{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "55ff98e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import sqrt\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io as sio\n",
    "import os\n",
    "import random\n",
    "import time\n",
    "import sys\n",
    "from matplotlib import rcParams\n",
    "from scipy.linalg import eigh\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from scipy import stats\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "mpl.rcParams['figure.dpi'] = 400 \n",
    "plt.rc('text',usetex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83688c61",
   "metadata": {},
   "source": [
    "# Transformações de variáveis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "620cee20",
   "metadata": {},
   "source": [
    "Imagine que a relação verdadeira entre os dados seja dada pelo seguinte modelo: \n",
    "\n",
    "$$ \\log Y =  1 - 2\\log X + \\varepsilon,  $$\n",
    "\n",
    "onde $\\varepsilon$ é ruído Gaussiano, satisfazendo as propriedades usuais que já vimos. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "74191cf6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4800x2400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Gerando os dados: \n",
    "\n",
    "X = np.exp(np.linspace(np.log(10),np.log(1000),100))\n",
    "e = np.random.normal(loc=0,scale=0.5,size=len(X))\n",
    "Y = np.exp(1 - 2*np.log(X) + e) \n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(12,6))\n",
    "ax1 = plt.subplot(121)\n",
    "plt.title('Relação entre $X$ e $Y$',fontsize=13)\n",
    "plt.plot(X,Y,'.')\n",
    "plt.xlabel(r'$X$',fontsize=13)\n",
    "plt.ylabel(r'$Y$',fontsize=13)\n",
    "ax2 = plt.subplot(122)\n",
    "plt.title('Relação entre $\\log X$ e $\\log Y$',fontsize=13)\n",
    "plt.plot(X,Y,'.')\n",
    "plt.xlabel(r'$X$',fontsize=13)\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.tight_layout()    \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e20afbc",
   "metadata": {},
   "source": [
    "## Os dados\n",
    "\n",
    "Suponha que os dados originais estejam na escala linear de $X$ e $Y$:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "de95ee3b",
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>const</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.003780</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.476158</td>\n",
       "      <td>0.024493</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10.974988</td>\n",
       "      <td>0.046417</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.497570</td>\n",
       "      <td>0.022517</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12.045035</td>\n",
       "      <td>0.032126</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12.618569</td>\n",
       "      <td>0.011933</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>13.219411</td>\n",
       "      <td>0.012383</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>13.848864</td>\n",
       "      <td>0.017673</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>14.508288</td>\n",
       "      <td>0.012775</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>15.199111</td>\n",
       "      <td>0.017480</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           X         Y  const\n",
       "0  10.000000  0.003780      1\n",
       "1  10.476158  0.024493      1\n",
       "2  10.974988  0.046417      1\n",
       "3  11.497570  0.022517      1\n",
       "4  12.045035  0.032126      1\n",
       "5  12.618569  0.011933      1\n",
       "6  13.219411  0.012383      1\n",
       "7  13.848864  0.017673      1\n",
       "8  14.508288  0.012775      1\n",
       "9  15.199111  0.017480      1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(X, columns=['X'])\n",
    "df['Y'] = Y\n",
    "df['const'] = 1\n",
    "df.head(10)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36a05f7e",
   "metadata": {},
   "source": [
    "Se notarmos que há uma relação não linear entre as variáveis, devemos transformá-las antes de ajustar o modelo: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "15323a08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>logY</td>       <th>  R-squared:         </th> <td>   0.961</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.961</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2445.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 06 Oct 2023</td> <th>  Prob (F-statistic):</th> <td>4.19e-71</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:36:15</td>     <th>  Log-Likelihood:    </th> <td> -82.994</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   170.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   175.