PythonDataBasics_DistributionsTransformations.ipynb

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    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Data Analytics \n",
    "\n",
    "### Distribution Transformations in Python \n",
    "\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
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    "### Data Analytics: Distribution Transformations\n",
    "\n",
    "Here's a demonstration of making and general use of distribution transformations in Python. This demonstration is part of the resources that I include for my courses in Spatial / Subsurface Data Analytics at the Cockrell School of Engineering at the University of Texas at Austin.  \n",
    "\n",
    "#### Distribution Transformations\n",
    "\n",
    "Why do we do this?\n",
    "\n",
    "* **Inference**: variable has expected shape \n",
    "\n",
    "* **Data Preparation / Cleaning**: correcting for too few data and outliers\n",
    "\n",
    "* **Theory**: a specific distribution assumption required for a method\n",
    "\n",
    "How do we do it?\n",
    "\n",
    "We apply this to all sample data, $x_{\\alpha}$ $\\forall$ $\\alpha = 1,\\ldots,n$.\n",
    "\n",
    "\\begin{equation}\n",
    "y_{\\alpha} = G^{-1}_Y\\left(F_X(x_{\\alpha})\\right)\n",
    "\\end{equation}\n",
    "\n",
    "were $X$ is the original feature with a $F_X$ original cumulative distribution function and $Y$ is transformed feature with a $G_Y$ transformed cumulative distribution function.\n",
    "\n",
    "* Mapping from one distribution to another through percentiles\n",
    "\n",
    "* This may be applied to any parametric or nonparametric distributions\n",
    "\n",
    "* This is a rank preserving transform, e.g. P50 of 𝑋 is P50 of 𝑌\n",
    "\n",
    "I have a lecture on distribution transformations available on [YouTube](https://www.youtube.com/watch?v=ZDIpE3OkAIU&list=PLG19vXLQHvSB-D4XKYieEku9GQMQyAzjJ&index=14).   \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "You will need to copy the data file to your working directory.  They are available here:\n",
    "\n",
    "* Tabular data - [sample_data.csv](https://github.com/GeostatsGuy/GeoDataSets/blob/master/sample_data.csv).\n",
    "\n",
    "#### Importing Packages\n",
    "\n",
    "We will need some standard packages. These should have been installed with Anaconda 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                        # ndarrys for gridded data\n",
    "import pandas as pd                       # DataFrames for tabular data\n",
    "import os                                 # set working directory, run executables\n",
    "import matplotlib.pyplot as plt           # plotting\n",
    "from scipy import stats                   # summary statistics\n",
    "import math                               # trigonometry etc.\n",
    "import scipy.signal as signal             # kernel for moving window calculation\n",
    "import random                             # randon numbers\n",
    "import seaborn as sns                     # matrix scatter plots\n",
    "from scipy.stats import norm              # Gaussian parametric distribution\n",
    "from sklearn import preprocessing\n",
    "import geostatspy.GSLIB as GSLIB\n",
    "from ipywidgets import interactive                      # widgets and interactivity\n",
    "from ipywidgets import widgets                            \n",
    "from ipywidgets import Layout\n",
    "from ipywidgets import Label\n",
    "from ipywidgets import VBox, HBox"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the Random Number Seed\n",
    "\n",
    "Set the random number seed so that we have a repeatable workflow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 73073"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the Working Directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.chdir(\"c:/PGE383\")                     # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading Tabular Data\n",
    "\n",
    "Here's the command to load our comma delimited data file in to a Pandas' DataFrame object.  For fun try misspelling the name. You will get an ugly, long error.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('sample_data.csv')     # load our data table (wrong name!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It worked, we loaded our file into our DataFrame called 'df'. But how do you really know that it worked? Visualizing the DataFrame would be useful and we already leard about these methods in this demo (https://git.io/fNgRW). \n",
    "\n",
