math-statistics/histogram_implementation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9511f878-78e5-42c4-98cf-0677b3e8ad9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fbe96960-1f00-4cd9-b07b-4440f972897c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.00052432, 0.00052432, 0.00262162, 0.00969999, 0.02464321,\n",
       "        0.04954858, 0.10407824, 0.19662136, 0.27291044, 0.3562779 ,\n",
       "        0.41133188, 0.39324271, 0.31275904, 0.22231321, 0.13711063,\n",
       "        0.07471612, 0.0322459 , 0.01205944, 0.00681621, 0.00157297]),\n",
       " array([-4.07256249, -3.69111867, -3.30967486, -2.92823105, -2.54678723,\n",
       "        -2.16534342, -1.78389961, -1.4024558 , -1.02101198, -0.63956817,\n",
       "        -0.25812436,  0.12331946,  0.50476327,  0.88620708,  1.2676509 ,\n",
       "         1.64909471,  2.03053852,  2.41198233,  2.79342615,  3.17486996,\n",
       "         3.55631377]),\n",
       " <BarContainer object of 20 artists>)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.random.normal(size=10000)\n",
    "plt.hist(X, bins=20, density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "90b1dc85-349a-4d83-a23f-6d60e3e151a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sturge_rule(input):\n",
    "    n = 1 + 3.322 * math.log(len(input))\n",
    "    n = math.ceil(n)\n",
    "    return n\n",
    "\n",
    "def doane_rule(input):\n",
    "    t = np.array(input) - np.mean(input)\n",
    "    b = np.sum(t**3) / np.power(np.sum(t**2), 3/2)\n",
    "    s = np.std(input)\n",
    "    n = math.log2(len(input)) + 1 + math.log2(1 + (math.sqrt(b) / (s * math.sqrt(b))))\n",
    "    n = math.ceil(n)\n",
    "    return n\n",
    "\n",
    "def scott_rule(input):\n",
    "    std = np.std(input)\n",
    "    n = math.ceil(3.49 * std * math.pow(len(input), 1/3))\n",
    "    return n\n",
    "\n",
    "def rice_rule(input):\n",
    "    n = math.ceil(2 * math.pow(len(input), 1/3))\n",
    "    return n\n",
    "\n",
    "def freedman_rule(input):\n",
    "    q3 = np.quantile(input, 0.75)\n",
    "    q1 = np.quantile(input, 0.25)\n",
    "    iqr = q3 - q1\n",
    "\n",
    "    n = math.ceil(2 * iqr * math.pow(len(input), 1/3))\n",
    "    return n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9e36c892-13bd-4ee3-a504-25576a6150f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def histogram(input: list, h: float=None, rule: str=\"sturge\"):\n",
    "    min_x = min(input)\n",
    "    max_x = max(input)\n",
    "    rule_dict = {\n",
    "        \"sturge\": sturge_rule,\n",
    "        \"scott\": scott_rule,\n",
    "        \"rice\": rice_rule,\n",
    "        \"doane\": doane_rule,\n",
    "        \"freedman\": freedman_rule\n",
    "    }\n",
    "    if h is None:\n",
    "        n = rule_dict[rule](input)\n",
    "        h = (max_x - min_x) / n\n",
    "    else:\n",
    "        n = math.ceil((max_x - min_x) / h)\n",
    "    \n",
    "    # print(\"Number of bins:\", n)\n",
    "    # print(\"Width of bin:\", h)\n",
    "    # print(\"Min,Max\", min(input), max(input))\n",
    "    height = [0]*n\n",
    "    bins = []\n",
    "\n",
    "    for i in range(n):\n",
    "        min_bin = min_x + h * i\n",
    "        max_bin = min_x + h * (i + 1)\n",
    "        bins.append(min_bin + (max_bin - min_bin) / 2)\n",
    "        # print(f\"Bin {i}, min={min_bin}, max={max_bin}\")\n",
    "\n",
    "    for x in input:\n",
    "        i = int((x - min_x - 0.0001) / h)\n",
    "        # print(\"Value:\", x,\"Index:\", i)\n",
    "        height[i] += 1\n",
    "    \n",
    "    height = np.array(height)\n",
    "    density = height / (len(input) * h)\n",
    "    return height, density, bins, n, h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a7f5bc03-d9bf-4a75-988f-9105c28b4485",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Normal Distribution(u=0, s=1)')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "H, D, bins, N, W = histogram(X, rule=\"sturge\")\n",
    "T = np.linspace(min(X), max(X), 100)\n",
    "U = norm.pdf(T)\n",
    "plt.bar(bins, D, width=W)\n",
    "plt.plot(T, U, c=\"r\")\n",
    "plt.title(f\"Normal Distribution(u=0, s=1)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fb787b84-6def-4651-b52c-679c14408b39",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}