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    1.2535</td> <td>    0.200</td> <td>    6.260</td> <td> 0.000</td> <td>    0.856</td> <td>    1.651</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>logX</th>  <td>   -2.0641</td> <td>    0.042</td> <td>  -49.446</td> <td> 0.000</td> <td>   -2.147</td> <td>   -1.981</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>10.274</td> <th>  Durbin-Watson:     </th> <td>   1.764</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.006</td> <th>  Jarque-Bera (JB):  </th> <td>  11.383</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.604</td> <th>  Prob(JB):          </th> <td> 0.00338</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.127</td> <th>  Cond. No.          </th> <td>    17.8</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &       logY       & \\textbf{  R-squared:         } &     0.961   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared:    } &     0.961   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       } &     2445.   \\\\\n",
       "\\textbf{Date:}             & Fri, 06 Oct 2023 & \\textbf{  Prob (F-statistic):} &  4.19e-71   \\\\\n",
       "\\textbf{Time:}             &     16:36:15     & \\textbf{  Log-Likelihood:    } &   -82.994   \\\\\n",
       "\\textbf{No. Observations:} &         100      & \\textbf{  AIC:               } &     170.0   \\\\\n",
       "\\textbf{Df Residuals:}     &          98      & \\textbf{  BIC:               } &     175.2   \\\\\n",
       "\\textbf{Df Model:}         &           1      & \\textbf{                     } &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     } &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "               & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{const} &       1.2535  &        0.200     &     6.260  &         0.000        &        0.856    &        1.651     \\\\\n",
       "\\textbf{logX}  &      -2.0641  &        0.042     &   -49.446  &         0.000        &       -2.147    &       -1.981     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 10.274 & \\textbf{  Durbin-Watson:     } &    1.764  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.006 & \\textbf{  Jarque-Bera (JB):  } &   11.383  \\\\\n",
       "\\textbf{Skew:}          & -0.604 & \\textbf{  Prob(JB):          } &  0.00338  \\\\\n",
       "\\textbf{Kurtosis:}      &  4.127 & \\textbf{  Cond. No.          } &     17.8  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   logY   R-squared:                       0.961\n",
       "Model:                            OLS   Adj. R-squared:                  0.961\n",
       "Method:                 Least Squares   F-statistic:                     2445.\n",
       "Date:                Fri, 06 Oct 2023   Prob (F-statistic):           4.19e-71\n",
       "Time:                        16:36:15   Log-Likelihood:                -82.994\n",
       "No. Observations:                 100   AIC:                             170.0\n",
       "Df Residuals:                      98   BIC:                             175.2\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          1.2535      0.200      6.260      0.000       0.856       1.651\n",
       "logX          -2.0641      0.042    -49.446      0.000      -2.147      -1.981\n",
       "==============================================================================\n",
       "Omnibus:                       10.274   Durbin-Watson:                   1.764\n",
       "Prob(Omnibus):                  0.006   Jarque-Bera (JB):               11.383\n",
       "Skew:                          -0.604   Prob(JB):                      0.00338\n",
       "Kurtosis:                       4.127   Cond. No.                         17.8\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['logX'] = np.log(X)\n",
    "df['logY'] = np.log(Y)\n",
    "\n",
    "model = sm.OLS(df.logY,df[['const','logX']]).fit()\n",
    "model_prediction = model.predict(df[['const','logX']])\n",
    "\n",
    "model.summary()\n",
    "#plt.plot(df['logX'],model_prediction,'r-')\n",
    "\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1a9c8185",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    1.253515\n",
       "logX    -2.064073\n",
       "dtype: float64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "1909b86b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2400x1600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Yfit = np.exp(model.params['const'] + model.params['logX']*np.log(X))\n",
    "\n",
    "\n",
    "fig= plt.figure(figsize=(6,4))\n",
    "plt.plot(X,Y,'.')\n",
    "plt.plot(X,Yfit,'r-',label=r'fit')\n",
    "plt.xlabel(r'$X$',fontsize=13)\n",
    "plt.ylabel(r'$Y$',fontsize=13)\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.legend(loc='upper right')\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b655fdde",
   "metadata": {},
   "source": [
    "# Aplicação - Ataques terroristas"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c70256da",
   "metadata": {},
