{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Empirical Cumulative Distribution Function Plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A function to conveniently plot an empirical cumulative distribution function. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> from mlxtend.ecdf import ecdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A function to conveniently plot an empirical cumulative distribution function (ECDF) and adding percentile thresholds for exploratory data analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "- -"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1 - ECDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2bVhZYGRmlsVjCtZ2Z5sUKKpt9+I0s3JyUrCO8eI0s/Jx95GZmVX5ScHmxOsQzHqTk4K1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\nZmZW9f8B84n/TcoSUzUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1161f3d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mlxtend.data import iris_data\n",
    "from mlxtend.plotting import ecdf\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X, y = iris_data()\n",
    "\n",
    "ax, _, _ = ecdf(x=X[:, 0], x_label='sepal length (cm)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2 - Multiple ECDFs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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l0a+lAn5tbd68maamJoYOHcq8efO45ZZb4q2zZ86cyZAhQxg6dCjPP/98/HPa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d30d898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mlxtend.data import iris_data\n",
    "from mlxtend.plotting import ecdf\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X, y = iris_data()\n",
    "\n",
    "# first ecdf\n",
    "x1 = X[:, 0]\n",
    "ax, _, _ = ecdf(x1, x_label='cm')\n",
    "\n",
    "# second ecdf\n",
    "x2 = X[:, 1]\n",
    "ax, _, _ = ecdf(x2, ax=ax)\n",
    "\n",
    "plt.legend(['sepal length', 'sepal width'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3 - ECDF with Percentile Thresholds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1161f36d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature threshold at the 80th percentile: 6.5\n",
      "Number of samples below the threshold: 120\n"
     ]
    }
   ],
   "source": [
    "from mlxtend.data import iris_data\n",
    "from mlxtend.plotting import ecdf\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X, y = iris_data()\n",
    "\n",
    "ax, threshold, count = ecdf(x=X[:, 0], \n",
    "                            x_label='sepal length (cm)',\n",
    "                            percentile=0.8)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print('Feature threshold at the 80th percentile:', threshold)\n",
    "print('Number of samples below the threshold:', count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "## ecdf\n",
      "\n",
      "*ecdf(x, y_label='ECDF', x_label=None, ax=None, percentile=None, ecdf_color=None, ecdf_marker='o', percentile_color='black', percentile_linestyle='--')*\n",
      "\n",
      "Plots an Empirical Cumulative Distribution Function\n",
      "\n",
      "**Parameters**\n",
      "\n",
      "- `x` : array or list, shape=[n_samples,]\n",
      "\n",
      "    Array-like object containing the feature values\n",
      "\n",
      "- `y_label` : str (default='ECDF')\n",
      "\n",
      "    Text label for the y-axis\n",
      "\n",
      "- `x_label` : str (default=None)\n",
      "\n",
      "    Text label for the x-axis\n",
      "\n",
      "- `ax` : matplotlib.axes.Axes (default: None)\n",
      "\n",
      "    An existing matplotlib Axes. Creates\n",
      "    one if ax=None\n",
      "\n",
      "- `percentile` : float (default=None)\n",
      "\n",
      "    Float between 0 and 1 for plotting a percentile\n",
      "    threshold line\n",
      "\n",
      "- `ecdf_color` : matplotlib color (default=None)\n",
      "\n",
      "    Color for the ECDF plot; uses matplotlib defaults\n",
      "    if None\n",
      "\n",
      "- `ecdf_marker` : matplotlib marker (default='o')\n",
      "\n",
      "    Marker style for the ECDF plot\n",
      "\n",
      "- `percentile_color` : matplotlib color (default='black')\n",
      "\n",
      "    Color for the percentile threshold if percentile is not None\n",
      "\n",
      "- `percentile_linestyle` : matplotlib linestyle (default='--')\n",
      "\n",
      "    Line style for the percentile threshold if percentile is not None\n",
      "\n",
      "**Returns**\n",
      "\n",
      "- `ax` : matplotlib.axes.Axes object\n",
      "\n",
      "\n",
      "- `percentile_threshold` : float\n",
      "\n",
      "    Feature threshold at the percentile or None if `percentile=None`\n",
      "\n",
      "- `percentile_count` : Number of if percentile is not None\n",
      "\n",
      "    Number of samples that have a feature less or equal than\n",
      "    the feature threshold at a percentile threshold\n",
      "    or None if `percentile=None`\n",
      "\n",
      "**Examples**\n",
      "\n",
      "For usage examples, please see\n",
      "    [http://rasbt.github.io/mlxtend/user_guide/plotting/ecdf/](http://rasbt.github.io/mlxtend/user_guide/plotting/ecdf/)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('../../api_modules/mlxtend.plotting/ecdf.md', 'r') as f:\n",
    "    print(f.read())"
   ]
  }
 ],
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