pz_stats_fakedatatest.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as ss\n",
    "import qp\n",
    "import individual_metrics as inmet\n",
    "import skgof\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "func1 = ss.norm(loc=3.0,scale=0.5)\n",
    "x = np.arange(0.5,10.0,0.02)\n",
    "y1 = func1.pdf(x)*20000./0.25*0.1\n",
    "func2= ss.norm(loc=5.0,scale=0.35)\n",
    "y2 = func2.pdf(x)*40000./0.35*0.1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ea46a90>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RWMD3E+BqEdkFLHB/RlV3AM/grGxaBdypqsEhp7uA5cBuYI+qxse1FU5XXs83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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102f4e990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples1 = np.array(func1.rvs(size=20000))\n",
    "samples2 = np.array(func2.rvs(size=40000))\n",
    "plt.hist(samples1, normed=False, histtype='stepfilled', alpha=0.2)\n",
    "plt.hist(samples2, normed=False, histtype='stepfilled', alpha=0.2)\n",
    "plt.plot(x,y1,lw=2,c='r')\n",
    "plt.plot(x,y2,lw=2,c='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "60000\n"
     ]
    }
   ],
   "source": [
    "bigsample = np.append(samples1,samples2)\n",
    "print len(bigsample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "made the pool of 4 in 0.0271141529083\n",
      "made the catalog in 215.73642683\n"
     ]
    }
   ],
   "source": [
    "smallgrid=np.zeros([60000,len(y1)])\n",
    "for i in range(20000):\n",
    "    smallgrid[i,:] = y1\n",
    "for i in range(20000,60000):\n",
    "    smallgrid[i,:] = y2\n",
    "approx_pdf = qp.Ensemble(smallgrid.shape[0],gridded=(x,smallgrid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "testme = inmet.EvaluateMetric(approx_pdf,bigsample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "testPIT = testme.PIT()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ks_stat,ks_pval = testme.KS(using='gridded',dx=0.0001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00301930182377\n",
      "0.64359100973\n"
     ]
    }
   ],
   "source": [
    "print ks_stat\n",
    "print ks_pval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0627640545957\n",
      "0.7965843292\n"
     ]
    }
   ],
   "source": [
    "cvm_stat,cvm_pval = testme.CvM(using='gridded',dx=0.0001)\n",
    "print cvm_stat\n",
    "print cvm_pval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34.6816493523\n",
      "1.02016526338e-08\n"
     ]
    }
   ],
   "source": [
    "ad_stat,ad_pval = testme.AD(using='gridded',dx=0.0001, vmin=0.01,vmax=0.99)\n",
    "print ad_stat\n",
    "print ad_pval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "change vmin,vmax, see effect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.86154801198\n",
      "8.72757016124e-06\n"
     ]
    }
   ],
   "source": [
    "ad_stat,ad_pval = testme.AD(using='gridded',dx=0.0001, vmin=0.005,vmax=0.995)\n",
    "print ad_stat\n",
    "print ad_pval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.793131023696\n",
      "0.4860236444\n"
     ]
    }
   ],
   "source": [
    "ad_stat,ad_pval = testme.AD(using='gridded',dx=0.0001, vmin=0.001,vmax=0.999)\n",
    "print ad_stat\n",
    "print ad_pval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.47833933145\n",
      "0.768996410141\n"
     ]
    }
   ],
   "source": [
    "ad_stat,ad_pval = testme.AD(using='gridded',dx=0.0001, vmin=0.000,vmax=1.1)\n",
    "print ad_stat\n",
    "print ad_pval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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X333nh9vAgY5uu41wA9Id8QYAIfP9994Vt++/98Nt8GBHN91EuAGZgHgDgBD5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\nJOrmntQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110fce250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot = testme.QQplot(using='gridded',dx=0.0001,Nquants=101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
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