   "source": [
    "Base de dados (https://aaronclauset.github.io/datacode.htm): \n",
    "\n",
    "> record (integer)\n",
    "Unique five-digit number indicating the RAND-MIPT record number of the event. Use this to join with other sources of data from RAND-MIPT.\n",
    "\n",
    "> YYYY (integer)\n",
    "Year of the event.\n",
    "\n",
    "> deaths (integer)\n",
    "Number of deaths. All events with deaths=0 have been dropped.\n",
    "\n",
    "> weapon (integer)\n",
    "Type of weapon used:\n",
    "1 = biological or chemical agents\n",
    "2 = explosives or remote detonated explosives\n",
    "3 = fire, firebomb or arson\n",
    "4 = firearms\n",
    "5 = knives or sharp objects\n",
    "6 = other or unknown\n",
    "\n",
    "> OECD (binary)\n",
    "1 = event occurred within an OECD nation (defined as the member nations  as of the 31 December 2007)\n",
    "0 = elsewhere\n",
    "\n",
    "> Iraq/Afghan (binary)\n",
    "1 = event occurred within either Iraq or Afghanistan\n",
    "0 = elsewhere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ae2e2e26",
   "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>record</th>\n",
       "      <th>YYYY</th>\n",
       "      <th>deaths</th>\n",
       "      <th>weapon</th>\n",
       "      <th>OECD</th>\n",
       "      <th>Iraq/Afghan</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>27</td>\n",
       "      <td>1968</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>45</td>\n",
       "      <td>1968</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>76</td>\n",
       "      <td>1968</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>78</td>\n",
       "      <td>1968</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>80</td>\n",
       "      <td>1968</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13269</th>\n",
       "      <td>38491</td>\n",
       "      <td>2007</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13270</th>\n",
       "      <td>38496</td>\n",
       "      <td>2007</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13271</th>\n",
       "      <td>38499</td>\n",
       "      <td>2007</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13272</th>\n",
       "      <td>38500</td>\n",
       "      <td>2007</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13273</th>\n",
       "      <td>38501</td>\n",
       "      <td>2007</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>13274 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       record  YYYY  deaths  weapon  OECD  Iraq/Afghan\n",
       "0          27  1968       2       2     0            0\n",
       "1          45  1968       1       6     0            0\n",
       "2          76  1968       1       4     0            0\n",
       "3          78  1968       1       2     0            0\n",
       "4          80  1968       5       6     0            0\n",
       "...       ...   ...     ...     ...   ...          ...\n",
       "13269   38491  2007       1       4     0            0\n",
       "13270   38496  2007       1       4     0            0\n",
       "13271   38499  2007       1       4     0            0\n",
       "13272   38500  2007       4       2     0            0\n",
       "13273   38501  2007       1       6     0            1\n",
       "\n",
       "[13274 rows x 6 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_table('terrorist_attacks.txt')\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "918b3216",
   "metadata": {},
   "source": [
    "Possível problema: encontrar a distribuição de probabilidade do número de mortes em um ataque terrorista."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "12163e01",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({1: 6912,\n",
       "         2: 2284,\n",
       "         3: 1095,\n",
       "         4: 680,\n",
       "         5: 490,\n",
       "         6: 295,\n",
       "         7: 232,\n",
       "         8: 159,\n",
       "         10: 140,\n",
       "         9: 133,\n",
       "         11: 93,\n",
       "         12: 87,\n",
       "         15: 60,\n",
       "         13: 58,\n",
       "         17: 50,\n",
       "         14: 46,\n",
       "         16: 41,\n",
       "         18: 26,\n",
       "         21: 26,\n",
       "         23: 24,\n",
       "         22: 24,\n",
       "         20: 23,\n",
       "         19: 22,\n",
       "         25: 19,\n",
       "         30: 17,\n",
       "         32: 11,\n",
       "         24: 10,\n",
       "         27: 10,\n",
       "         31: 9,\n",
       "         26: 9,\n",
       "         43: 9,\n",
       "         29: 9,\n",
       "         60: 8,\n",
       "         40: 7,\n",
       "         36: 7,\n",
       "         34: 7,\n",
       "         28: 6,\n",
       "         35: 6,\n",
