{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "range_end = 26\n",
    "max_count = 1_000_000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "def make_barchart(title, random_ints, show_line=False):\n",
    "    \"\"\"Draw a frequency barchart.\"\"\"\n",
    "    values, frequencies = np.unique(random_ints, return_counts=True)\n",
    "    \n",
    "    plt.figure(figsize=(10, 4))\n",
    "    sns.set_style('whitegrid')\n",
    "    \n",
    "    full_values = []  # values starting with 0 without any missing\n",
    "    full_freqs  = []  # frequencies of the full values\n",
    "    \n",
    "    # Fill in missing values with 0 frequencies.\n",
    "    index = 0\n",
    "    for i in range(range_end):\n",
    "        full_values += [i]\n",
    "\n",
    "        if (index >= len(frequencies)) or (i < values[index]):\n",
    "            full_freqs += [0]  # missing value\n",
    "        else:\n",
    "            full_freqs += [frequencies[index]]\n",
    "            index += 1           \n",
    "    \n",
    "    axes = sns.barplot(x=full_values, y=full_freqs, color='blue')\n",
    "    \n",
    "    # Show a line plot only if requested.\n",
    "    if show_line:\n",
    "        axes = sns.lineplot(x=full_values, y=full_freqs, color='red')\n",
    "        \n",
    "    axes.set_title(title)\n",
    "    axes.set(xlabel='Value', ylabel='Frequency')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "def make_histogram(title, random_values):\n",
    "    \"\"\"Make a histogram.\"\"\"\n",
    "    plt.figure(figsize=(10, 4))\n",
    "    sns.set_style('whitegrid')\n",
    "    \n",
    "    axes = sns.distplot(random_values)\n",
    "    axes.set_title(title)\n",
    "    axes.set(xlabel='Value', ylabel='Frequency')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "uniform_ints = [int(random.uniform(0, range_end)) for _ in range(max_count)]\n",
    "make_barchart('Uniform Distribution', uniform_ints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "uniform_values = [random.uniform(0, range_end) for _ in range(max_count)]\n",
    "make_histogram('Uniform Distribution', uniform_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal_ints = []\n",
    "\n",
    "while len(normal_ints) < max_count:\n",
    "    n = int(random.gauss(12.5, 3.3))\n",
    "    if n in range(0, range_end):\n",
    "        normal_ints += [n]\n",
    "        \n",
    "title = 'Normal Distribution' + \", count = \" + str(max_count);\n",
    "        \n",
    "values, frequencies = np.unique(normal_ints, return_counts=True)\n",
    "make_barchart(title, normal_ints, show_line=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal_values = [random.gauss(12.5, 3.3) for _ in range(max_count)]\n",
    "make_histogram(title, normal_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "expo_ints = []\n",
    "lambd = 1/12.5\n",
    "\n",
    "while len(expo_ints) < max_count:\n",
    "    n = int(random.expovariate(lambd))\n",
    "    if n < 2*range_end:\n",
    "        expo_ints += [n]\n",
    "        \n",
    "make_barchart('Exponential Distribution', expo_ints, show_line=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "expo_values = []\n",
    "lambd = 1/12.5\n",
    "\n",
    "while len(expo_values) < max_count:\n",
    "    n = random.expovariate(lambd)\n",
    "    if n < 2*range_end:\n",
    "        expo_values += [n]\n",
    "        \n",
    "make_histogram('Exponential Distribution', expo_values)"
   ]
  }
 ],
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