comcon1/skew-removing.ipynb

## skew-removing.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1ff35b38-a530-4b93-bee6-b66ea403fd3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.special import erf\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "766375fc-d3e6-4638-a327-b2ff2d854804",
   "metadata": {},
   "source": [
    "# How to remove skewness from a sample\n",
    "- [About statistical moments moments (at libretexts)](https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/04%3A_Expected_Value/4.04%3A_Skewness_and_Kurtosis)\n",
    "- [Skew normal distribution](https://en.wikipedia.org/wiki/Skew_normal_distribution)\n",
    "- [About Yeo-Johnson and Cox-Box transormations](https://statisticaloddsandends.wordpress.com/2021/02/19/the-box-cox-and-yeo-johnson-transformations-for-continuous-variables/)\n",
    "## Simulate a skewed sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6f2d6d80-16af-4ce0-91c1-c2d283bd810c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# decorator for sampling over arbitrary distribution function\n",
    "# https://stackoverflow.com/questions/21100716/fast-arbitrary-distribution-random-sampling-inverse-transform-sampling\n",
    "\n",
    "def inverse_sample_decorator(dist):\n",
    "    def wrapper(pnts, x_min=-100, x_max=100, n=1e5, **kwargs):\n",
    "        x = np.linspace(x_min, x_max, int(n))\n",
    "        cumulative = np.cumsum(dist(x, **kwargs))\n",
    "        cumulative -= cumulative.min()\n",
    "        f = interp1d(cumulative/cumulative.max(), x)\n",
    "        return f(np.random.random(pnts))\n",
    "    return wrapper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "3cbdb224-b755-4e99-a997-bfabfa0c9c4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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L2t/9dbEhVNVTwMnbMhwG7qmqQ0lel+R13WoPMvhH9yhwJ/D7MwnbQ8/x/CnwE8Bfd7+PxRnFHarneJrRZzxVdRj4JHAAeBh4X1UdnFXm1XgpvSQ16kzcA5ekZwULXJIaZYFLUqMscElqlAUuSY2ywCWpURa4JDXqfwHKDSfGZAUCewAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# be sure that it works\n",
    "@inverse_sample_decorator\n",
    "def gauss(x, amp=1.0, mean=0.0, std=0.2):\n",
    "    return amp*np.exp(-(x-mean)**2/std**2/2.0)\n",
    "_ = plt.hist(gauss(150))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "7d137008-c6a3-4aab-b429-ab8509be8508",
   "metadata": {},
   "outputs": [],
   "source": [
    "# function for simulate skew normal distribution with mean=0\n",
    "@inverse_sample_decorator\n",
    "def gauss_skew(x, amp=1.0, std=1, alpha=1.5):\n",
    "    return amp*np.exp(-x**2/std**2/2.0) * (0.5 - 0.5*erf(alpha*x/np.sqrt(2)) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "bbc080ae-ea74-4026-8f60-5751e834902d",
   "metadata": {},
   "outputs": [
    {
     "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.hist(gauss_skew(1500, alpha=4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28b43366-0f90-4b6d-9343-99fc03d1bf2e",
   "metadata": {},
   "source": [
    "## Skew-removing transofrmations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "4d2ae5ef-7920-481b-b1a1-f0e29e413ac1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import yeojohnson\n",
    "from scipy.stats import skew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "643dedde-f3be-41aa-bda1-0bbb40b28459",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Skew of our sample:    0.780\n"
     ]
    },
    {
     "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": [
    "# make model skewed sample\n",
    "xds = gauss_skew(1500, alpha=-5)\n",
    "_ = plt.hist( xds )\n",
    "print(\"Skew of our sample: %8.3f\" % skew(xds))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d85a5b5c-71ac-4697-892e-b2ad5ce25699",
   "metadata": {},
   "source": [
    "**Performing Yeo-Johnson transormation...**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "789fe26f-03b1-4f98-a801-55612e65902c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lambda parameter of the transformation:   0.0291\n"
     ]
    }
   ],
   "source": [
    "# perform the transformation\n",
    "res = yeojohnson(xds)\n",
    "print (\"Lambda parameter of the transformation: %8.4f\" % res[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "12ebb68b-857f-416a-bdc4-54e28b686907",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Skew of our sample:   -0.001\n"
     ]
    },
    {
     "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.hist(res[0])\n",
    "print(\"Skew of our sample: %8.3f\" % skew(res[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96e8b366-a8b3-46e7-a4e2-ed8adb839740",
   "metadata": {},
   "source": [
    "**Performing Yeo-Johnson transormation...**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "0a207319-c7b8-433b-9d54-9932937e45a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "xds += 2 # Box-Cox works with only positive values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "648970e1-0516-46dd-8372-d9a2f169446c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import boxcox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "4374d4ac-1061-485f-aea4-651865527620",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lambda parameter of the transformation:   0.0291\n"
     ]
    }
   ],
   "source": [
    "# perform the transformation\n",
    "res = boxcox(xds)\n",
    "print (\"Lambda parameter of the transformation: %8.4f\" % res[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "8336fe11-a440-4814-b8b4-d0bcb60766d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Skew of our sample:   -0.001\n"
     ]
    },
    {
     "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.hist(res[0])\n",
    "print(\"Skew of our sample: %8.3f\" % skew(res[0]))"
   ]
  }
 ],
 "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": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}