generalized-esd-test-for-outliers.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.random.random(100)\n",
    "x = np.arange(len(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x115f9d908>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y[14] = 9\n",
    "y[83] = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x116095c88>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grubbs_stat(y):\n",
    "    std_dev = np.std(y)\n",
    "    avg_y = np.mean(y)\n",
    "    abs_val_minus_avg = abs(y - avg_y)\n",
    "    max_of_deviations = max(abs_val_minus_avg)\n",
    "    max_ind = np.argmax(abs_val_minus_avg)\n",
    "    Gcal = max_of_deviations/ std_dev\n",
    "    print(\"Grubbs Statistics Value : {}\".format(Gcal))\n",
    "    return Gcal, max_ind"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_critical_value(size, alpha):\n",
    "    t_dist = stats.t.ppf(1 - alpha / (2 * size), size - 2)\n",
    "    numerator = (size - 1) * np.sqrt(np.square(t_dist))\n",
    "    denominator = np.sqrt(size) * np.sqrt(size - 2 + np.square(t_dist))\n",
    "    critical_value = numerator / denominator\n",
    "    print(\"Grubbs Critical Value: {}\".format(critical_value))\n",
    "    return critical_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_G_values(Gs, Gc, inp, max_index):\n",
    "    if Gs > Gc:\n",
    "        print('{} is an outlier. G > G-critical: {:.4f} > {:.4f} \\n'.format(inp[max_index], Gs, Gc))\n",
    "    else:\n",
    "        print('{} is not an outlier. G > G-critical: {:.4f} > {:.4f} \\n'.format(inp[max_index], Gs, Gc))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ESD_Test(input_series, alpha, max_outliers):\n",
    "    for iterations in range(max_outliers):\n",
    "        Gcritical = calculate_critical_value(len(input_series), alpha)\n",
    "        Gstat, max_index = grubbs_stat(input_series)\n",
    "        check_G_values(Gstat, Gcritical, input_series, max_index)\n",
    "        input_series = np.delete(input_series, max_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Grubbs Critical Value: 3.384082902288351\n",
      "Grubbs Statistics Value : 7.193272867546962\n",
      "10.0 is an outlier. G > G-critical: 7.1933 > 3.3841 \n",
      "\n",
      "Grubbs Critical Value: 3.380650508067058\n",
      "Grubbs Statistics Value : 9.350050320562449\n",
      "9.0 is an outlier. G > G-critical: 9.3501 > 3.3807 \n",
      "\n",
      "Grubbs Critical Value: 3.377175980782947\n",
      "Grubbs Statistics Value : 1.6804988446150868\n",
      "0.021952769648038606 is not an outlier. G > G-critical: 1.6805 > 3.3772 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "ESD_Test(y, 0.05, 3)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}