    "We can preview the DataFrame by printing a slice or by utilizing the 'head' DataFrame member function (with a nice and clean format, see below). With the slice we could look at any subset of the data table and with the head command, add parameter 'n=13' to see the first 13 rows of the dataset.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>Facies</th>\n",
       "      <th>Porosity</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.0</td>\n",
       "      <td>900.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.100187</td>\n",
       "      <td>1.363890</td>\n",
       "      <td>5110.699751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100.0</td>\n",
       "      <td>800.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.107947</td>\n",
       "      <td>12.576845</td>\n",
       "      <td>4671.458560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100.0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.085357</td>\n",
       "      <td>5.984520</td>\n",
       "      <td>6127.548006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>100.0</td>\n",
       "      <td>600.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.108460</td>\n",
       "      <td>2.446678</td>\n",
       "      <td>5201.637996</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100.0</td>\n",
       "      <td>500.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.102468</td>\n",
       "      <td>1.952264</td>\n",
       "      <td>3835.270322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>100.0</td>\n",
       "      <td>400.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.110579</td>\n",
       "      <td>3.691908</td>\n",
       "      <td>5295.267191</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "       X      Y  Facies  Porosity       Perm           AI\n",
       "0  100.0  900.0     1.0  0.100187   1.363890  5110.699751\n",
       "1  100.0  800.0     0.0  0.107947  12.576845  4671.458560\n",
       "2  100.0  700.0     0.0  0.085357   5.984520  6127.548006\n",
       "3  100.0  600.0     0.0  0.108460   2.446678  5201.637996\n",
       "4  100.0  500.0     0.0  0.102468   1.952264  3835.270322\n",
       "5  100.0  400.0     0.0  0.110579   3.691908  5295.267191"
      ]
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     "execution_count": 19,
     "metadata": {},
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   "source": [
    "df.head(n=6)                           # we could also use this command for a table preview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculating and Plotting a CDF by Hand\n",
    "\n",
    "Let's demonstrate the calculation and plotting of a non-parametric CDF by hand\n",
    "\n",
    "1. make a copy of the feature as a 1D array (ndarray from NumPy)\n",
    "2. sort the data in ascending order\n",
    "3. assign cumulative probabilities based on the tail assumptions\n",
    "4. plot cumuative probability vs. value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The ndarray has a shape of (261,).\n"
     ]
    },
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "por = df['Porosity'].copy(deep = True).values # make a deepcopy of the feature from the DataFrame\n",
    "print('The ndarray has a shape of ' + str(por.shape) + '.')\n",
    "\n",
    "por = np.sort(por)                           # sort the data in ascending order\n",
    "n = por.shape[0]                             # get the number of data samples\n",
    "\n",
    "cprob = np.zeros(n)\n",
    "for i in range(0,n):\n",
    "    index = i + 1\n",
    "    cprob[i] = index / n                     # known upper tail\n",
    "    # cprob[i] = (index - 1)/n               # known lower tail\n",
    "    # cprob[i] = (index - 1)/(n - 1)         # known upper and lower tails\n",
    "    # cprob[i] = index/(n+1)                 # unknown tails  \n",
    "\n",
    "plt.subplot(111)\n",
    "plt.plot(por,cprob, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "plt.scatter(por,cprob,s = 10, alpha = 1.0, c = 'red', edgecolor = 'black') # plot the CDF points\n",
    "plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Non-parametric Porosity Cumulative Distribution Function\")\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.1, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transformation to a Parametric Distribution\n",
    "\n",
    "We can transform our data feature distribution to any parametric distribution with this workflow.\n",
    "\n",
    "1. Calculate the cumulative probability value of each of our data values, $p_{\\alpha} = F_x(x_\\alpha)$, $\\forall$ $\\alpha = 1,\\ldots, n$.\n",
    "\n",
    "2. Apply the inverse of the target parametric cumulative distribution function (CDF) to calculate the transformed values. $y_{\\alpha} = G_y^{-1}\\left(F_x(x_\\alpha)\\right)$, $\\forall$ $\\alpha = 1,\\ldots, n$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = np.zeros(n)\n",
