BinomialDistributionExample

BinomialDistributionExample.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import binom\n",
    "import matplotlib.pyplot as plt\n",
    "# experiment: 10 balls, 7 are white and 3 black\n",
    "# we pick a ball 10 times with replacement\n",
    "# What is the probability that there are:\n",
    "# - 0 white balls\n",
    "# - 1 white ball\n",
    "# - 2 white balls\n",
    "# - 3 white balls \n",
    "# ..\n",
    "# - 10 white balls\n",
    "# So the number of white balls is what we are interested in. \n",
    "# This number we call x, so since we are asking for the probability\n",
    "# for various numbers of white balls (here 0 to 10) we create\n",
    "# a vector X=[0,1,..10] for convenience\n",
    "\n",
    "n = 10 #number of trials\n",
    "p = 7/10 #probability for the occurrence of p\n",
    "q = 1-p #probability for the occurrence of q\n",
    "X = list(range(n+1))\n",
    "\n",
    "#What we can do is, we can make different plots for\n",
    "#different ratios of black and white balls, thus\n",
    "#changing the probability for the occurrence of the balls\n",
    "#we can then see how the distribtion changes\n",
    "\n",
    "dist = [binom.pmf(x,n,p) for x in X]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "P=[0.2, 0.5, 0.8]\n",
    "fig,ax1 = plt.subplots(figsize=(6,6)) \n",
    "ax1.set_ylabel(\"probability\", color=\"blue\")\n",
    "ax1.set_xlabel(\"number of occurrences of our favored event, i.e. draw of a white ball\")\n",
    "ax1.bar(X, dist,color='blue')\n",
    "ax1.set_title('p='+str(p))\n",
    "   \n",
    "plt.interactive(True)\n",
    "plt.show()\n",
    "#plot alternatively like this\n",
    "#sns.distplot(x, hist=True, kde=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How to print several distributions in a loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#array with the probabilites for the occurrence of the event of interest\n",
    "#(in our example this would be the ratio of white balls to the total number of balls)\n",
    "P=[0.2, 0.5, 0.8]\n",
    "#make a figure with one row and 3 ( len(P) ) columns\n",
    "fig, axes =plt.subplots(1,len(P),figsize=(18,6))\n",
    "colors=['blue', 'red','green']\n",
    "for i in list(range(len(P))):\n",
    "    ax1=axes[i]\n",
    "    ax1.set_ylabel(\"probability\", color=colors[i])\n",
    "    ax1.set_xlabel(\"number of occurrences of our favored event, i.e. draw of a white ball\")\n",
    "    #compute the distribution for the p value in P[i]\n",
    "    dist=[binom.pmf(x,n,P[i]) for x in X]  \n",
    "    ax1.bar(X, dist,color=colors[i])\n",
    "    ax1.set_title('p='+str(P[i]))\n",
    "plt.tight_layout()\n",
    "plt.interactive(True)\n",
    "plt.show()\n"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  "toc-autonumbering": true,
  "toc-showcode": true,
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  "varInspector": {
   "cols": {
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    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
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     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
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   "types_to_exclude": [
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 "nbformat": 4,
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}