\\\\n",
       "\t14 & 14 & b &  5.052664\\\\\n",
       "\t15 & 15 & a &  3.564134\\\\\n",
       "\t16 & 16 & b &  3.250415\\\\\n",
       "\t17 & 17 & a & 10.281266\\\\\n",
       "\t18 & 18 & b &  2.987387\\\\\n",
       "\t19 & 19 & a &  3.656736\\\\\n",
       "\t20 & 20 & b &  2.773202\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 3\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 |  1 | a | 10.345366 |\n",
       "| 2 |  2 | b |  1.409266 |\n",
       "| 3 |  3 | a |  6.433979 |\n",
       "| 4 |  4 | b |  3.092545 |\n",
       "| 5 |  5 | a |  3.943187 |\n",
       "| 6 |  6 | b |  2.696895 |\n",
       "| 7 |  7 | a |  4.507424 |\n",
       "| 8 |  8 | b |  2.838128 |\n",
       "| 9 |  9 | a |  5.451457 |\n",
       "| 10 | 10 | b | 11.115251 |\n",
       "| 11 | 11 | a |  5.308393 |\n",
       "| 12 | 12 | b |  2.263850 |\n",
       "| 13 | 13 | a |  6.573330 |\n",
       "| 14 | 14 | b |  5.052664 |\n",
       "| 15 | 15 | a |  3.564134 |\n",
       "| 16 | 16 | b |  3.250415 |\n",
       "| 17 | 17 | a | 10.281266 |\n",
       "| 18 | 18 | b |  2.987387 |\n",
       "| 19 | 19 | a |  3.656736 |\n",
       "| 20 | 20 | b |  2.773202 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X Y        \n",
       "1   1 a 10.345366\n",
       "2   2 b  1.409266\n",
       "3   3 a  6.433979\n",
       "4   4 b  3.092545\n",
       "5   5 a  3.943187\n",
       "6   6 b  2.696895\n",
       "7   7 a  4.507424\n",
       "8   8 b  2.838128\n",
       "9   9 a  5.451457\n",
       "10 10 b 11.115251\n",
       "11 11 a  5.308393\n",
       "12 12 b  2.263850\n",
       "13 13 a  6.573330\n",
       "14 14 b  5.052664\n",
       "15 15 a  3.564134\n",
       "16 16 b  3.250415\n",
       "17 17 a 10.281266\n",
       "18 18 b  2.987387\n",
       "19 19 a  3.656736\n",
       "20 20 b  2.773202"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has one factor (X) w/two levels (a,b) and continuous response Y\n",
    "df <- read.csv(\"data/1F2LBs_gamma.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "210c6c78-3e9c-43c3-977a-afd62375f184",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df[df$X == \"a\", ]$Y\n",
       "D = 0.11585, p-value = 0.7732\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df[df$X == \"b\", ]$Y\n",
       "D = 0.14293, p-value = 0.5258\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(MASS) # for fitdistr\n",
    "fa = fitdistr(df[df$X == \"a\",]$Y, \"gamma\")$estimate # create fit for X.a\n",
    "ks.test(df[df$X == \"a\",]$Y, \"pgamma\", shape=fa[1], rate=fa[2])\n",
    "fb = fitdistr(df[df$X == \"b\",]$Y, \"gamma\")$estimate # create fit for X.b\n",
    "ks.test(df[df$X == \"b\",]$Y, \"pgamma\", shape=fb[1], rate=fb[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1a0dc6ef-2aaf-48b2-a2b2-5ba55bb37e05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SFbpLi3/PJjIpWGbJHCT4FSYSKVhmyRTpKJZBicl8xkchc74/C3j/Xr//iKxD7P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\nLIfo0QrOyQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "\n",
    "# Plot gamma histograms\n",
    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
    "ggplot(data=df, aes(x=Y, col=X, fill=X)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font style for the facet labels\n",
    "  theme(strip.text = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5)) + \n",
    "  # create the histogram; the alpha value ensures overlaps can be seen\n",
    "  geom_histogram(color=\"darkgray\", binwidth=2, breaks=seq(0,12,by=2), alpha=0.25, position=\"identity\") + \n",
    "  # create stacked plots by X, one for each histogram\n",
    "  facet_grid(X ~ .) + \n",
    "  # determine the fill color values of each histogram\n",
    "  scale_fill_manual(values=c(\"#69b3a2\",\"#404080\")) + \n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Histograms of Y by X\", x=\"Y\", y=\"Count\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_continuous(breaks=seq(0,12,by=2), labels=seq(0,12,by=2), limits=c(0,12)) +\n",
    "  scale_y_continuous(breaks=seq(0,14,by=2), labels=seq(0,14,by=2), limits=c(0,14))"
   ]
  }
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