20191121-Theorems.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import sqrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create chi-square specimen\n",
    "\n",
    "chi = np.random.chisquare(2, 10000)\n",
    "chi_ave = [sum(chi[:i]) / i for i in range(1, 10001)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x119e800b8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "n = [i for i in range(1, 10001)]\n",
    "ave = [2 for i in range(1, 10001)]\n",
    "\n",
    "plt.ylim([0, 4])\n",
    "plt.plot(n, chi_ave, label=\"actual\")\n",
    "plt.plot(n, ave, color = \"black\", linestyle = \":\", label=\"μ(2.0)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi_x_1 = chi[:1000]\n",
    "chi_x_2 = [sum(chi[2*i:2*(i+1)]) / 2 for i in range(1000)]\n",
    "chi_x_5 = [sum(chi[5*i:5*(i+1)]) / 5 for i in range(1000)]\n",
    "chi_x_10 = [sum(chi[10*i:10*(i+1)]) / 10 for i in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi_z_1 = [(chi_x_1[i] - 2) / (4 / sqrt(1)) for i in range(1000)]\n",
    "chi_z_2 = [(chi_x_2[i] - 2) / (4 / sqrt(2)) for i in range(1000)]\n",
    "chi_z_5 = [(chi_x_5[i] - 2) / (4 / sqrt(5)) for i in range(1000)]\n",
    "chi_z_10 = [(chi_x_10[i] - 2) / (4 / sqrt(10)) for i in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(chi_z_1, bins=40, label=\"n = 1\")\n",
    "plt.legend()\n",
    "1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(chi_z_2, bins=40, label=\"n = 2\")\n",
    "plt.legend()\n",
    "2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(chi_z_5, bins=40, label=\"n = 5\")\n",
    "plt.legend()\n",
    "5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(chi_z_10, bins=40, label=\"n = 10\")\n",
    "plt.legend()\n",
    "10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# t distribution\n",
    "\n",
    "t = np.random.standard_t(2, 10000)\n",
    "t_ave = [sum(t[:i]) / i for i in range(1, 10001)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11a964eb8>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "n = [i for i in range(1, 10001)]\n",
    "ave = [0 for i in range(1, 10001)]\n",
    "\n",
    "plt.ylim([-2, 2])\n",
    "plt.plot(n, t_ave, label=\"actual\")\n",
    "plt.plot(n, ave, color = \"black\", linestyle = \":\", label=\"μ(0.0)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_x_1 = t[:1000]\n",
    "t_x_2 = [sum(t[2*i:2*(i+1)]) / 2 for i in range(1000)]\n",
    "t_x_5 = [sum(t[5*i:5*(i+1)]) / 5 for i in range(1000)]\n",
    "t_x_10 = [sum(t[10*i:10*(i+1)]) / 10 for i in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_z_1 = [t_x_1[i] / (1 / sqrt(1)) for i in range(1000)]\n",
    "t_z_2 = [t_x_2[i] / (1 / sqrt(2)) for i in range(1000)]\n",
    "t_z_5 = [t_x_5[i] / (1 / sqrt(5)) for i in range(1000)]\n",
    "t_z_10 = [t_x_10[i] / (1 / sqrt(10)) for i in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(t_z_1, bins=40, label=\"n = 1\")\n",
    "plt.legend()\n",
    "1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(t_z_2, bins=40, label=\"n = 2\")\n",
    "plt.legend()\n",
    "2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(t_z_5, bins=40, label=\"n = 5\")\n",
    "plt.legend()\n",
    "5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(t_z_10, bins=40, label=\"n = 10\")\n",
    "plt.legend()\n",
    "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}