       "         50: 6,\n",
       "         47: 5,\n",
       "         38: 5,\n",
       "         52: 5,\n",
       "         45: 4,\n",
       "         46: 4,\n",
       "         70: 4,\n",
       "         59: 3,\n",
       "         88: 3,\n",
       "         73: 3,\n",
       "         100: 3,\n",
       "         39: 3,\n",
       "         42: 3,\n",
       "         63: 3,\n",
       "         68: 3,\n",
       "         82: 2,\n",
       "         61: 2,\n",
       "         72: 2,\n",
       "         96: 2,\n",
       "         127: 2,\n",
       "         53: 2,\n",
       "         65: 2,\n",
       "         58: 2,\n",
       "         66: 2,\n",
       "         241: 1,\n",
       "         158: 1,\n",
       "         83: 1,\n",
       "         64: 1,\n",
       "         80: 1,\n",
       "         329: 1,\n",
       "         69: 1,\n",
       "         115: 1,\n",
       "         270: 1,\n",
       "         171: 1,\n",
       "         317: 1,\n",
       "         2749: 1,\n",
       "         44: 1,\n",
       "         189: 1,\n",
       "         74: 1,\n",
       "         252: 1,\n",
       "         33: 1,\n",
       "         400: 1,\n",
       "         103: 1,\n",
       "         213: 1,\n",
       "         71: 1,\n",
       "         202: 1,\n",
       "         162: 1,\n",
       "         95: 1,\n",
       "         121: 1,\n",
       "         126: 1,\n",
       "         117: 1,\n",
       "         55: 1,\n",
       "         239: 1,\n",
       "         191: 1,\n",
       "         331: 1,\n",
       "         118: 1,\n",
       "         168: 1,\n",
       "         106: 1,\n",
       "         125: 1,\n",
       "         98: 1,\n",
       "         102: 1,\n",
       "         77: 1,\n",
       "         56: 1,\n",
       "         90: 1,\n",
       "         57: 1,\n",
       "         190: 1,\n",
       "         37: 1,\n",
       "         215: 1,\n",
       "         137: 1,\n",
       "         79: 1,\n",
       "         41: 1,\n",
       "         120: 1,\n",
       "         152: 1,\n",
       "         49: 1,\n",
       "         87: 1,\n",
       "         85: 1,\n",
       "         500: 1,\n",
       "         67: 1,\n",
       "         76: 1})"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "\n",
    "Nk = Counter(df.deaths)\n",
    "Nk\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "af42b3b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = []; y = []\n",
    "for k in sorted(Nk):\n",
    "    x.append(k)\n",
    "    y.append(Nk[k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8e1fb859",
   "metadata": {},
   "outputs": [
    {
     "data": {
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6nYVAxil3savqlFWlKqTy3BKZy3gpnDIejxe6UK0S/MqybCb8dXt7u/L4lul69WQ+hJll2VIhqnnzHRSrlm/dlH6//+rxN+0QrusmHOI9cyhzcJX7ZtO2Pb/mA6VlWc4siwsAAAD8IWAHAAAAcAbmQyan3MVumeVAIyLevXu38NqHDx+WPs4qSyn++PFjZnudUNJ0sGbZZTKfXF1drTTe+VBRVeeyZVQtOTkcDtfa12t+//49s50kydJzYV37vq6bcoj3zCHMwVXvm03bxfyaD9l9/Phxa/coAAAAHCsBOwAAAIAzUBUUOcUudn8bhllnidBlzAdWGo3Gyvuo1WqT71ddynHZDmVP5se7Tuew5z67rRDZ/JiXXfZ0k8fc9XXdhGO5Z/YxB1e9bzZtF/Nr/n8HyrKMRqMRtVot2u32XpcuBgAAgEMhYAcAAABwJqq62O0j0LNNVR22VrGtblXz57nRaMSbN29W+poO+6xy3ZIkWSkEVbXvvwlRzX92W0tQzoeApoNF27LP67oph3jPHMIcXPW+2YZdzK9Wq1XZwbAoiri+vo5GoxFv376NWq0Wl5eXutsBAABwlgTsAAAAAM7EOXSx+9uwz9+GjZ6z6Q5Qq+xv1ZBQ1b7/5rz+888/M9v39/dr7+sl8+GhXSztuc/ruimHeM8cwhzcd7guYnfz69evX6/+vEVRxM3NTTQajajX61sLygIAAMAhErADAAAAOCPzXez6/f7JdbE7B6uE1FYNQG16PswHo3Y137YVltymbYUPj80hzMFjnD+veW5+JUkSo9Eoms3mUvsZj8dRr9fj5uZmk8MDAACAgyVgBwAAAHBGzqGL3aFL0zQeHx//6uvh4WHp463a+WvTnd/mu2adYnApYvfX9ZQdwhzcRQfEVWx7fiVJEr1eL0ajUbRaraU6+FkyFgAAgHMhYAcAAABwZjqdzsy2LnbbNx3WOfRzXRU++psx393dzWxvK7g0v99ddIM7put6TI51Dm7aPuZXlmXR7Xbj7u4uHh4eYjAYxNXVVWRZVvn+i4uLnYwLAAAA9knADgAAAODMtFotXex2bL4b1CGHsao6V43H47X3d3t7++r+N2F+v6PRaCvHeemYh3xdj8mxzsFN2/f8SpIk8jyPTqcTo9EoRqPRQtCuLMvo9/s7HRcAAADsmoAdAAAAwBnSxW638jyf2T7kZRWTJFkI9gwGg7X3Nx+MajQaa+/rJe/fv5/Zng9VbcMxXddjcqxzcNMObX5lWRaj0WhhXD9+/NjTiAAAAGA3BOwAAAAAztChdbEry3Jvx96Fz58/z2zPBxwPTbPZnNn++fPnWvu5ublZeO3Tp09r7es186Gp8Xi89Xl1bNf1mBzjHNy0Q51f8+MQzgYAAODUCdgBAAAAnKlD6mL3+/fvvRx3V7Ism+nIVRRFXF9f73FEL7u8vJzZLsuyMqj0mvk5luf5QrBzU+a7akVEfPv2baV9rDoPj+26HpNjnIMvWSfseajza7674KkHpAEAAEDADgAAAOBMtVqthaDEJrvYrRK66Pf7GzvuoZoP+rTb7bWCKWVZbj0ImabpQgexy8vLlY7bbrcX3r/NDlxJkiyM+fr6eqUxbyLAdcjX9Zgc4xx8ybrXdtvza5193d/fz2zvI7AIAAAAuyRgBwAAAHDGNtnFrlarzWzPhzCes2po5lg1m83IsmzmtY8fP64cRPz3339jOBxueHSLqoJIjUZjqWt1c3Oz0Gmr6ufftK9fvy681mg0ljrHy75v3rFd12NyjHPwyXx4uSiKF+fEcz/TtufXv//+u3JXvKqugAAAAHDKBOwAAAAAzliz2VwIgqzbTe7du3cz22VZvhoYur6+Xqtr2LH69evXTLen8Xgc9Xr91fPU7/ej0WjExcVFlGUZd3d3Wx7pn4BQr9ebea0oiqjX689es7Is4+LiYmF5z6p9bUOWZdFqtWZeK4rixfDa08/0N+G2Y7qux+QY5+CT+f8eRlR3CB0Oh1Gr1RbGO21b86ssyyjLMtrtdrx9+zba7XaMx+MX93l5eblw7j9//vziZwAAAODY/WffAwAAAABgvzqdTlxcXPz1fqq6GDUajeh0OpMg39Myhbe3t9HpdM6ic920JEni169fUa/XJ68VRRGNRmOyJOZTJ8CyLOP3798xHA4XulWt02ltHc1mMzqdzkwwqCzLuLy8jHa7HXmeT4JEt7e3leGcNE1jMBjsZLwRf+bzcDicmVtlWUaj0YgsyyLP86jVapPzOx0oTdN0rTl5bNf1mBzjHIz4MyeyLJsZz83NTdze3sb79+8n/x18uuYvzbttza/b29uZf7u+vo7r6+tIkiTev38faZpGkiTxzz//PLvPPM931hUQAAAA9kXADgAAAODMPYXf/jbsliRJtFqthe5G7Xa7snPTkzzPo9vtLiwxe6qyLIvRaLSwzGNRFEst1Zim6Yvdrjbt6uoq0jRdCGGWZflqt8Msyxa6b21bkiQxGAyiXq8vhIHG4/GzHbq63W68e/du7bDpsV3XY3Jsc/DJ58+fF+bbS3NwPB4/G1bb5fxapvvo0z532RUQAAAA9sUSsQAAAABEp9PZ2H6W7WaU53kMBoMYDAaVyymesizL4uHhIa6urpb+TJqm0e124+7ubucdo5rNZjw8PESz2Vzq/UmSRLfbjdFotJdgU5qm8d///reyq+K8PM9jNBotLC27jmO7rsfk2OZgxJ9g4LJzsNfrvXr9Nz2/8jyPh4eH6HQ6C0uFv6bZbO713AIAAMAuvXl8fHzc9yAAAAAAOC3X19fx48ePKIoiyrKMJEni3bt3kWVZNBqNyPN8IdAx3/luE4GnY1CWZfz8+TN6vV4URTHpJJimaaRpOjlfhxK+Kooi+v1+DAaDyXinr+/nz5+XDkHtwnA4jG63G+PxeDLWNE0jz/P4/PnzzHktimKhc9e68/DYrusxOaY5WJZltNvt+Pnz59L/LVx2v5ueX+PxOIbDYfz+/Xuyz6duedP3zeXl5VpjBgAAgGMlYAcAAAAAAAAAAAAVLBELAAAAAAAAAAAAFQTsAAAAAAAAAAAAoIKAHQAAAAAAAAAAAFQQsAMAAAAAAAAAAIAKAnYAAAAAAAAAAABQQcAOAAAAAAAAAAAAKgjYAQAAAAAAAAAAQAUBOwAAAAAAAAAAAKggYAcAAAAAAAAAAAAVBOwAAAAAAAAAAACggoAdAAAAAAAAAAAAVBCwAwAAAAAAAAAAgAoCdgAAAAAAAAAAAFBBwA4AAAAAAAAAAAAqCNgBAAAAAAAAAABABQE7AAAAAAAAAAAAqCBgBwAAAAAAAAAAABUE7AAAAAAAAAAAAKCCgB0AAAAAAAAAAABUELADAAAAAAAAAACACgJ2AAAAAAAAAAAAUEHADgAAAAAAAAAAACoI2AEAAAAAAAAAAEAFATsAAAAAAAAAAACoIGAHAAAAAAAAAAAAFQTsAAAAAAAAAAAAoIKAHQAAAAAAAAAAAFQQsAMAAAAAAAAAAIAKAnYAAAAAAAAAAABQQcAOAAAAAAAAAAAAKgjYAQAAAAAAAAAAQAUBOwAAAAAAAAAAAKggYAcAAAAAAAAAAAAVBOwAAAAAAAAAAACggoAdAAAAAAAAAAAAVBCwAwAAAAAAAAAAgAoCdgAAAAAAAAAAAFBBwA4AAAAAAAAAAAAqCNgBAAAAAAAAAABABQE7AAAAAAAAAAAAqCBgBwAAAAAAAAAAABUE7AAAAAAAAAAAAKCCgB0AAAAAAAAAAABUELADAAAAAAAAAACACgJ2AAAAAAAAAAAAUEHADgAAAAAAAAAAACoI2AEAAAAAAAAAAEAFATsAAAAAAAAAAACoIGAHAAAAAAAAAAAAFf4fozzX9DDAfV0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.loglog(x,y,'.')\n",
    "plt.xlabel(r'Número de mortes')\n",
    "plt.ylabel(r'Frequência')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c44ef799",
   "metadata": {},
   "source": [
    "### Caixas em tamanho log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "6ad3fbd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+00, 1.26638017e+00, 1.60371874e+00, 2.03091762e+00,\n",
       "       2.57191381e+00, 3.25702066e+00, 4.12462638e+00, 5.22334507e+00,\n",
       "       6.61474064e+00, 8.37677640e+00, 1.06081836e+01, 1.34339933e+01,\n",
       "       1.70125428e+01, 2.15443469e+01, 2.72833338e+01, 3.45510729e+01,\n",
       "       4.37547938e+01, 5.54102033e+01, 7.01703829e+01, 8.88623816e+01,\n",
       "       1.12533558e+02, 1.42510267e+02, 1.80472177e+02, 2.28546386e+02,\n",
       "       2.89426612e+02, 3.66524124e+02, 4.64158883e+02, 5.87801607e+02,\n",
       "       7.44380301e+02, 9.42668455e+02, 1.19377664e+03, 1.51177507e+03,\n",
       "       1.91448198e+03, 2.42446202e+03, 3.07029063e+03, 3.88815518e+03,\n",
       "       4.92388263e+03, 6.23550734e+03, 7.89652287e+03, 1.00000000e+04])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins = np.logspace(0.0, 4.0, num=40)\n",
    "bins\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "847eab89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tFuvr63HlypW4dOnS4Bij92ccnU5n6DE5qc5OpzN03HHDXf1+f/C4jz6m03xcpuXg8T2o9byP76THndbzOi0X4TUzi3Nw1q+baZvV+dXtdo+MezB2uVyOarU61nkAAACwtPYBAAAATlEqlfYjYvCzsbFx5Dabm5tDt4mI/cePH481/ui+xWJxpvvt7+/vb29vH6n3LMdsNBonXnfSz+F9DteTJMmp+1YqlbHv46jd3d39YrF46jGKxeL+zs7O2OM2Go2h/ZvN5pHrj7tv45wfGxsbYz2maZrub29vT/qQTF2lUjm11iRJBufA7u7umc7Dw2b1vE7LMr9m9vdndw6e93UzTk2TPqbHmdX5tb29vZ+m6UQ1F4vFI48TAADAstNxBwAAAJiKO3fuHLnsonbdGdXv9wfdQcZRr9eHbluv16NcLo/VSeOgS8ekOp1OFAqF6PV6p9621+vF+vr6ubu0HDwuZ1k6rdfrxZUrV6LVao11+yzLBt058tDv96NQKIz1mPX7/ajX62M/H0+Tx/M6DcvwmsnrHDzP62baZnV+HTwnk3bR6fV6x3Z4AwAAWGaX8y4AAAAAuBiSJInNzc2hL9e3trbizp07kSRJfoXNwc2bNwdfbBeLxSiVSlEoFKLf78f29vaxS+DU6/XY2NiIVqs1eMySJInXX3891tfXo9/vx+7ubrzzzjtHvrzvdrvR6XSiUqmMVd/BUkKjKpVK3LhxIyIiHjx4EN1ud+hY1Wo1dnZ2olgsjnWcw7IsG9yP4zztnOh2u8cGLUYf2+Men4NAwPb29sQ1n8fNmzePDSEkSRKlUilu3LgRSZLE7u5udDqdyLIssiw7V8gjj+d1Whb9NZPXOXie1820zer8Ou68T5IkNjY2Bq+Tfr8fe3t7sbOzE91ud+i1led5CwAAMBN5t/wBAAAAFt84S2Xt7+/vP378+MjSJpubm6eOv8xLZR3+OWkJl5OWmjl8WalUOvGYxy3VM+59PW4ppjRN93d3d4/c9vHjx0eWekrT9NRjHLfkz3H3d2Nj49SldI6r97QleEaPf9rjOW0nnRNPW4qo3W6feB6NYx7P67RchNfMLM7B875udnZ2hn5GxyuVSkduc/jnaUvVzfL8Gn1uSqXSqcvm7e7uDs6jcZf4AgAAWBaCOwAAAMCpxg3u7O8f/yX9aV/KXoTgzmkBpeNCTZPUPfocjPO47u/v76dpOnGgZTQAsL29PdHtkySZ+Iv589S7v/9FiGH0uCeFQqbpuIBDRJwaUDqo+azBnXk8r9OyCq+Z/f3Jz8Fpvm7294/+TatUKmPvO2qW59fo/ZzkPj5+/PjY8BAAAMAy+1IAAAAATNGdO3eOXFav13OoZH6SJIlGo3HqbU5apue0fSMiarXakcuOW5rpsFarNXSbJEmi3W6feqzNzc0olUoT1XfY4WVzNjY2Ynt7e6wlfra2tobqTdN07OWGisXikftWq9VOXHJoWo57bNrt9ljL+RSLxYkf24j8ntdpWtTXTJ7n4FlfN9M26/Pr8P0sFosT3cckSSJN07FvDwAAsAwEdwAAAICpSpIkNjc3hy5rtVozD1Dk6fXXXx/rdm+88caRy5IkGfqy+yTHBRj29vaeus/oF+f3798f+0vyw/t2u90zPX+lUimazebYt7979+7Q9iT7Hhxv9HEaHXPaWq3W0HalUjkxbHKcs4QQ8n5ep2FRXzOLcA5O+rqZtlmeX6PBqdOCVAAAAKtAcAcAAACYukajceSL3ovcdee4zh7HOe7L742NjTMf92lfevd6vSNdMyYJlBSLxaFQycOHDyeub5wuHQdGw13FYnGscMao0Y5PW1tbE48xrk6nc+rxp20RntdpWMTXzKKcg5O8bqZt1ufXaFCt3+9Hr9c7Y7UAAAAXg+AOAAAAMBOjX15f5K474yyLFBGxtrZ25LIbN26MfZxJlpR5++23h7bPEnY4/IX9uMsFHdjc3Jyo3tGwwnGdVsZx3NI73W73TGOd5sGDB0PbSZKMfS6cVd7P67Qs4mtmEc7BSV830zaP82s0vHPz5s2ZvUYBAACWgeAOAAAAMBPHfQF9EbvunPdL9rMslTSO0S/Cy+XyxGMUCoXB75MuaTNuR5UDo/WepdPJSfvOKpwyWvO4yz9N85jzfl6nYVleM3mcg5O+bqZtHufX6DzQ7/ejXC5HoVCIer2e6xJuAAAAeRDcAQAAAGbmuK47eQQFZum4jiCTmFV3jdHHuVwux6VLlyb6ORwimOR5S5JkonDFcWOfJ5wxuu+sluIZDRccDizMSp7P67Qs4mtmEc7BSV83szCP82tjY+PYjktZlsXW1laUy+W4cuVKFAqFqNVquvEAAAAXnuAOAAAAMDOr0HXnvCGC84YYTjLtjhWTjDdp+OC4sc/zuL7wwgtD23t7e2ce62lGQwnzWOIoz+d1WhbxNbMI52DeoZ2I+Z1f77777qn3N8uyaLVaUS6XY319fWYBPAAAgLwJ7gAAAAAzNdp1p9PpXLiuO6tgkvDLpMGKaZ8Po4GLeZ1vswphzdKsQk3LZhHOwWU8f05z0vmVJEns7OxEpVIZa5xerxfr6+vRarWmWR4AAMBCENwBAAAAZmoVuu4sujRNY39//1w/jx8/Hvt4k3YqmXanmtEuHxcxEBEx/+f1IluEc3AeHZsmMevzK0mSaLfbsbOzExsbG2N1HLJ0FgAAcBEJ7gAAAAAz12g0hrZ13Zm9wyGARX+sjws1nKfm3d3doe1ZBSJGx51H95plel6XybKeg9OWx/lVLBaj2WzG7u5uPH78OLa3t2NzczOKxeKxt69Wq3OpCwAAYF4EdwAAAICZ29jY0HVnzka7VyxyyOO4Thu9Xu/M4z18+PDU8adhdNydnZ2ZHOdpx1zk53WZLOs5OG15n19JkkSpVIpGoxE7Ozuxs7NzJMDT7/ej0+nMtS4AAIBZEtwBAAAA5kLXnfkqlUpD24u8vEySJEcCA9vb22cebzRwUS6XzzzW01y/fn1oezSsMQvL9Lwuk2U9B6dt0c6vYrEYOzs7R+p6++23c6oIAABg+gR3AAAAgLlYtK47/X4/t2PPwxtvvDG0PRqcWjSVSmVo+5133jnTOK1W68hlr7/++pnGOs1oGKPX6838vFq253WZLOM5OG2Len6N1iH0CQAAXCSCOwAAAMDcLFLXnQcPHuRy3HkpFotDHUSyLIutra0cK3q6Wq02tN3v948NQJxm9BwrlUpHAmPTMtoFJCLi7t27E40x6Xm4bM/rMlnGc/BpzhIiW9Tza7Qb0kUPXgIAAKtFcAcAAACYm42NjSNfwE6z684kX+Z2Op2pHXdRjQYI6vX6mb7w7vf7Mw9YpWl6pONJrVab6Lj1ev3I7WfZMSRJkiM1b21tTVTzNIIhi/y8LpNlPAef5qzP7azPr7OMtbe3N7SdRxAKAABgVgR3AAAAgLmaZtedQqEwtD365e5JJv0yfllVKpUoFotDl928eXPigNPLL78c3W53ytUddVzAoVwuj/VctVqtI51Bjrv/03bnzp0jl5XL5bEe43FvN2rZntdlsozn4IHRUGSWZU89J066T7M+v15++eWJu/gc18UIAADgohDcAQAAAOaqUqkc+YL5rN1v1tbWhrb7/f6pQYStra0zdTlZVu++++5Qd4perxfr6+unPk6dTifK5XJUq9Xo9/uxu7s740q/CB602+2hy7Isi/X19ROfs36/H9Vq9cgyR8eNNQvFYjE2NjaGLsuy7KmhmIP7dJ7QzDI9r8tkGc/BA6N/DyOO72jW7XajUCgcqfewWZ1f/X4/+v1+1Ov1uHLlStTr9ej1ek8ds1arHXns33jjjafuAwAAsEwu510AAAAAsHoajUZUq9Vzj3Nc14VyuRyNRmMQEDpYruXhw4fRaDRWotPOYUmSxLvvvhvr6+uDy7Isi3K5PFga6KBzUb/fjwcPHkS32z3SXeMsnWHOolKpRKPRGAoc9Pv9qNVqUa/Xo1QqDQIKDx8+PPZL/zRNY3t7ey71RnxxPne73aFzq9/vR7lcjmKxGKVSKQqFwuDxPRxUS9P0TOfksj2vy2QZz8GIL86JYrE4VE+r1YqHDx/G9evXB38HD57zp513szq/Hj58OHTd1tZWbG1tRZIkcf369UjTNJIkiRdeeOHEMUul0ty6GAEAAMyD4A4AAAAwdwehmvOGaJIkiY2NjSPdGOr1+rGdJg6USqVoNptHltq6qIrFYuzs7BxZ7ibLsrGWrEnT9KndOaZtc3Mz0jQ9Eu7q9/undmcqFotHuoXMWpIksb29Hevr60dCBr1e78SOIs1mM9bW1s4cYlu253WZLNs5eOCNN944cr497Rzs9XonhmDmeX6N0y3tYMx5djECAACYB0tlAQAAALloNBpTG2fc7gulUim2t7dje3v72GVlLrJisRiPHz+Ozc3NsfdJ0zSazWbs7u7OvcNFpVKJx48fR6VSGev2SZJEs9mMnZ2dXAITaZrGr371q2O7QI0qlUqxs7NzZImts1i253WZLNs5GPFF4Gjcc7Ddbp/6/E/7/CqVSvH48eNoNBpHlkw8TaVSyfWxBQAAmJVL+/v7+3kXAQAAAHBeW1tb8fbbb0eWZdHv9yNJklhbW4tisRjlcjlKpdKRL4pHO/VMI0ixDPr9frzzzjvRbrcjy7JB56M0TSNN08HjtSihjizLotPpxPb29qDew8/vG2+8MXa4Yh663W40m83o9XqDWtM0jVKpFG+88cbQ45pl2ZFOI2c9D5fteV0my3QO9vv9qNfr8c4774z9t3Dccad9fvV6veh2u/HgwYPBmAfdfQ6/bmq12plqBgAAWAaCOwAAAAAAAAAAkANLZQEAAAAAAAAAQA4EdwAAAAAAAAAAIAeCOwAAAAAAAAAAkAPBHQAAAAAAAAAAyIHgDgAAAAAAAAAA5EBwBwAAAAAAAAAAciC4AwAAAAAAAAAAORDcAQAAAAAAAACAHAjuAAAAAAAAAABADgR3AAAAAAAAAAAgB4I7AAAAAAAAAACQA8EdAAAAAAAAAADIgeAOAAAAAAAAAADkQHAHAAAAAAAAAAByILgDAAAAAAAAAAA5ENwBAAAAAAAAAIAcCO4AAAAAAAAAAEAOBHcAAAAAAAAAACAHgjsAAAAAAAAAAJADwR0AAAAAAAAAAMiB4A4AAAAAAAAAAORAcAcAAAAAAAAAAHIguAMAAAAAAAAAADkQ3AEAAAAAAAAAgBwI7gAAAAAAAAAAQA4EdwAAAAAAAAAAIAeCOwAAAAAAAAAAkAPBHQAAAAAAAAAAyIHgDgAAAAAAAAAA5EBwBwAAAAAAAAAAciC4AwAAAAAAAAAAORDcAQAAAAAAAACAHAjuAAAAAAAAAABADgR3AAAAAAAAAAAgB4I7AAAAAAAAAACQA8EdAAAAAAAAAADIgeAOAAAAAAAAAADkQHAHAAAAAAAAAAByILgDAAAAAAAAAAA5ENwBAAAAAAAAAIAcCO4AAAAAAAAAAEAOBHcAAAAAAAAAACAHgjsAAAAAAAAAAJADwR0AAAAAAAAAAMiB4A4AAAAAAAAAAORAcAcAAAAAAAAAAHIguAMAAAAAAAAAADkQ3AEAAAAAAAAAgBwI7gAAAAAAAAAAQA4EdwAAAAAAAAAAIAf/H5RBcRQ7cw7tAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y, X = np.histogram(df.deaths, bins=bins, density=True)\n",
    "\n",
    "X = [x*np.sqrt(bins[1]) for x in X][:-1]  # encontrando o centro da caixa\n",
    "\n",
    "plt.ylim((0.000001, 1))\n",
    "plt.xlabel('Número de mortes')\n",
    "plt.ylabel('PDF')\n",
    "plt.loglog(X,Y, '.')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "55feef5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.95478960e+00, 0.00000000e+00, 4.02776556e-01, 0.00000000e+00,\n",
       "       1.20407627e-01, 5.90452124e-02, 3.35975612e-02, 1.59723783e-02,\n",
       "       1.67170725e-02, 9.21683925e-03, 6.34500868e-03, 4.14722299e-03,\n",
       "       1.61249655e-03, 1.26018466e-03, 6.21942312e-04, 3.43782718e-04,\n",
       "       1.87442750e-04, 1.73534354e-04, 7.65765937e-05, 3.50083003e-05,\n",
       "       2.51312585e-05, 9.92247789e-06, 9.40236883e-06, 4.94973470e-06,\n",