    "\n",
    "for i in range(0,n):\n",
    "    y[i] = norm.ppf(cprob[i],loc=0.0,scale=1.0)\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(por,cprob, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "plt.scatter(por,cprob,s = 10, alpha = 1.0, c = 'red', edgecolor = 'black') # plot the CDF points\n",
    "plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Non-parametric Porosity Cumulative Distribution Function\")\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(y,cprob, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "plt.scatter(y,cprob,s = 10, alpha = 1.0, c = 'red', edgecolor = 'black') # plot the CDF points\n",
    "plt.grid(); plt.xlim([-3.0,3.0]); plt.ylim([0.0,1.0])\n",
    "plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"After Distribution Transformation to Gaussian\")\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make an interactive version of this plot to visualize the transformation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# widgets and dashboard\n",
    "l = widgets.Text(value='                                                  Data Analytics, Distribution Transformation, Prof. Michael Pyrcz, The University of Texas at Austin',layout=Layout(width='950px', height='30px'))\n",
    "\n",
    "data_index = widgets.IntSlider(min=1, max = n-1, value=1.0, step = 10.0, description = 'Data Index, $\\\\alpha$',orientation='horizontal', style = {'description_width': 'initial'}, continuous_update=False)\n",
    "\n",
    "ui = widgets.VBox([l,data_index],)\n",
    "\n",
    "def run_plot(data_index):                       # make data, fit models and plot\n",
    "    plt.subplot(131)\n",
    "    plt.plot(por,cprob, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "    plt.scatter(por,cprob,s = 10, alpha = 1.0, c = 'red', edgecolor = 'black') # plot the CDF points\n",
    "    plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "    plt.xlabel(\"Original Feature, $x$\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Original Cumulative Distribution Function\")\n",
    "    plt.plot([por[data_index-1],por[data_index-1]],[0.0,cprob[data_index-1]],color = 'red',linestyle='dashed')\n",
    "    plt.plot([por[data_index-1],3.0],[cprob[data_index-1],cprob[data_index-1]],color = 'red',linestyle='dashed')\n",
    "    plt.annotate('x = ' + str(round(por[data_index-1],2)), xy=(por[data_index-1]+0.003, 0.01))\n",
    "    plt.annotate('p = ' + str(round(cprob[data_index-1],2)), xy=(0.225, cprob[data_index-1]+0.02))\n",
    "\n",
    "    \n",
    "    plt.subplot(132)\n",
    "    plt.plot(y,cprob, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "    plt.scatter(y,cprob,s = 10, alpha = 1.0, c = 'red', edgecolor = 'black') # plot the CDF points\n",
    "    plt.grid(); plt.xlim([-3.0,3.0]); plt.ylim([0.0,1.0])\n",
    "    plt.xlabel(\"Gaussian Transformed Feature, $y$\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"After Distribution Transformation to Gaussian\")\n",
    "    plt.plot([-3.0,y[data_index-1]],[cprob[data_index-1],cprob[data_index-1]],color = 'red',linestyle='dashed')\n",
    "    plt.plot([y[data_index-1],y[data_index-1]],[0.0,cprob[data_index-1]],color = 'red',linestyle='dashed')\n",
    "    #plt.arrow(y[data_index-1],cprob[data_index-1],0.0,-1.0*(cprob[data_index-1]-0.01),color = 'red',width = 0.02, head_width = 0.1, linestyle='dashed', head_length = 0.01)\n",
    "    plt.annotate('p = ' + str(round(cprob[data_index-1],2)), xy=(-2.90, cprob[data_index-1]+0.02)) \n",
    "    plt.annotate('y = ' + str(round(y[data_index-1],2)), xy=(y[data_index-1]+0.1, 0.01))\n",
    "    \n",
    "    plt.subplot(133)\n",
    "    plt.plot(por,y, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "    plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([-3.0,3.0])\n",
    "    plt.xlabel(\"Original Porosity (fraction)\"); plt.ylabel(\"Gaussian Transformed Porosity (N[fraction])\"); plt.title(\"Parametric Distribution Transformation, Q-Q Plot\")\n",
    "    #plt.plot([0.05,0.25],[0.05,0.25],color = 'red',linestyle='dashed', alpha = 0.4)\n",
    "    plt.scatter(por[data_index-1],y[data_index-1],s = 50, c = 'red', edgecolor = 'black', alpha = 1.0, zorder=200) # plot the CDF points\n",
    "    plt.scatter(por,y,s = 20, c = 'red', edgecolor = 'black', alpha = 0.1, zorder=100) # plot the CDF points\n",
    "   \n",
    "    plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "    plt.show()\n",
    "    \n",
    "# connect the function to make the samples and plot to the widgets    \n",
    "interactive_plot = widgets.interactive_output(run_plot, {'data_index':data_index})\n",
