Normal Distribution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MSDS 400 Normal Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linspace, math\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This particular module takes a few seconds to load.  Be patient. Using the\n",
    "NumPy math library does speed things up somewhat.  When the prompt asks for a\n",
    "value, enter it and a plot will appear.\n",
    "\n",
    "The program will ask for a user supplied value to be entered at the prompt.\n",
    "The integration will use the standard normal density function to find the\n",
    "probability that a standard normal random variable will be <= the value\n",
    "specified by the user  A plot will show the area integrated, the user\n",
    "supplied value and the area under the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This is the density function for a standard normal distribution.\n",
    "def f(inp):\n",
    "    return (math.exp(-inp * inp / 2)) / math.sqrt(2.0 * math.pi)\n",
    "\n",
    "# Simpson's rule is used to integrate over [a,b].\n",
    "def integrate(a, b, delta):  \n",
    "    total = 0.0\n",
    "    i = 0\n",
    "    n = int(float((b - a) / delta))\n",
    "    if b == a:\n",
    "        return\n",
    "    else:\n",
    "        while i < n:\n",
    "            x0 = a + delta * i\n",
    "            x1 = x0 + delta / 2\n",
    "            x2 = x0 + delta\n",
    "            total = total + delta * (f(x0) + 4.0 * f(x1) + f(x2)) / 6\n",
    "            i = i + 1\n",
    "        return total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following values determine the total interval considered and also\n",
    "the increment used for numerical integration.  We are dividing 12 standard\n",
    "deviations into 1200 subintervals thus defining delta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of the variable x for integration?.0863\n",
      "Area with x= 0.0863 equals 0.5319\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "alpha must be a float or None",
     "output_type": "error",
     "traceback": [
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      "\u001b[0;32m/opt/anaconda3/lib/python3.8/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mfill_between\u001b[0;34m(x, y1, y2, where, interpolate, step, data, **kwargs)\u001b[0m\n\u001b[1;32m   2636\u001b[0m         \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my2\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwhere\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minterpolate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2637\u001b[0m         data=None, **kwargs):\n\u001b[0;32m-> 2638\u001b[0;31m     return gca().fill_between(\n\u001b[0m\u001b[1;32m   2639\u001b[0m         \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my2\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0my2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwhere\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mwhere\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minterpolate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minterpolate\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2640\u001b[0m         **({\"data\": data} if data is not None else {}), **kwargs)\n",
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      "\u001b[0;32m/opt/anaconda3/lib/python3.8/site-packages/matplotlib/collections.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, verts, sizes, closed, **kwargs)\u001b[0m\n\u001b[1;32m   1121\u001b[0m             \u001b[0mForwarded\u001b[0m \u001b[0mto\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mCollection\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1122\u001b[0m         \"\"\"\n\u001b[0;32m-> 1123\u001b[0;31m         \u001b[0mCollection\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1124\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_sizes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msizes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1125\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_verts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mverts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclosed\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.8/site-packages/matplotlib/cbook/deprecation.py\u001b[0m in \u001b[0;36mwrapper\u001b[0;34m(*inner_args, **inner_kwargs)\u001b[0m\n\u001b[1;32m    409\u001b[0m                          \u001b[0;32melse\u001b[0m \u001b[0mdeprecation_addendum\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    410\u001b[0m                 **kwargs)\n\u001b[0;32m--> 411\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0minner_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0minner_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    412\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    413\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.8/site-packages/matplotlib/collections.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, edgecolors, facecolors, linewidths, linestyles, capstyle, joinstyle, antialiaseds, offsets, transOffset, norm, cmap, pickradius, hatch, urls, offset_position, zorder, **kwargs)\u001b[0m\n\u001b[1;32m    211\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    212\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_path_effects\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 213\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    214\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_paths\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    215\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py\u001b[0m in \u001b[0;36mupdate\u001b[0;34m(self, props)\u001b[0m\n\u001b[1;32m    996\u001b[0m                         raise AttributeError(f\"{type(self).__name__!r} object \"\n\u001b[1;32m    997\u001b[0m                                              f\"has no property {k!r}\")\n\u001b[0;32m--> 998\u001b[0;31m                     \u001b[0mret\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    999\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mret\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1000\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpchanged\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.8/site-packages/matplotlib/collections.py\u001b[0m in \u001b[0;36mset_alpha\u001b[0;34m(self, alpha)\u001b[0m\n\u001b[1;32m    832\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mset_alpha\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    833\u001b[0m         \u001b[0;31m# docstring inherited\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 834\u001b[0;31m         \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_alpha\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    835\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_update_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'array'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    836\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_set_facecolor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_original_facecolor\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py\u001b[0m in \u001b[0;36mset_alpha\u001b[0;34m(self, alpha)\u001b[0m\n\u001b[1;32m    928\u001b[0m         \"\"\"\n\u001b[1;32m    929\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0malpha\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 930\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'alpha must be a float or None'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    931\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_alpha\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    932\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpchanged\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: alpha must be a float or None"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xa = -6.0\n",
    "xb = 6.0\n",
    "num = 1200\n",
    "delta_calc = float((xb - xa) / num)\n",
    "\n",
    "x = linspace(xa, xb, num)\n",
    "y = []\n",
    "cdf = []\n",
    "\n",
    "for z in x:\n",
    "    y = y + [f(z)]\n",
    "    cdf = cdf + [integrate(xa, z, delta_calc)]\n",
    "\n",
    "value = float(input('Value of the variable x for integration?'))\n",
    "\n",
    "fvalue = integrate(-6, value, delta_calc)\n",
    "fvalue = round(fvalue, 4)\n",
    "print('Area with x= {} equals {}'.format(value, fvalue))\n",
    "\n",
    "plt.xlim(xa - 1, xb + 1)\n",
    "plt.ylim(0, 1)\n",
    "\n",
    "string = ' with x = ' + str(value) + ' and area = ' + str(fvalue)\n",
    "plt.title('Normal Density and CDF with x = {} and area = {}'.format(value, fvalue))\n",
    "plt.xlabel('x-axis')\n",
    "\n",
    "plt.plot(x, y, 'b', label='Density')\n",
    "plt.plot(x, cdf, 'r', label='CDF')\n",
    "plt.legend()\n",
    "\n",
    "plt.fill_between(x, y, where=(x <= value), color='grey', alpha='0.3')\n",
    "plt.scatter(value, fvalue, s=30, c='r', marker='o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.10"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}