       "       2.93142699e-06, 7.71602676e-07, 6.09297818e-07, 0.00000000e+00,\n",
       "       0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n",
       "       0.00000000e+00, 1.16648969e-07, 0.00000000e+00, 0.00000000e+00,\n",
       "       0.00000000e+00, 0.00000000e+00, 0.00000000e+00])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "7c94cd20",
   "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>logX</th>\n",
       "      <th>logY</th>\n",
       "      <th>const</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.051282</td>\n",
       "      <td>0.291100</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.256410</td>\n",
       "      <td>-0.394936</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.461538</td>\n",
       "      <td>-0.919346</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.564103</td>\n",
       "      <td>-1.228815</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>-1.473692</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.769231</td>\n",
       "      <td>-1.796630</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.871795</td>\n",
       "      <td>-1.776840</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.974359</td>\n",
       "      <td>-2.035418</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.076923</td>\n",
       "      <td>-2.197568</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.179487</td>\n",
       "      <td>-2.382243</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.282051</td>\n",
       "      <td>-2.792501</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.384615</td>\n",
       "      <td>-2.899566</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.487179</td>\n",
       "      <td>-3.206250</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.589744</td>\n",
       "      <td>-3.463716</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.692308</td>\n",
       "      <td>-3.727131</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.794872</td>\n",
       "      <td>-3.760615</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.897436</td>\n",
       "      <td>-4.115904</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>-4.455829</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2.102564</td>\n",
       "      <td>-4.599786</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2.205128</td>\n",
       "      <td>-5.003380</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2.307692</td>\n",
       "      <td>-5.026763</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2.410256</td>\n",
       "      <td>-5.305418</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2.512821</td>\n",
       "      <td>-5.532921</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2.615385</td>\n",
       "      <td>-6.112606</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2.717949</td>\n",
       "      <td>-6.215170</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>3.435897</td>\n",
       "      <td>-6.933119</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        logX      logY  const\n",
       "0   0.051282  0.291100      1\n",
       "1   0.256410 -0.394936      1\n",
       "2   0.461538 -0.919346      1\n",
       "3   0.564103 -1.228815      1\n",
       "4   0.666667 -1.473692      1\n",
       "5   0.769231 -1.796630      1\n",
       "6   0.871795 -1.776840      1\n",
       "7   0.974359 -2.035418      1\n",
       "8   1.076923 -2.197568      1\n",
       "9   1.179487 -2.382243      1\n",
       "10  1.282051 -2.792501      1\n",
       "11  1.384615 -2.899566      1\n",
       "12  1.487179 -3.206250      1\n",
       "13  1.589744 -3.463716      1\n",
       "14  1.692308 -3.727131      1\n",
       "15  1.794872 -3.760615      1\n",
       "16  1.897436 -4.115904      1\n",
       "17  2.000000 -4.455829      1\n",
       "18  2.102564 -4.599786      1\n",
       "19  2.205128 -5.003380      1\n",
       "20  2.307692 -5.026763      1\n",
       "21  2.410256 -5.305418      1\n",
       "22  2.512821 -5.532921      1\n",
       "23  2.615385 -6.112606      1\n",
       "24  2.717949 -6.215170      1\n",
       "25  3.435897 -6.933119      1"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_pdf = pd.DataFrame()\n",
    "X = np.array(X)\n",
    "df_pdf['logX'] = np.log10(X[Y>0])\n",
    "df_pdf['logY'] = np.log10(Y[Y>0])\n",
    "df_pdf['const'] = 1\n",
    "\n",