    "interactive_plot.clear_output(wait = True)               # reduce flickering by delaying plot updating"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactive Data Analytics Distribution Transformation Demonstration \n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, The University of Texas at Austin \n",
    "\n",
    "Select any data value and observe the distribution transform by mapping through cumulative probability.\n",
    "\n",
    "### The Inputs\n",
    "\n",
    "* **data_index** - the data index from 1 to n in the sorted ascending order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b5a3cf769d3c49b9acb1d3468c838176",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(Text(value='                                                  Data Analytics, Distribution Tran…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7f377c0d01184e90a9c6011035d2b5c6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output(outputs=({'output_type': 'display_data', 'data': {'text/plain': '<Figure size 432x288 with 3 Axes>', 'i…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(ui, interactive_plot)                           # display the interactive plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Distribution Transform to a Non-Parametric Distribution\n",
    "\n",
    "We can apply the mapping through cumulative probabilities to transform from any distribution to any other distribution.\n",
    "\n",
    "* let's make a new data set by randomly sampling from the previous one and adding error\n",
    "\n",
    "Then we can demonstrate transforming this dataset to match the original distribution\n",
    "\n",
    "* this is mimicking the situation where we transform a dataset to match the distribution of a better sampled analog distribution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sample ndarray has a shape of (30,).\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_sample = 30\n",
    "df_sample = df.sample(n_sample,random_state = seed)\n",
    "                      \n",
    "df_sample = df_sample.copy(deep = True) # make a deepcopy of the feature from the DataFrame\n",
    "\n",
    "df_sample['Porosity'] = df_sample['Porosity'].values + np.random.normal(loc = 0.0, scale = 0.01, size = n_sample)\n",
    "\n",
    "df_sample = df_sample.sort_values(by = 'Porosity')                # sort the DataFrame\n",
    "por_sample = df_sample['Porosity'].values\n",
    "print('The sample ndarray has a shape of ' + str(por_sample.shape) + '.')\n",
    "\n",
    "cprob_sample = np.zeros(n_sample)\n",
    "for i in range(0,n_sample):\n",
    "    index = i + 1\n",
    "    cprob_sample[i] = index / n_sample       # known upper tail\n",
    "    # cprob[i] = (index - 1)/n               # known lower tail\n",
    "    # cprob[i] = (index - 1)/(n - 1)         # known upper and lower tails\n",
    "    # cprob[i] = index/(n+1)                 # unknown tails  \n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(por_sample,cprob_sample, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "plt.scatter(por_sample,cprob_sample,s = 10, alpha = 1.0, c = 'red', edgecolor = 'black') # plot the CDF points\n",
    "plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Sparse Sample with Noise Cumulative Distribution Function\")\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(por,cprob, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "plt.scatter(por,cprob,s = 10, alpha = 1.0, c = 'red', edgecolor = 'black') # plot the CDF points\n",
    "plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Non-parametric Porosity Cumulative Distribution Function\")\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's transform the values and show them on the target distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_sample = np.zeros(n_sample)\n",
    "\n",
    "for i in range(0,n_sample):\n",
    "    y_sample[i] = np.percentile(por,cprob_sample[i]*100, interpolation = 'linear') # piecewise linear interpolation of inverse of target CDF \n",
    "    \n",
    "plt.subplot(121)\n",
    "plt.plot(por_sample,cprob_sample, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "plt.scatter(por_sample,cprob_sample,s = 30, alpha = 1.0, c = 'green', edgecolor = 'black', zorder = 100) # plot the CDF points\n",
    "plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Sparse Sample with Noise Cumulative Distribution Function\")\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(por,cprob, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "plt.scatter(por,cprob,s = 10, c = 'red', edgecolor = 'black', alpha = 0.3) # plot the CDF points\n",
