BellCurve.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Distribution (Normal or Bell Curve)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Think of a Jupyter Notebook file as a Python script, but with comments given the seriousness they deserve, meaning inserted Youtubes if necessary.  We also adopt a more conversational style with the reader, and with Python, pausing frequently to take stock, because we're telling a story.\n",
    "\n",
    "One might ask, what is the benefit of computer programs if we read through them this slowly?  Isn't the whole point that they run blazingly fast, and nobody needs to read them except those tasked with maintaining them, the programmer cast?\n",
    "\n",
    "First, lets point out the obvious:  even when reading slowly, we're not keeping Python from doing its part as fast as it can, and what it does would have taken a single human ages to do, and would have occupied a team of secretaries for ages.  Were you planning to pay them?  Python effectively puts a huge staff at your disposal, ready to do your bidding.  But that doesn't let you off the hook.  They need to be managed, told what to do.\n",
    "\n",
    "Here's what you'll find at the top of your average script.  A litany of players, a congress of agents, need to be assembled and made ready for the job at hand.  But don't worry, as you remember to include necessary assets, add them at will as you need them.  We rehearse the script over and over while building it.  Nobody groans, except maybe you, when the director says \"take it from the top\" once again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as st\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll be glad to have np.linspace as a friend, as so often you know exactly what the upper and lower bounds, of a domain, might be.  You'll be computing a range.  Do you remember these terms from high school?  A domain is like a pile of cannon balls that we feed to our cannon, which them fires them, testing our knowledge of ballistics.  It traces a parabola.  We plot that in our tables.  A lot of mathematics traces to developing tables for battle field use.  Leonardo da Vinci, a great artist, was also an architect of defensive fortifications.\n",
    "\n",
    "Anyway, np.linspace lets to give exactly the number of points you would like of this linear one dimensional array space, as a closed set, meaning -5 and 5 are included, the minimum and maximum you specify.  Ask for a healthy number of points, as points are cheap.  All they require is memory.  But then it's up to you not to overdo things.  Why waste CPU cycles on way too many points?\n",
    "\n",
    "I bring up this niggling detail about points as a way of introducing what they're calling \"hyperparameters\" in Machine Learning, meaning settings or values that come from outside the data, so also \"metadata\" in some ways.  You'll see in other notebooks how we might pick a few hyperparameters and ask scikit-learn to try all combinations of same.\n",
    "\n",
    "Here's what you'll be saying then:\n",
    "\n",
    "from sklearn.model_selection import GridSearchCV  #CV = cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "domain = np.linspace(-5, 5, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I know mu sounds like \"mew\", the sound a kitten makes, and that's sometimes insisted upon by sticklers, for when we have a continuous function, versus one that's discrete.  Statisticians make a big deal about the difference between digital and analog, where the former is seen as a \"sampling\" of the latter.  Complete data may be an impossibility.  We're always stuck with something digital trying to approximate something analog, or so it seems.  Turn that around in your head sometimes:  we smooth it over as an approximation, because a discrete treatment would require too high a level of precision.\n",
    "\n",
    "The sticklers say \"mu\" for continuous, but \"x-bar\" (an x with a bar over it) for plain old \"average\" of discrete sets.  I don't see this conventions holding water necessarily, for one thing because it's inconvenient to always reach for the most fancy typography.  Python does have full access to Unicode, and to LaTex, but do we have to bother?  Lets leave that question for another day and move on to...\n",
    "\n",
    "## The Guassian (Binomial if Discrete)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "mu = 0  # might be x-bar if discrete\n",
    "sigma = 1  # standard deviation, more below"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we have here (below) is a typical Python numeric function, although it does get its pi from numpy instead of math.  That won't matter.  The sigma and mu in this function are globals and set above.  Some LaTex would be in order here, I realize.  Let me scavange the internet for something appropriate...\n",
