Normal Distribution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "#### Let's learn the normal distribution! Note: You should check out the binomial distribution first."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start with the definition of the PDF, we'll see how to create the distribution in python using scipy and numpy, and discuss some properties of the normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution is defined by the probability density function equation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $$  f(x,\\mu,\\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}}e^\\frac{-1}{2z^2} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where: $$z=\\frac{(X-\\mu)}{\\sigma}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where: μ=mean , σ=standard deviation , π=3.14... , e=2.718... The total area bounded by curve of the probability density function equation and the X axis is 1; thus the area under the curve between two ordinates X=a and X=b, where a<b, represents the probability that X lies between a and b. This probability can be expressed as: $$Pr(a<X<b)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
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   },
   "source": [
    "----------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the curve. The normal distribution has several characteristics:\n",
    "\n",
    "    1.) It has a lower tail (on the left) and an upper tail (on the right)\n",
    "    2.) The curve is symmetric (for the theoretical distribution)\n",
    "    3.) The peak occurs at the mean.\n",
    "    4.) The standard deviation gives the curve a different shape:\n",
    "        -Narrow and tall for a smaller standard deviation.\n",
    "        -Shallower and fatter for a larger standard deviation.\n",
    "    5.) The area under the curve is equal to 1 (the total probaility space)\n",
    "    6.) The mean=median=mode.\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the normal distribution, we can see what percentage of values lie between +/- a standard deviation. 68% of the values lie within 1 TSD, 95% between 2 STDs, and 99.7% between 3 STDs. The number of standard deviations is also called the z-score, which we saw above in the PDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://upload.wikimedia.org/wikipedia/commons/thumb/2/25/The_Normal_Distribution.svg/725px-The_Normal_Distribution.svg.png\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(url='http://upload.wikimedia.org/wikipedia/commons/thumb/2/25/The_Normal_Distribution.svg/725px-The_Normal_Distribution.svg.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's learn how to use scipy to create a normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x240a7931d30>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Import\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "#Import the stats library\n",
    "from scipy import stats\n",
    "\n",
    "# Set the mean\n",
    "mean = 0\n",
    "\n",
    "#Set the standard deviation\n",
    "std = 1\n",
    "\n",
    "\n",
    "# Create a range\n",
    "X = np.arange(-4,4,0.01)\n",
    "\n",
    "#Create the normal distribution for the range\n",
    "Y = stats.norm.pdf(X,mean,std)\n",
    "\n",
    "#\n",
    "plt.plot(X,Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's learn how to use numpy to create the normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "#Set the mean and the standard deviaiton\n",
    "mu,sigma = 0,0.1\n",
    "\n",
    "# Now grab 1000 random numbers from the normal distribution\n",
    "norm_set = np.random.normal(mu,sigma,1000)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  1.,  0.,  0.,  0.,  1.,  1.,  2.,  4.,  4.,  7.,  6.,  7.,\n",
       "         5., 12., 12., 25., 32., 29., 40., 34., 42., 52., 42., 47., 58.,\n",
       "        72., 52., 55., 39., 42., 49., 32., 36., 27., 20., 26., 18., 19.,\n",
       "        13., 15.,  6.,  5.,  2.,  3.,  1.,  1.,  1.,  0.,  2.]),\n",
       " array([-0.356904  , -0.34361366, -0.33032332, -0.31703298, -0.30374264,\n",
       "        -0.29045229, -0.27716195, -0.26387161, -0.25058127, -0.23729092,\n",
       "        -0.22400058, -0.21071024, -0.1974199 , -0.18412956, -0.17083921,\n",
       "        -0.15754887, -0.14425853, -0.13096819, -0.11767784, -0.1043875 ,\n",
       "        -0.09109716, -0.07780682, -0.06451648, -0.05122613, -0.03793579,\n",
       "        -0.02464545, -0.01135511,  0.00193524,  0.01522558,  0.02851592,\n",
       "         0.04180626,  0.05509661,  0.06838695,  0.08167729,  0.09496763,\n",
       "         0.10825797,  0.12154832,  0.13483866,  0.148129  ,  0.16141934,\n",
       "         0.17470969,  0.18800003,  0.20129037,  0.21458071,  0.22787105,\n",
       "         0.2411614 ,  0.25445174,  0.26774208,  0.28103242,  0.29432277,\n",
       "         0.30761311]),\n",
       " <BarContainer object of 50 artists>)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now let's plot it using seaborn\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "plt.hist(norm_set,bins=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "There's a ton on information to go over for the normal distribution, this notebook should just serve as a very mild introduction, for more info check out the following sources:\n",
    "\n",
    "1.) http://en.wikipedia.org/wiki/Normal_distribution\n",
    "\n",
    "2.) http://mathworld.wolfram.com/NormalDistribution.html\n",
    "\n",
    "3.) http://stattrek.com/probability-distributions/normal.aspx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thanks!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}