    "plt.scatter(y_sample,cprob_sample,s = 30, c = 'green', edgecolor = 'black', alpha = 1.0, zorder = 100) # plot the CDF points\n",
    "plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Non-parametric Porosity Cumulative Distribution Function\")\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make an interactive version of this plot to visualize the transformation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# widgets and dashboard\n",
    "l_sample = widgets.Text(value='                                                  Data Analytics, Distribution Transformation, Prof. Michael Pyrcz, The University of Texas at Austin',layout=Layout(width='950px', height='30px'))\n",
    "\n",
    "data_index_sample = widgets.IntSlider(min=1, max = n_sample, value=1.0, step = 1.0, description = 'Data Sample Index, $\\\\beta$',orientation='horizontal', style = {'description_width': 'initial'}, continuous_update=False)\n",
    "\n",
    "ui_sample = widgets.VBox([l_sample,data_index_sample],)\n",
    "\n",
    "def run_plot_sample(data_index_sample):                       # make data, fit models and plot\n",
    "    plt.subplot(131)\n",
    "    plt.plot(por_sample,cprob_sample, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "    plt.scatter(por_sample,cprob_sample,s = 30, alpha = 1.0, c = 'green', edgecolor = 'black',zorder = 100) # plot the CDF points\n",
    "    plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "    plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Original Sparse Sample with Noise, Cumulative Distribution Function\")\n",
    "    plt.plot([por_sample[data_index_sample-1],por_sample[data_index_sample-1]],[0.0,cprob_sample[data_index_sample-1]],color = 'red',linestyle='dashed')\n",
    "    plt.plot([por_sample[data_index_sample-1],3.0],[cprob_sample[data_index_sample-1],cprob_sample[data_index_sample-1]],color = 'red',linestyle='dashed')\n",
    "    plt.annotate('x = ' + str(round(por_sample[data_index_sample-1],2)), xy=(por_sample[data_index_sample-1]+0.003, 0.01))\n",
    "    plt.annotate('p = ' + str(round(cprob_sample[data_index_sample-1],2)), xy=(0.225, cprob_sample[data_index_sample-1]+0.02))\n",
    "    \n",
    "    plt.subplot(132)\n",
    "    plt.plot(por,cprob, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "    plt.scatter(por,cprob,s = 10, c = 'red', edgecolor = 'black', alpha = 1.0) # plot the CDF points\n",
    "    plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.0,1.0])\n",
    "    plt.xlabel(\"Porosity (fraction)\"); plt.ylabel(\"Cumulative Probability\"); plt.title(\"Non-parametric Target Porosity Cumulative Distribution Function\")\n",
    "    plt.plot([0.0,y_sample[data_index_sample-1]],[cprob_sample[data_index_sample-1],cprob_sample[data_index_sample-1]],color = 'red',linestyle='dashed')\n",
    "    plt.plot([y_sample[data_index_sample-1],y_sample[data_index_sample-1]],[0.0,cprob_sample[data_index_sample-1]],color = 'red',linestyle='dashed')\n",
    "    plt.annotate('p = ' + str(round(cprob_sample[data_index_sample-1],2)), xy=(0.053, cprob_sample[data_index_sample-1]+0.02)) \n",
    "    plt.annotate('y = ' + str(round(y_sample[data_index_sample-1],2)), xy=(y_sample[data_index_sample-1]+0.003, 0.01))\n",
    "    plt.scatter(y_sample[data_index_sample-1],cprob_sample[data_index_sample-1],s = 50, c = 'green', edgecolor = 'black', alpha = 1.0, zorder=100) # plot the CDF points\n",
    "    \n",
    "    plt.subplot(133)\n",
    "    plt.plot(por_sample,y_sample, alpha = 0.2, c = 'black') # plot piecewise linear interpolation\n",
    "    plt.grid(); plt.xlim([0.05,0.25]); plt.ylim([0.05,0.25])\n",
    "    plt.xlabel(\"Original Porosity (fraction)\"); plt.ylabel(\"Transformed Porosity (fraction)\"); plt.title(\"Non-parametric Distribution Transformation, Q-Q Plot\")\n",
    "    plt.plot([0.05,0.25],[0.05,0.25],color = 'red',linestyle='dashed', alpha = 0.4)\n",
    "    plt.scatter(por_sample[data_index_sample-1],y_sample[data_index_sample-1],s = 50, c = 'green', edgecolor = 'black', alpha = 1.0, zorder=200) # plot the CDF points\n",
    "    plt.scatter(por_sample,y_sample,s = 20, c = 'green', edgecolor = 'black', alpha = 0.3, zorder=100) # plot the CDF points\n",
    "        \n",
    "    plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    \n",
    "# connect the function to make the samples and plot to the widgets    \n",
    "interactive_plot_s = widgets.interactive_output(run_plot_sample, {'data_index_sample':data_index_sample})\n",
    "#interactive_plot_sample.clear_output(wait = True)               # reduce flickering by delaying plot updating"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactive Data Analytics Distribution Transformation Demonstration \n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, The University of Texas at Austin \n",