    "df_pdf.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "95054384",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>logY</td>       <th>  R-squared:         </th> <td>   0.991</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.990</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2528.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 03 Oct 2023</td> <th>  Prob (F-statistic):</th> <td>7.74e-26</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:04:43</td>     <th>  Log-Likelihood:    </th> <td>  7.3688</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    26</td>      <th>  AIC:               </th> <td>  -10.74</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    24</td>      <th>  BIC:               </th> <td>  -8.221</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.1215</td> <td>    0.078</td> <td>    1.550</td> <td> 0.134</td> <td>   -0.040</td> <td>    0.283</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>logX</th>  <td>   -2.2384</td> <td>    0.045</td> <td>  -50.282</td> <td> 0.000</td> <td>   -2.330</td> <td>   -2.147</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>16.394</td> <th>  Durbin-Watson:     </th> <td>   1.476</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  23.749</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.262</td> <th>  Prob(JB):          </th> <td>6.96e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.943</td> <th>  Cond. No.          </th> <td>    4.70</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   logY   R-squared:                       0.991\n",
       "Model:                            OLS   Adj. R-squared:                  0.990\n",
       "Method:                 Least Squares   F-statistic:                     2528.\n",
       "Date:                Tue, 03 Oct 2023   Prob (F-statistic):           7.74e-26\n",
       "Time:                        13:04:43   Log-Likelihood:                 7.3688\n",
       "No. Observations:                  26   AIC:                            -10.74\n",
       "Df Residuals:                      24   BIC:                            -8.221\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.1215      0.078      1.550      0.134      -0.040       0.283\n",
       "logX          -2.2384      0.045    -50.282      0.000      -2.330      -2.147\n",
       "==============================================================================\n",
       "Omnibus:                       16.394   Durbin-Watson:                   1.476\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               23.749\n",
       "Skew:                           1.262   Prob(JB):                     6.96e-06\n",
       "Kurtosis:                       6.943   Cond. No.                         4.70\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.OLS(df_pdf.logY,df_pdf[['const','logX']]).fit()\n",
    "model_prediction = model.predict(df_pdf[['const','logX']])\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "fe65cb9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    0.121497\n",
       "logX    -2.238381\n",
       "dtype: float64"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "471fb19d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Yfit = np.exp(model.params['const'] + model.params['logX']*np.log(X))\n",
    "\n",
    "plt.title(r'$P_{\\rm{morte}}(k) \\propto k^{-2.23}$')\n",
    "plt.loglog(X,Y,'.')\n",
    "plt.loglog(X,Yfit,'r-',label=r'fit')\n",
    "plt.ylim((0.000001, 1))\n",
    "plt.xlabel(r'Mortes num ataque terrorista',fontsize=13)\n",
    "plt.ylabel(r'Probabilidade',fontsize=13)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e892455d",
   "metadata": {},
   "source": [
    "## Mais sobre leis de potência: "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ccef36e",
   "metadata": {},
   "source": [
    "https://arxiv.org/pdf/cond-mat/0412004v3.pdf\n",
    "    \n",
    "https://arxiv.org/pdf/0706.1062.pdf\n",
    "\n",
    "https://aaronclauset.github.io/powerlaws/\n",
    "\n",
    "Veja também o pacote ```powerlaw``` (https://pythonhosted.org/powerlaw/).\n",
    "\n",
    "```pip install powerlaw```\n",
    "\n",
    "```import powerlaw as pwl```\n",
    "\n",
    "Exemplos no artigo: \n",
    "*powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions*\n",
    "https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0085777\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19daedd7",
   "metadata": {},
   "source": [
    "## Apêndice: Por que usar caixas em tamanho logaritmo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "78bd3060",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 4000x1600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.title('Caixas de tamanho linear')\n",
    "plt.hist(y,density=True,bins=50,edgecolor='black',facecolor='lightgray',linewidth=0.5)\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'Número de mortes')\n",
    "plt.ylabel(r'Frequência')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.title('Caixas em tamanho log')\n",
    "plt.hist(y,bins=np.logspace(0,4, 15),density=True,edgecolor='black',facecolor='lightgray',linewidth=0.5)\n",
    "plt.xlabel(r'Número de mortes')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8abff22a",
   "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}