    "\n",
    "$pdf(x,\\mu,\\sigma) = \\frac{1}{ \\sigma \\sqrt{2 \\pi}} e^{\\left(-\\frac{{\\left(\\mu - x\\right)}^{2}}{2 \\, \\sigma^{2}}\\right)}$\n",
    "\n",
    "Use of dollar signs is key.\n",
    "\n",
    "Here's another way, in a code cell instead of a Markdown cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$ pdf(x,\\mu,\\sigma) = \\frac{1}{ \\sigma\\sqrt{2 \\pi}} e^{\\left(-\\frac{{\\left(\\mu - x\\right)}^{2}}{2 \\, \\sigma^{2}}\\right)} $"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import display, Latex\n",
    "\n",
    "ltx = '$ pdf(x,\\\\mu,\\\\sigma) = \\\\frac{1}{ \\\\sigma' + \\\n",
    " '\\\\sqrt{2 \\\\pi}} e^{\\\\left(-\\\\frac{{\\\\left(\\\\mu - ' + \\\n",
    " 'x\\\\right)}^{2}}{2 \\\\, \\\\sigma^{2}}\\\\right)} $'\n",
    "display(Latex(ltx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'm really tempted to try out [PrettyPy](https://github.com/charliekawczynski/prettyPy)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "def g(x):\n",
    "    return (1/(sigma * math.sqrt(2 * np.pi))) * math.exp(-0.5 * ((mu - x)/sigma)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What I do below is semi-mysterious, and something I'd like to get to in numpy in more detail.  The whole idea behind numpy is every function, or at least the unary ones, are vectorized, meaning the work element-wise through every cell, with no need for any for loops.\n",
    "\n",
    "My Gaussian formula above won't natively understand how to have relations with a numpy array, unless we store it in vectorized form.  I'm not claiming this will make it run any faster than under the control of for loops, we can test that.  Even without a speedup, here we have a recipe for shortening our code.\n",
    "\n",
    "As many have proclaimed around numpy: one of its primary benefits is it allows one to \"lose the loops\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 5.55 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "100000 loops, best of 3: 4.1 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit vg = np.vectorize(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At any rate, this way, with a list comprehension, is orders of magnitude slower:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 263 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit vg2 = np.array([g(x) for x in domain])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "vg = np.vectorize(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 89.97 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "1 loop, best of 3: 2.49 ms per loop\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD8CAYAAACb4nSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxpgo8v8BnX5Uh+g5oJYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a11ab6b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%timeit plt.plot(domain, vg(domain))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I bravely built my own version of the Gaussian distribution, a continuous function (any real number input is OK, from negative infinity to infinity, but not those (keep it in between). The thing about a Gaussian is you can shrink it and grow it while keeping the curve itself, self similar.  Remember \"hyperparamters\"?  They control the shape.  We should be sure to play around with those parameters.\n",
    "\n",
    "Of course the stats.norm section of scipy comes pre-equipped with the same PDF (probability distribution function).  You'll see this curve called many things in the literature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 28.99 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "100 loops, best of 3: 2.7 ms per loop\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD8CAYAAACb4nSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a192c22b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%timeit plt.plot(domain, st.norm.pdf(domain))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Gaussian Distributions')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhSy5G2NMFPp/NZOJNL0Ec/8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a19872940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 0\n",
    "sigma = math.sqrt(0.2)\n",
    "plt.plot(domain, vg(domain), color = 'blue')\n",
    "sigma = math.sqrt(1)\n",
    "plt.plot(domain, vg(domain), color = 'red')\n",
    "sigma = math.sqrt(5)\n",
    "plt.plot(domain, vg(domain), color = 'orange')\n",
    "mu = -2\n",
    "sigma = math.sqrt(.5)\n",
    "plt.plot(domain, vg(domain), color = 'green')\n",
    "plt.title(\"Gaussian Distributions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[see Wikipedia figure](https://en.wikipedia.org/wiki/Gaussian_function#Properties)\n",
    "\n",