    "\n",
    "Select any data value and observe the distribution transform by mapping through cumulative probability.\n",
    "\n",
    "#### The Inputs\n",
    "\n",
    "* **data_index** - the data index from 1 to n in the sorted ascending order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c8b4739803ef48a3b0bd61fd80f71d32",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(Text(value='                                                  Data Analytics, Distribution Tran…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b744c53cf7f24ef18e2b819c241dd156",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output(outputs=({'output_type': 'display_data', 'data': {'text/plain': '<Figure size 432x288 with 3 Axes>', 'i…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(ui_sample, interactive_plot_s)                           # display the interactive plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To summarize let's look at a DataFrame with the original noisey sample and the transformed to match the original distribution.\n",
    "\n",
    "* we're making and showing a table of original values, $x_{\\beta}$ $\\forall$ $\\beta = 1, \\ldots, n_{sample}$, and the transformed values, $y_{\\beta}$ $\\forall$ $\\beta = 1, \\ldots, n_{sample}$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>Facies</th>\n",
       "      <th>Porosity</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "      <th>Transformed_Por</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>900.0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.077913</td>\n",
       "      <td>1.280257</td>\n",
       "      <td>4573.656072</td>\n",
       "      <td>0.081044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>189</th>\n",
       "      <td>201.0</td>\n",
       "      <td>456.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.091533</td>\n",
       "      <td>0.546396</td>\n",
       "      <td>5018.355476</td>\n",
       "      <td>0.085867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>218</th>\n",
       "      <td>251.0</td>\n",
       "      <td>416.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.093602</td>\n",
       "      <td>1.003374</td>\n",
       "      <td>5822.467914</td>\n",
       "      <td>0.091834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>207</th>\n",
       "      <td>201.0</td>\n",
       "      <td>426.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.101475</td>\n",
       "      <td>0.400658</td>\n",
       "      <td>5263.542112</td>\n",
       "      <td>0.095628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>100.0</td>\n",
       "      <td>400.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.108655</td>\n",
       "      <td>3.691908</td>\n",
       "      <td>5295.267191</td>\n",
       "      <td>0.099378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>500.0</td>\n",
       "      <td>400.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.109365</td>\n",
       "      <td>6.312198</td>\n",
       "      <td>5515.918646</td>\n",
       "      <td>0.101987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>100.0</td>\n",
       "      <td>600.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.112756</td>\n",
       "      <td>2.446678</td>\n",
       "      <td>5201.637996</td>\n",
       "      <td>0.103970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>900.0</td>\n",
       "      <td>900.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.118671</td>\n",
       "      <td>12.433996</td>\n",
       "      <td>6242.704810</td>\n",
       "      <td>0.106704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>600.0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.120329</td>\n",
       "      <td>12.384496</td>\n",
       "      <td>3595.586977</td>\n",
       "      <td>0.108460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>800.0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.120578</td>\n",
       "      <td>7.739105</td>\n",
       "      <td>5274.532660</td>\n",
       "      <td>0.111491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>210</th>\n",
       "      <td>231.0</td>\n",
       "      <td>426.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.125237</td>\n",
       "      <td>5.584040</td>\n",
       "      <td>4919.074871</td>\n",
       "      <td>0.113887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>600.0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.126804</td>\n",
       "      <td>42.396044</td>\n",
       "      <td>4204.150893</td>\n",
       "      <td>0.117984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226</th>\n",
