PaCal.ipynb

{
 "cells": [
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Illustration of [PaCal](http://pacal.sourceforge.net/) (Arithmetic with random variables)"
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "%matplotlib inline\nfrom matplotlib import pyplot as plt",
   "execution_count": 1,
   "outputs": []
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "from pacal import *",
   "execution_count": 2,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Using compiled interpolation routine\nUsing compiled sparse grid routine\n"
    }
   ]
  },
  {
   "metadata": {
    "collapsed": true,
    "trusted": true
   },
   "cell_type": "code",
   "source": "NormalDistr?",
   "execution_count": 52,
   "outputs": []
  },
  {
   "metadata": {
    "collapsed": true,
    "trusted": true
   },
   "cell_type": "code",
   "source": "X = NormalDistr(sym='X')",
   "execution_count": 3,
   "outputs": []
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "Y = NormalDistr(0,2, sym='Y')",
   "execution_count": 4,
   "outputs": []
  },
  {
   "metadata": {
    "collapsed": true,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S = X + Y",
   "execution_count": 5,
   "outputs": []
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S",
   "execution_count": 6,
   "outputs": [
    {
     "execution_count": 6,
     "output_type": "execute_result",
     "data": {
      "text/plain": "#22190_4434034128+#22190_4402720528"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S.summary()",
   "execution_count": 7,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "============= summary =============\n  N(0.0,1.0)+N(0,2)\n                mean  =  8.3266726846886741e-16\n                 var  =  5.0000000000000036\n            skewness  =  -4.7664655742347595e-16\n            kurtosis  =  2.9999999999999996\n             entropy  =  2.2236574894217238\n              median  =  -1.3322676295501878e-15\n                mode  =  1.0674499837498935e-08\n            medianad  =  1.5082049315656938\n      iqrange(0.025)  =  8.765225405765802\n      interval(0.95)  =  (-4.382612702882908, 4.382612702882893)\n               range  =  (-inf, inf)\n             tailexp  =  (-216.5841427655505, -216.5841427655505)\n             int_err  =  -4.4408920985006262e-16\n"
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S.plot()\nY.plot(color='b')\nX.plot(color='r')",
   "execution_count": 8,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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PnDYzSE1PtZgCvA1iOPDfeFSt1ahSsh8KzCvZnp/tq/acAG6TNE3SKd0J1Hqf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\nzhcZvcsAAAAASUVORK5CYII=\n",
      "text/plain": "<matplotlib.figure.Figure at 0x10a2b7090>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S.hist()",
   "execution_count": 9,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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      "text/plain": "<matplotlib.figure.Figure at 0x10a472b50>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S.boxplot()",
   "execution_count": 10,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwLKXpAZY9pLUAMtekhpg2UtSA/4ft+wGvl6B1nQAAAAASUVORK5CYII=\n",
      "text/plain": "<matplotlib.figure.Figure at 0x10cdd3210>"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S.cdf(-5)",
   "execution_count": 11,
   "outputs": [
    {
     "execution_count": 11,
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.012673659338734152"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S.cdf(5)",
   "execution_count": 12,
   "outputs": [
    {
     "execution_count": 12,
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.98732634066126623"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "S.ccdf_value(0.5)",
   "execution_count": 13,
   "outputs": [
    {
     "execution_count": 13,
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.41153163687906058"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "collapsed": true,
    "trusted": true
   },
   "cell_type": "code",
   "source": "a = S.rand(10000)",
   "execution_count": 14,
   "outputs": []
  },
  {
   "metadata": {
    "collapsed": false,
    "trusted": true
   },
   "cell_type": "code",
   "source": "plt.hist(a, bins=20); ",
   "execution_count": 16,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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