    "These are Gaussian PDFs or Probability Density Functions.\n",
    "\n",
    "68.26% of values happen within -1 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": "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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/xgQhefFOXrM\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x10f4026d8>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"xgQhefFOXrM\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.68268949213708585"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = st.norm.cdf(-1)  #  Cumulative distribution function\n",
    "b = st.norm.cdf(1)\n",
    "b - a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.95449973610364158"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = st.norm.cdf(-2)\n",
    "b = st.norm.cdf(2)\n",
    "b - a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99730020393673979"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 99.73% is more correct than 99.72% \n",
    "a = st.norm.cdf(-3)\n",
    "b = st.norm.cdf(3)\n",
    "b - a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.95000420970355903"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 95%\n",
    "a = st.norm.cdf(-1.96)\n",
    "b = st.norm.cdf(1.96)\n",
    "b - a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9901199684844586"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 99% \n",
    "a = st.norm.cdf(-2.58)\n",
    "b = st.norm.cdf(2.58)\n",
    "b - a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": "/9j/4AAQSkZJRgABAQAAAQABAAD/2wCEAAUDBAgHCAgICAgICAgHBwcHBwcHCAgHBwgHBwcIBwgH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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/zZWd56VlN7w\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1a193bb828>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"zZWd56VlN7w\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the chances a value is less than -1.32?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.093417508993471787"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "st.norm.cdf(-1.32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the chances a value is between -0.21 and 0.85?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.41683383651755768"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - st.norm.sf(-0.21) # filling in from the right (survival function)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.80233745687730762"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = st.norm.cdf(0.85) # filling in from the left\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.41683383651755768"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = st.norm.cdf(-0.21) # from the left\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.38550362035974994"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a-b # getting the difference (per the Youtube)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets plot the integral of the Bell Curve.  This curve somewhat describes the temporal pattern whereby a new technology is adopted, first by early adopters, then comes the bandwagon effect, then come the stragglers.  Not the every technology gets adopted in this way.  Only some do."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1a20d320>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a19856588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(domain, st.norm.cdf(domain))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Standard Deviation](https://en.wikipedia.org/wiki/Standard_deviation)\n",
    "\n",
    "Above is the Bell Curve integral.\n",
    "\n",
    "Remember the derivative is obtain from small differences: (f(x+h) - f(x))/x\n",
    "\n",
    "Given x is our entire domain and operations are vectorized, it's easy enough to plot said derivative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1a2bfd68>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD8CAYAAACb4nSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMXHEQt8YY+KIhb4xxsSR/w9PoGlpRYLV7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a198724a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = st.norm.cdf(domain)\n",
    "diff = st.norm.cdf(domain + 0.01)\n",
    "plt.plot(domain, (diff-x)/0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1a3854e0>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1a2b3518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = st.norm.pdf(domain)\n",
    "diff = st.norm.pdf(domain + 0.01)\n",
    "plt.plot(domain, (diff-x)/0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1a3042e8>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyd8YYxLQ/we5gZcU2ywAIgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1a3040f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = st.norm.pdf(domain)\n",