       "      <td>211.0</td>\n",
       "      <td>396.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.129894</td>\n",
       "      <td>6.368529</td>\n",
       "      <td>5725.334803</td>\n",
       "      <td>0.121592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>955.0</td>\n",
       "      <td>559.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.184568</td>\n",
       "      <td>74.215058</td>\n",
       "      <td>3386.182722</td>\n",
       "      <td>0.127131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>955.0</td>\n",
       "      <td>529.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.187061</td>\n",
       "      <td>1113.971076</td>\n",
       "      <td>3177.635737</td>\n",
       "      <td>0.137062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>985.0</td>\n",
       "      <td>489.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.187291</td>\n",
       "      <td>73.133040</td>\n",
       "      <td>2672.294567</td>\n",
       "      <td>0.153759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>955.0</td>\n",
       "      <td>549.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.190464</td>\n",
       "      <td>374.298925</td>\n",
       "      <td>3181.557281</td>\n",
       "      <td>0.176536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>174</th>\n",
       "      <td>955.0</td>\n",
       "      <td>459.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.192032</td>\n",
       "      <td>45.002088</td>\n",
       "      <td>3394.563038</td>\n",
       "      <td>0.185270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>245</th>\n",
       "      <td>690.0</td>\n",
       "      <td>529.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.194038</td>\n",
       "      <td>316.905689</td>\n",
       "      <td>4271.013148</td>\n",
       "      <td>0.188136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>181</th>\n",
       "      <td>935.0</td>\n",
       "      <td>449.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.194922</td>\n",
       "      <td>368.507601</td>\n",
       "      <td>4249.477923</td>\n",
       "      <td>0.191655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>151</th>\n",
       "      <td>995.0</td>\n",
       "      <td>489.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.195531</td>\n",
       "      <td>460.494986</td>\n",
       "      <td>2792.804322</td>\n",
       "      <td>0.195998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>955.0</td>\n",
       "      <td>469.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.200185</td>\n",
       "      <td>26.197239</td>\n",
       "      <td>2889.196647</td>\n",
       "      <td>0.198182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>158</th>\n",
       "      <td>975.0</td>\n",
       "      <td>479.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.201035</td>\n",
       "      <td>69.336576</td>\n",
       "      <td>2493.128177</td>\n",
       "      <td>0.199315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>125</th>\n",
       "      <td>1005.0</td>\n",
       "      <td>519.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.204180</td>\n",
       "      <td>54.667195</td>\n",
       "      <td>2577.714678</td>\n",
       "      <td>0.201943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>925.0</td>\n",
       "      <td>539.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.206040</td>\n",
       "      <td>211.163296</td>\n",
       "      <td>3442.885245</td>\n",
       "      <td>0.206934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>985.0</td>\n",
       "      <td>499.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.211892</td>\n",
       "      <td>68.276148</td>\n",
       "      <td>2547.526113</td>\n",
       "      <td>0.209051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>975.0</td>\n",
       "      <td>529.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.215852</td>\n",
       "      <td>1548.094062</td>\n",
       "      <td>3167.185377</td>\n",
       "      <td>0.211638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>935.0</td>\n",
       "      <td>499.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.223535</td>\n",
       "      <td>523.287810</td>\n",
       "      <td>2579.032897</td>\n",
       "      <td>0.215686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>129</th>\n",
       "      <td>955.0</td>\n",
       "      <td>509.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.225374</td>\n",
       "      <td>1525.247066</td>\n",
       "      <td>2512.061434</td>\n",
