14.2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import optimize\n",
    "import scipy.stats as sts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>count_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   time  count_rate\n",
       "0     0          32\n",
       "1     5          28\n",
       "2    10          29\n",
       "3    15          28\n",
       "4    20          25"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('proctatinium_data.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f86565a9d90>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "t_vals = np.array(df[\"time\"], dtype=float)\n",
    "count_rate = np.array(data[\"count_rate\"], dtype=float) \n",
    "plt.plot(t_vals, count_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 2.280e+02,\n",
       "        1.472e+03, 4.627e+03, 3.169e+03, 5.040e+02]),\n",
       " array([0.        , 0.00155746, 0.00311492, 0.00467238, 0.00622984,\n",
       "        0.0077873 , 0.00934476, 0.01090222, 0.01245968, 0.01401714,\n",
       "        0.0155746 ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZW34bo8PtDKi/Z4D3tOVrgcfWsrex9Vs4+6LkVOfDIr1NdT4s1Nu058Mi79uS58Oy3txp3Bhdef8PRlfoPzH2gj/SlsPoH/D5FvAksH2hsa3+s8Bh4Ll2f8mAejvW/gM+3m5/M5TezsUkWMX37U3A54CngK8D7x3Yn7lfAR5jNOkfBa6eQm9fAE4A/8vob5I3D2g+zNfbEObDnL0NZD7M974teT74MxeSpO58uaYgSVoDhoIkqTMUJEmdoSBJ6gwFSVJnKEiSOkNBktT9HyF8bQjiudxyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def N(x, lamb):\n",
    "    return 32 * np.exp(-lamb * x)\n",
    "  \n",
    "trials = 10000\n",
    "lambdas = []\n",
    "lambdas.append(0)\n",
    "for i in range(trials): \n",
    "    count_rate = count_rate + np.random.normal(0,1, size=len(count_rate))\n",
    "    estimate = optimize.curve_fit(N, t_vals, count_rate, lambdas[0])\n",
    "    lambdas.append(estimate[0][0])\n",
    "plt.hist(lambdas)"
   ]
  },
  {
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}