    "plt.plot(domain, x, color = \"red\")\n",
    "\n",
    "x = st.norm.pdf(domain)\n",
    "diff = st.norm.pdf(domain + 0.01)\n",
    "plt.plot(domain, (diff-x)/0.01, color = \"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Integrating the Gaussian\n",
    "\n",
    "Apparently there's no closed form, however sympy is able to do an integration somehow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$ cdf(a,b,\\mu,\\sigma) = - \\frac{1}{2} \\operatorname{erf}{\\left (\\frac{\\sqrt{2} \\left(a - \\mu\\right)}{2 \\sigma} \\right )} + \\frac{1}{2} \\operatorname{erf}{\\left (\\frac{\\sqrt{2} \\left(b - \\mu\\right)}{2 \\sigma} \\right )}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a197a4978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import var, Lambda, integrate, sqrt, pi, exp, latex\n",
    "\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(8,5)\n",
    "var('a b x sigma mu')\n",
    "pdf = Lambda((x,mu,sigma),\n",
    "  (1/(sigma * sqrt(2*pi)) * exp(-(mu-x)**2 / (2*sigma**2)))\n",
    ")\n",
    "cdf = Lambda((a,b,mu,sigma),\n",
    "  integrate(\n",
    "    pdf(x,mu,sigma),(x,a,b)\n",
    "  )\n",
    ")\n",
    "display(Latex('$ cdf(a,b,\\mu,\\sigma) = ' + latex(cdf(a,b,mu,sigma)) + '$'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets stop right here and note the pdf and cdf have been defined, using sympy's Lambda and integrate, and the cdf will be fed a lot of data, one hundred points, along with mu and sigma.  Then it's simply a matter of plotting.\n",
    "\n",
    "What's amazing is our ability to get something from sympy that works to give a cdf, independently of scipy.stats.norm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'function'>\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEWCAYAAACJ0YulAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niLRSUhARkVZKCiIi0kpJQUREWv1fzy/vH/H/epsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1af1b080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(50,159,100)\n",
    "y = np.array([cdf(-1e99,v,100,15) for v in x],dtype='float')\n",
    "plt.grid(True)\n",
    "plt.title('Cumulative Distribution Function')\n",
    "plt.xlabel('IQ')\n",
    "print(type(plt.xlabel))\n",
    "plt.ylabel('Y')\n",
    "plt.text(65,.75,'$\\mu = 100$',fontsize=16)\n",
    "plt.text(65,.65,'$\\sigma = 15$',fontsize=16)\n",
    "plt.plot(x,y,color='gray')\n",
    "plt.fill_between(x,y,0,color='#c0f0c0')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above is truly a testament to Python's power, or the Python ecosystem's power.  We've brought in sympy, able to do symbolic integration, and talk LaTeX at the same time.  That's impressive.  Here's [the high IQ source](https://arachnoid.com/IPython/normal_distribution.html) for the original version of the above code.\n",
    "\n",
    "There's no indefinite integral of the Gaussian, but there's a definite one.  sympy comes with its own generic sympy.stats.cdf function which produces Lambdas (symbolic expressions) when used to integrate different types of probability spaces, such as Normal (a continuous PDF).  It also accepts discrete PMFs as well.\n",
    "\n",
    "<pre>\n",
    "Examples\n",
    "========\n",
    "    \n",
    ">>> from sympy.stats import density, Die, Normal, cdf\n",
    ">>> from sympy import Symbol\n",
    "    \n",
    ">>> D = Die('D', 6)\n",
    ">>> X = Normal('X', 0, 1)\n",
    "    \n",
    ">>> density(D).dict\n",
    "{1: 1/6, 2: 1/6, 3: 1/6, 4: 1/6, 5: 1/6, 6: 1/6}\n",
    ">>> cdf(D)\n",
    "{1: 1/6, 2: 1/3, 3: 1/2, 4: 2/3, 5: 5/6, 6: 1}\n",
    ">>> cdf(3*D, D > 2)\n",
    "{9: 1/4, 12: 1/2, 15: 3/4, 18: 1}\n",
    "    \n",
    ">>> cdf(X)\n",
    "Lambda(_z, -erfc(sqrt(2)*_z/2)/2 + 1)\n",
    "</pre>   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LAB:  convert the Normal Distribution Below to IQ Curve...\n",
    "\n",
    "\n",
    "That means domain is 0-200, standard deviation 15, mean = 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1b342a90>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAD8CAYAAAB3u9PLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nM/cWuSMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1b385710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "domain = np.linspace(0, 200, 3000)\n",
    "IQ = st.norm.pdf(domain, 100, 15)\n",
    "plt.plot(domain, IQ, color = \"red\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1af06e48>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAD8CAYAAAB3u9PLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1b347b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "domain = np.linspace(0, 200, 3000)\n",
    "mu = 100\n",
    "sigma = 15\n",
    "IQ = vg(domain)\n",
    "plt.plot(domain, IQ, color = \"green\")"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}