       "      <td>0.224214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>975.0</td>\n",
       "      <td>489.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.243111</td>\n",
       "      <td>21.109085</td>\n",
       "      <td>2412.875330</td>\n",
       "      <td>0.242298</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X      Y  Facies  Porosity         Perm           AI  \\\n",
       "80    900.0  100.0     0.0  0.077913     1.280257  4573.656072   \n",
       "189   201.0  456.0     0.0  0.091533     0.546396  5018.355476   \n",
       "218   251.0  416.0     0.0  0.093602     1.003374  5822.467914   \n",
       "207   201.0  426.0     0.0  0.101475     0.400658  5263.542112   \n",
       "5     100.0  400.0     0.0  0.108655     3.691908  5295.267191   \n",
       "41    500.0  400.0     0.0  0.109365     6.312198  5515.918646   \n",
       "3     100.0  600.0     0.0  0.112756     2.446678  5201.637996   \n",
       "72    900.0  900.0     0.0  0.118671    12.433996  6242.704810   \n",
       "47    600.0  700.0     0.0  0.120329    12.384496  3595.586977   \n",
       "71    800.0  100.0     0.0  0.120578     7.739105  5274.532660   \n",
       "210   231.0  426.0     0.0  0.125237     5.584040  4919.074871   \n",
       "53    600.0  100.0     1.0  0.126804    42.396044  4204.150893   \n",
       "226   211.0  396.0     0.0  0.129894     6.368529  5725.334803   \n",
       "84    955.0  559.0     1.0  0.184568    74.215058  3386.182722   \n",
       "111   955.0  529.0     1.0  0.187061  1113.971076  3177.635737   \n",
       "150   985.0  489.0     1.0  0.187291    73.133040  2672.294567   \n",
       "93    955.0  549.0     1.0  0.190464   374.298925  3181.557281   \n",
       "174   955.0  459.0     1.0  0.192032    45.002088  3394.563038   \n",
       "245   690.0  529.0     1.0  0.194038   316.905689  4271.013148   \n",
       "181   935.0  449.0     1.0  0.194922   368.507601  4249.477923   \n",
       "151   995.0  489.0     1.0  0.195531   460.494986  2792.804322   \n",
       "165   955.0  469.0     1.0  0.200185    26.197239  2889.196647   \n",
       "158   975.0  479.0     1.0  0.201035    69.336576  2493.128177   \n",
       "125  1005.0  519.0     1.0  0.204180    54.667195  2577.714678   \n",
       "99    925.0  539.0     1.0  0.206040   211.163296  3442.885245   \n",
       "141   985.0  499.0     1.0  0.211892    68.276148  2547.526113   \n",
       "113   975.0  529.0     1.0  0.215852  1548.094062  3167.185377   \n",
       "136   935.0  499.0     1.0  0.223535   523.287810  2579.032897   \n",
       "129   955.0  509.0     1.0  0.225374  1525.247066  2512.061434   \n",
       "149   975.0  489.0     1.0  0.243111    21.109085  2412.875330   \n",
       "\n",
       "     Transformed_Por  \n",
       "80          0.081044  \n",
       "189         0.085867  \n",
       "218         0.091834  \n",
       "207         0.095628  \n",
       "5           0.099378  \n",
       "41          0.101987  \n",
       "3           0.103970  \n",
       "72          0.106704  \n",
       "47          0.108460  \n",
       "71          0.111491  \n",
       "210         0.113887  \n",
       "53          0.117984  \n",
       "226         0.121592  \n",
       "84          0.127131  \n",
       "111         0.137062  \n",
       "150         0.153759  \n",
       "93          0.176536  \n",
       "174         0.185270  \n",
       "245         0.188136  \n",
       "181         0.191655  \n",
       "151         0.195998  \n",
       "165         0.198182  \n",
       "158         0.199315  \n",
       "125         0.201943  \n",
       "99          0.206934  \n",
       "141         0.209051  \n",
       "113         0.211638  \n",
       "136         0.215686  \n",
       "129         0.224214  \n",
       "149         0.242298  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sample['Transformed_Por'] = y_sample\n",
    "df_sample.head(n=n_sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It would be straitforward to modify the code above to perform distribution transformations:\n",
    "\n",
    "* to a parametric distribution like Gaussian\n",
    "\n",
    "* to a non-parametric distribution from actual data (build a CDF and interpolate between the data samples)\n",
    "\n",
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of distribution transformations. \n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at [Python Demos](https://github.com/GeostatsGuy/PythonNumericalDemos) and a Python package for data analytics and geostatistics at [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy). \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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