01 Drawing random numbers.ipynb

{
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   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "slideshow": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (16.0, 8.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Drawing random numbers in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 1. Drawing using the rectangular distribution\n",
    "\n",
    "The prerequisite for drawing from a probability distribution is the ability to draw randomly from the rectangular or uniform distribution on $(0,1)$.\n",
    "\n",
    "For any other distribution, draws can be generated by\n",
    "\n",
    "  1) draw $\\xi$ randomly from the uniform distribution\n",
    "\n",
    "  2) evaluate the inverse cumulative distribution function $G^{-1}(x)$ at $\\xi$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "subslide"
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   },
   "source": [
    "### Implementation in Python\n",
    "\n",
    "Uniform numbers in Python are drawn by\n",
    "``` python\n",
    "    import numpy as np\n",
    "    xi = np.random.rand(size)\n",
    "```\n",
    "with *size* the number of random draws."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Probability distributions are implemented in _scipy_ with inverse cumulative distributions being implemented as **ppf** for the individual probability distributions:\n",
    "``` python\n",
    "    import scipy.stats as stats\n",
    "    # normal distribution\n",
    "    stats.norm.ppf(q, loc = 0, scale = 1)   \n",
    "    # gamma distribution\n",
    "    stats.gamma.ppf(q, a, loc = 0, scale = 1)\n",
    "    # t-distribution\n",
    "    stats.t.ppf(q, dof, loc = 0, scale = 1) \n",
    "    # poisson distribution\n",
    "    stats.poisson.ppf(q, mu, loc = 0)       \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Exercise 1.1\n",
    "\n",
    "Using the rectangular distribution, draw 1000 random numbers from \n",
    "- normal distribution with mean $\\mu=0.2$ and standard deviation $\\sigma=0.1$\n",
    "- gamma distribution with shape parameter $a=2.5$ and scale parameter $s=0.2$\n",
    "- t-distribution with 5 degrees of freedom, located around $3.5$ and with scale $s=0.8$\n",
    "\n",
    "Plot a histogram for each outcome."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
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   },
   "outputs": [
    {
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      "text/plain": [
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110787cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Aq2a7L3S0nVfffWmS/5Xknmw8O3eSNye5I8lN2Tgrem+SV3f3Xyy2uS7Jv03yUDam+95y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110749ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution for Exercise 1.1\n",
    "\n",
    "from numpy.random import rand    # import function for drawing random numbers\n",
    "import scipy.stats as stats      # import statistics package\n",
    "\n",
    "# uniformly distributed values\n",
    "q = rand(1000)\n",
    "\n",
    "# normal distribution with mean=0.2 and std=0.1\n",
    "nxi = stats.norm.ppf(q, loc = 0.2, scale = 0.1)\n",
    "figure()\n",
    "hist(nxi);\n",
    "\n",
    "# gamma distribution with a=2.5, scale=0.2\n",
    "gxi = stats.gamma.ppf(q, 2.5, scale = 0.2)\n",
    "figure()\n",
    "hist(gxi);\n",
    "\n",
    "# t-distribution with 5 degrees-of-freedom, mean=3.5 and std=0.8\n",
    "txi = stats.t.ppf(q, 5, loc = 3.5, scale = 0.8)\n",
    "figure()\n",
    "hist(txi);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 2. Drawing using the built-in generator functions\n",
    "\n",
    "The **scipy.stats** package provides over 90 different probability distributions, each with its own random number generating function.\n",
    "\n",
    "The basic usage is\n",
    "\n",
    "1) Import the **scipy.stats** package\n",
    "``` python\n",
    "    import scipy.stats as stats\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "2) Call the **rvs** function of the sought probalitity distribution with size as keyword argument\n",
    "``` python\n",
    "    xi = stats.norm.rvs(size=1000)\n",
    "    xi = stats.gamma.rvs(a, size=1000)\n",
    "    xi = stats.t.rvs(dof, size=1000)\n",
    "```\n",
    "\n",
    "The optional keyword parameters for each distribution correspond to those of the call for the inverse cumulative distribution function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Exercise 1.2\n",
    "\n",
    "Repeat the random number generation from Exercise 1.1, but now use the built-in **rvs** function for each example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113ce320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11080da20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YQaACAAAwgkAFAABgBIEKAADACAIVAACAEQQqAAAAIwhUAAAARhCoAAAAjCBQAQAAGEGg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\nYIT/D7F9FBBTuoEyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110be2160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# solution for exercise 1.2\n",
    "\n",
    "# normal distribution with mean=0.2 and std=0.1\n",
    "nxi = stats.norm.rvs(loc = 0.2, scale = 0.1, size = 1000)\n",
    "figure()\n",
    "hist(nxi);\n",
    "\n",
    "# gamma distribution with a=2.5, scale=0.2\n",
    "gxi = stats.gamma.rvs(2.5, scale = 0.2, size = 1000)\n",
    "figure()\n",
    "hist(gxi);\n",
    "\n",
    "# t-distribution with 5 degrees-of-freedom, mean=3.5 and std=0.8\n",
    "txi = stats.t.rvs(5, loc = 3.5, scale = 0.8, size = 1000)\n",
    "figure()\n",
    "hist(txi);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bonus: Advanced plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# import advanced plotting color pallettes\n",
    "from palettable.colorbrewer.qualitative import Dark2_8\n",
    "colors = Dark2_8.mpl_colors\n",
    "\n",
    "# probability distribution as an object\n",
    "dist = stats.t(5, loc=3.5, scale=0.8)\n",
    "# random number generator is method of the distribution object\n",
    "xi = dist.rvs(size = 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4JaV1xEoym/cA5BNKMoCS1zK8aY9V5Fw7XFGnvrIKJfo7FO8+4DoOAAyjJAMo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\nxaqrgAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111b2da58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(12,8))\n",
    "hist(xi, bins = 100, edgecolor=\"none\", color=colors[0], normed=True);\n",
    "plot(np.sort(xi), dist.pdf(np.sort(xi)), color=colors[1], linewidth=2)\n",
    "tick_params(which=\"major\", labelsize=16)\n",
    "xlim(-2,9);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}