binomial_vs_multinomial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# coin toss (p=0.5), binomial (n=20 attempts)\n",
    "# https://en.wikipedia.org/wiki/Binomial_distribution\n",
    "\n",
    "x = np.random.binomial(n=20, p=0.5, size=1000)\n",
    "plt.hist(x, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tmiew5h3A5xhcSXMn8KZp17zG9X4CeAT4NoPfxPYC7wLeteQ5/lD797h7FN/XfvyAJHVovZyWkSStguEuSR0y3CWpQ4a7JHXIcJekDhnuktQhw12SOvT/uPkHRV3fd0AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coin toss p=0.5, berounulli (n=1 attempts)\n",
    "x = np.random.binomial(n=1, p=0.5, size=1000)\n",
    "plt.hist(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 6)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# dice p = [1/6, 1/6, 1/6, 1/6, 1/6, 1/6], multinomial (n=30 attempts)\n",
    "# https://en.wikipedia.org/wiki/Multinomial_distribution\n",
    "# For example, it models the probability of counts for each side of a k-sided die rolled n times\n",
    "# f(x1, x2,... xk; p1, p2,... pk, n)\n",
    "\n",
    "X = np.random.multinomial(n=30, pvals=[1 / 6] * 6, size=1000)\n",
    "print(X.shape)\n",
    "\n",
    "fig, ax = plt.subplots(2, 3, figsize=(10, 7))\n",
    "ax = ax.flatten()\n",
    "\n",
    "# each side ladning 5 times (30 / 6) is the most common outcome\n",
    "for i in range(6):\n",
    "    ax[i].hist(X[:, i])\n",
    "    ax[i].set_title(f'Side={i}')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 6)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# dice p = [1/6, 1/6, 1/6, 1/6, 1/6, 1/6], multinoulli (n=1 attempts)\n",
    "X = np.random.multinomial(n=1, pvals=[1 / 6] * 6, size=1000)\n",
    "print(X.shape)\n",
    "\n",
    "fig, ax = plt.subplots(2, 3, figsize=(10, 7))\n",
    "ax = ax.flatten()\n",
    "\n",
    "# each side ladning 0 times out of one attempt is the most common outcome\n",
    "for i in range(6):\n",
    "    ax[i].hist(X[:, i])\n",
    "    ax[i].set_title(f'Side={i}')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = np.random.multinomial(n=30, pvals=[1 / 2] * 2, size=1000)\n",
    "X = np.random.binomial(n=30, p=0.5, size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[16, 14],\n",
       "       [11, 19],\n",
       "       [16, 14],\n",
       "       ...,\n",
       "       [11, 19],\n",
       "       [18, 12],\n",
       "       [15, 15]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([17, 20, 14, 15, 17, 13, 18, 15, 16, 18])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:10]"
   ]
  }
 ],
 "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": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}