{
 "metadata": {
  "name": "kernel_density"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Kernel Density Estimation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from scipy import stats\n",
      "import statsmodels.api as sm\n",
      "import matplotlib.pyplot as plt\n",
      "from statsmodels.distributions.mixture_rvs import mixture_rvs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "A univariate example."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(12345)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "obs_dist1 = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.norm],\n",
      "                kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kde = sm.nonparametric.KDEUnivariate(obs_dist1)\n",
      "kde.fit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111)\n",
      "ax.hist(obs_dist1, bins=50, normed=True, color='red')\n",
      "ax.plot(kde.support, kde.density, lw=2, color='black');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "obs_dist2 = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.beta],\n",
      "            kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=1,args=(1,.5))))\n",
      "\n",
      "kde2 = sm.nonparametric.KDEUnivariate(obs_dist2)\n",
      "kde2.fit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111)\n",
      "ax.hist(obs_dist2, bins=50, normed=True, color='red')\n",
      "ax.plot(kde2.support, kde2.density, lw=2, color='black');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "The fitted KDE object is a full non-parametric distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "obs_dist3 = mixture_rvs([.25,.75], size=1000, dist=[stats.norm, stats.norm],\n",
      "                kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))\n",
      "kde3 = sm.nonparametric.KDEUnivariate(obs_dist3)\n",
      "kde3.fit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kde3.entropy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kde3.evaluate(-1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "CDF"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111)\n",
      "ax.plot(kde3.support, kde3.cdf);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Cumulative Hazard Function"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111)\n",
      "ax.plot(kde3.support, kde3.cumhazard);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Inverse CDF"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111)\n",
      "ax.plot(kde3.support, kde3.icdf);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Survival Function"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(12,8))\n",
      "ax = fig.add_subplot(111)\n",
      "ax.plot(kde3.support, kde3.sf);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}