{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algums experimentos com estatísticas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "generator = np.random.default_rng()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Leis de potência."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 1\n",
    "gamma = 3\n",
    "data_powerlaw3 = (generator.pareto(gamma - 1, size=1000000) + 1) * x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0000000093921515, 2619.6123113980357)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.amin(data_powerlaw3), np.amax(data_powerlaw3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.15460482, 1.41428394, 2.00007764])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(data_powerlaw3, [0.25, 0.5, 0.75])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.9996987481231208, 4.329529262868717, 18.744823638036532)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(data_powerlaw3), np.std(data_powerlaw3, ddof=1), np.var(data_powerlaw3, ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.pareto.mean(3 - 1, loc=0, scale=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4XK6ZTS0iIleV9swhkUjQ1tbGc889R3NzMz09PZw5c2bCmK6uLnJycmhpaWHz5s10dHQAkJWVxWOPPcbjjz9uWffw4cM89dRTHDhwgK+++oqBgQEAjh49ytq1azlw4ABr167l6NGjM5FTRESuQdpyCIVCFBUVUVhYiNPppKKigmAwOGFMf38/VVVVAJSXl3PixAlM02Tx4sWsWbOGRYsWTRg/OjrKpUuXuP3227HZbDzwwAPJNYPBIJWVlQBUVlZa3ktERGZf2stKkUgEwzCS24ZhcPLkyUnHOBwOsrOziUajLF26dMprRiIRAM6fP4/b7QbA7XZz4cKFlGsEAgECgQAATU1NeDyedFFSOjfJ/umuN1c5nc4FlymVTMkJmZNVOW+OtOVgmqZln81mu+Yx6cZfK7/fj9/vT26PjIxc95rfNdPr3Wwej2fBZUolU3JC5mRVztlTXFw86WtpLysZhkE4HE5uh8Ph5Hf2qcbE43HGxsauehM51Zr5+fkA5OXlMTo6Cnx7+Wmysw8REZk9acvB6/UyNDTE8PAwsViM3t5efD7fhDFlZWV0d3cD0NfXR2lp6VXPHNxuN0uWLOGzzz7DNE2OHz+eXNPn83Hs2DEAjh07xoYNG6abTUREpintZSWHw8H27dtpbGwkkUhQXV1NSUkJnZ2deL1efD4fmzZtorW1lbq6OlwuF/X19cn5u3btYmxsjFgsRjAYpKGhgRUrVvD3f//3HDp0iCtXrrBu3TrWr18PQG1tLc3NzXR1deHxeNizZ8/spRcRkZRs5kzcAJgDzp49O6158SceTrnfcfjt6zmcOUfXbReeTMmqnLPnuu45iIhI5lE5iIiIhcpBREQsVA4iImKhchAREQuVg4iIWKgcRETEQuUgIiIWKgcREbFQOYiIiIXKQURELFQOIiJioXIQERELlYOIiFioHERExELlICIiFioHERGxUDmIiIhF2t8hDTAwMEB7ezuJRIKamhpqa2snvD4+Pk5rayuDg4Pk5uZSX19PQUEBAEeOHKGrqwu73c62bdtYt24dZ8+epbm5OTl/eHiYH//4x2zevJk333yTd999l6VLlwKwZcsW7r777pnKKyIiU5C2HBKJBG1tbTQ0NGAYBnv37sXn87FixYrkmK6uLnJycmhpaaGnp4eOjg52797NmTNn6O3tZf/+/YyOjvLiiy/y6quvUlxczEsvvZRc/6mnnuIHP/hBcr3Nmzfz8MOpf7eziIjMvrSXlUKhEEVFRRQWFuJ0OqmoqCAYDE4Y09/fT1VVFQDl5eWcOHEC0zQJBoNUVFSQlZVFQUEBRUVFhEKhCXP/67/+i6KiIpYtWzZzqURE5LqkPXOIRCIYhpHcNgyDkydPTjrG4XCQnZ1NNBolEolw2223Jcfl5+cTiUQmzO3p6eHee++dsO+dd97h+PHjrFq1ir/7u7/D5XJZjisQCBAIBABoamrC4/Gki5LSuUn2T3e9ucrpdC64TKlkSk7InKzKeXOkLQfTNC37bDbblMak2v9dsViMDz74gL/9279N7nvwwQd59NFHAejs7OS1115j586dlrl+vx+/35/cHhkZuXqQazTT691sHo9nwWVKJVNyQuZkVc7ZU1xcPOlraS8rGYZBOBxObofDYdxu96Rj4vE4Y2NjuFwuy9xIJEJ+fn5y+6OPPmLlypXccsstyX233HILdrsdu91OTU0Np06dmkJEERGZSWnLwev1MjQ0xPDwMLFYjN7eXnw+34QxZWVldHd3A9DX10dpaSk2mw2fz0dvby/j4+MMDw8zNDTE6tWrk/NSXVIaHR1Nfv3+++9TUlJyPflERGQa0l5WcjgcbN++ncbGRhKJBNXV1ZSUlNDZ2YnX68Xn87Fp0yZaW1upq6vD5XJRX18PQElJCRs3bmTPnj3Y7XZ27NiB3f5tH/3pT3/ik08+4cknn5zwfm+88QZffPEFNpuNZcuWWV4XEZHZZzPT3RiYJ86ePTutefEnUv/IrOPw29dzOHOOrtsuPJmSVTlnz3XdcxARkcyjchAREQuVg4iIWKgcRETEQuUgIiIWKgcREbFQOYiIiIXKQURELFQOIiJioXIQERELlYOIiFioHERExELlICIiFioHERGxUDmIiIiFykFERCxUDiIiYqFyEBERi7S/QxpgYGCA9vZ2EokENTU11NbWTnh9fHyc1tZWBgcHyc3Npb6+noKCAgCOHDlCV1cXdrudbdu2sW7dOgB27drF4sWLsdvtOBwOmpqaALh48SLNzc18/fXXLFu2jN27d+NyuWYys4iIpJH2zCGRSNDW1sZzzz1Hc3MzPT09nDlzZsKYrq4ucnJyaGlpYfPmzXR0dABw5swZent72b9/P88//zxtbW0kEonkvBdeeIGXXnopWQwAR48eZe3atRw4cIC1a9dy9OjRmcoqIiJTlLYcQqEQRUVFFBYW4nQ6qaioIBgMThjT399PVVUVAOXl5Zw4cQLTNAkGg1RUVJCVlUVBQQFFRUWEQqGrvl8wGKSyshKAyspKy3uJiMjsS3tZKRKJYBhGctswDE6ePDnpGIfDQXZ2NtFolEgkwm233ZYcl5+fTyQSSW43NjYC8Jd/+Zf4/X4Azp8/j9vtBsDtdnPhwoXpZhMRkWlKWw6maVr22Wy2KY1Jtf9/vfjii+Tn53P+/Hl++ctfUlxczB133DGVYwYgEAgQCAQAaGpqwuPxTHnud52bZP9015urnE7ngsuUSqbkhMzJqpw3R9pyMAyDcDic3A6Hw8nv7P98jGEYxONxxsbGcLlclrmRSIT8/HyA5P/m5eWxYcMGQqEQd9xxB3l5eYyOjuJ2uxkdHWXp0qUpj8vv9yfPNgBGRkauIXZ6M73ezebxeBZcplQyJSdkTlblnD3FxcWTvpb2noPX62VoaIjh4WFisRi9vb34fL4JY8rKyuju7gagr6+P0tJSbDYbPp+P3t5exsfHGR4eZmhoiNWrV3P58mUuXboEwOXLl/nkk0+49dZbAfD5fBw7dgyAY8eOsWHDhmmFFhGR6Ut75uBwONi+fTuNjY0kEgmqq6spKSmhs7MTr9eLz+dj06ZNtLa2UldXh8vlor6+HoCSkhI2btzInj17sNvt7NixA7vdzvnz53n55ZcBiMfj3Hfffckfca2traW5uZmuri48Hg979uyZxfgiIpKKzbzajYF55OzZs9OaF3/i4ZT7HYffvp7DmXN0ar7wZEpW5Zw913VZSUREMo/KQURELFQOIiJioXIQERELlYOIiFioHERExELlICIiFioHERGxUDmIiIiFykFERCxUDiIiYqFyEBERC5WDiIhYqBxERMRC5SAiIhYqBxERsVA5iIiIhcpBREQs0v4OaYCBgQHa29tJJBLU1NRQW1s74fXx8XFaW1sZHBwkNzeX+vp6CgoKADhy5AhdXV3Y7Xa2bdvGunXrGBkZ4eDBg/zxj3/EZrPh9/t56KGHAHjzzTd59913Wbp0KQBbtmzh7rvvnsnMIiKSRtpySCQStLW10dDQgGEY7N27F5/Px4oVK5Jjurq6yMnJoaWlhZ6eHjo6Oti9ezdnzpyht7eX/fv3Mzo6yosvvsirr76Kw+Hg8ccfZ9WqVVy6dImf//zn3HXXXck1N2/ezMMPp/7dziIiMvvSXlYKhUIUFRVRWFiI0+mkoqKCYDA4YUx/fz9VVVUAlJeXc+LECUzTJBgMUlFRQVZWFgUFBRQVFREKhXC73axatQqAJUuWsHz5ciKRyMynExGRaUlbDpFIBMMwktuGYVj+Iv/uGIfDQXZ2NtFo1DI3Pz/fMnd4eJjPP/+c1atXJ/e98847PPPMMxw6dIiLFy9OL5mIiExb2stKpmla9tlstimNSbX/uy5fvsy+ffvYunUr2dnZADz44IM8+uijAHR2dvLaa6+xc+dOy9xAIEAgEACgqakJj8eTLkpK5ybZP9315iqn07ngMqWSKTkhc7Iq582RthwMwyAcDie3w+Ewbrc75RjDMIjH44yNjeFyuSxzI5EI+fn5AMRiMfbt28f999/PPffckxxzyy23JL+uqanhn//5n1Mel9/vx+/3J7dHRkbSRbkmM73ezebxeBZcplQyJSdkTlblnD3FxcWTvpb2spLX62VoaIjh4WFisRi9vb34fL4JY8rKyuju7gagr6+P0tJSbDYbPp+P3t5exsfHGR4eZmhoiNWrV2OaJr/61a9Yvnw5P/rRjyasNTo6mvz6/fffp6Sk5FqyiojIDEh75uBwONi+fTuNjY0kEgmqq6spKSmhs7MTr9eLz+dj06ZNtLa2UldXh8vlor6+HoCSkhI2btzInj17sNvt7NixA7vdzh/+8AeOHz/Orbfeyj/8wz8A//cjq2+88QZffPEFNpuNZcuW8eSTT87ufwEREbGwmeluDMwTZ8+enda8+BOpf2TWcfjt6zmcOUen5gtPpmRVztlzXZeVREQk86gcRETEQuUgIiIWKgcREbFQOYiIiIXKQURELFQOIiJioXIQERELlYOIiFioHERExELlICIiFioHERGxUDmIiIiFykFERCxUDiIiYqFyEBERC5WDiIhYqBxERMQi7e+QBhgYGKC9vZ1EIkFNTQ21tbUTXh8fH6e1tZXBwUFyc3Opr6+noKAAgCNHjtDV1YXdbmfbtm2sW7fuqmsODw/zyiuvcPHiRVauXEldXR1O55QOU0REZkjaM4dEIkFbWxvPPfcczc3N9PT0cObMmQljurq6yMnJoaWlhc2bN9PR0QHAmTNn6O3tZf/+/Tz//PO0tbWRSCSuuuYbb7zB5s2bOXDgADk5OXR1dc1CbBERuZq05RAKhSgqKqKwsBCn00lFRQXBYHDCmP7+fqqqqgAoLy/nxIkTmKZJMBikoqKCrKwsCgoKKCoqIhQKTbqmaZp8+umnlJeXA1BVVWV5LxERmX1pyyESiWAYRnLbMAwikcikYxwOB9nZ2USjUcvc/Px8IpHIpGtGo1Gys7NxOBwTxouIyI2V9mK+aZqWfTabbUpjUu2f6prpBAIBAoEAAE1NTRQXF1/T/KR/75/evHlo2v+N5plMyQmZk1U5b7y0Zw6GYRAOh5Pb4XAYt9s96Zh4PM7Y2Bgul8syNxKJkJ+fP+maubm5jI2NEY/HJ4xPxe/309TURFNT0zXEtfr5z39+XfPnC+VceDIlq3LeHGnLwev1MjQ0xPDwMLFYjN7eXnw+34QxZWVldHd3A9DX10dpaSk2mw2fz0dvby/j4+MMDw8zNDTE6tWrJ13TZrNRWlpKX18fAN3d3Zb3EhGR2Zf2spLD4WD79u00NjaSSCSorq6mpKSEzs5OvF4vPp+PTZs20draSl1dHS6Xi/r6egBKSkrYuHEje/bswW63s2PHDuz2b/so1ZoAP/nJT3jllVf4zW9+w8qVK9m0adMsxhcRkVRs5mQ3BjJEIBDA7/ff7MOYdcq58GRKVuW8OTK+HERExEqPzxAREYuMfi5FuseCzDe7du1i8eLF2O12HA4HTU1NXLx4kebmZr7++muWLVvG7t27cblcmKZJe3s7H330Ed/73vfYuXMnq1atutkRUjp06BAffvgheXl57Nu3D2Baubq7u3nrrbcAeOSRR5L/cHOuSJXzzTff5N1332Xp0qUAbNmyhbvvvhu49kfTzBUjIyMcPHiQP/7xj9hsNvx+Pw899NCC+0wnyzlvPlMzQ8XjcfNnP/uZ+dVXX5nj4+PmM888Y54+ffpmH9Z12blzp3n+/PkJ+15//XXzyJEjpmma5pEjR8zXX3/dNE3T/OCDD8zGxkYzkUiY//M//2Pu3bv3hh/vVH366afmqVOnzD179iT3XWuuaDRq7tq1y4xGoxO+nktS5ezs7DT/7d/+zTL29OnT5jPPPGNeuXLFPHfunPmzn/3MjMfj8+LPdSQSMU+dOmWapmmOjY2ZTz/9tHn69OkF95lOlnO+fKYZe1lpKo8FWQiCwSCVlZUAVFZWJjP29/fzwAMPYLPZuP322/nmm28YHR29mYc6qTvuuAOXyzVh37XmGhgY4K677sLlcuFyubjrrrsYGBi44VmuJlXOyVzro2nmErfbnfzOf8mSJSxfvpxIJLLgPtPJck5mrn2mGVsOU3ksyHzU2NjIsxO3+1UAAAKhSURBVM8+m/zX4+fPn0/+o0W3282FCxeAb/N7PJ7kvPmW/1pzTfYol/ngnXfe4ZlnnuHQoUNcvHgRsP75TfdomrlqeHiYzz//nNWrVy/oz/S7OWF+fKYZe8/BnIFHeMw1L774Ivn5+Zw/f55f/vKXV/2n+AsxP1xbrvmQ98EHH+TRRx8FoLOzk9dee42dO3fO6qNpbpTLly+zb98+tm7dSnZ29qTj5vtn+uc558tnmrFnDlN5LMh887+PGsnLy2PDhg2EQiHy8vKSl4tGR0eTN8EMw2BkZCQ5d77lv9Zc+fn5lke5zIe8t9xyC3a7HbvdTk1NDadOnQKsf37TPZpmronFYuzbt4/777+fe+65B1iYn2mqnPPlM83YcpjKY0Hmk8uXL3Pp0qXk15988gm33norPp+PY8eOAXDs2DE2bNgAgM/n4/jx45imyWeffUZ2dvac+z/W1VxrrnXr1vHxxx9z8eJFLl68yMcff5z8SZC57Lv3gd5///3kkwSu9dE0c4lpmvzqV79i+fLl/OhHP0ruX2if6WQ558tnmtH/CO7DDz/k17/+dfIRHo888sjNPqRpO3fuHC+//DLw7cMP77vvPh555BGi0SjNzc2MjIzg8XjYs2dP8scD29ra+Pjjj1m0aBE7d+7E6/Xe5BSpvfLKK/z3f/830WiUvLw8fvzjH7Nhw4ZrztXV1cWRI0eAb3/ssbq6+mbGskiV89NPP+WLL77AZrOxbNkynnzyyWSJv/XWW/zHf/wHdrudrVu3sn79emDu/7n+wx/+wC9+8QtuvfXW5OWRLVu2cNttty2oz3SynD09PfPiM83ochARkdQy9rKSiIhMTuUgIiIWKgcREbFQOYiIiIXKQURELFQOIiJioXIQERELlYOIiFj8f/f9KK5ddcelAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data_powerlaw3, bins=50, density=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start = np.amin(data_powerlaw3)\n",
    "finish = np.amax(data_powerlaw3)\n",
    "bins = np.logspace(np.log10(start), np.log10(finish), 50)\n",
    "h, b = np.histogram(data_powerlaw3, bins=bins, density=True)\n",
    "plt.loglog(b[:-1], h, label='data')\n",
    "plt.loglog(b[:-1], stats.pareto.pdf(b[:-1], 3 - 1, loc=0, scale=1), label='density')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora vamos tentar um expoente menor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 3\n",
    "gamma = 2\n",
    "data_powerlaw2 = (generator.pareto(gamma - 1, size=10000) + 1) * x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.0005602028028173, 40441.24673460653)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.amin(data_powerlaw2), np.amax(data_powerlaw2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.00689422,  5.97077317, 12.11415698])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(data_powerlaw2, [0.25, 0.5, 0.75])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(37.00432575373651, 679.3043263722989, 461454.3678281228)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(data_powerlaw2), np.std(data_powerlaw2, ddof=1), np.var(data_powerlaw2, ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data_powerlaw2, bins=50, density=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rtyr4/0sKftNoVsuZB60Ub+C0v4kvr7yT9092xGhQ+OuADozsacLgZqN9Pf9i2pvkynZ6zpVbNU/Te3tkR1LMHfB44CkM6S/g0a0Hf/zyJbKKXqWHVkn2+v089t0eyqUZmxBtkozwnaA1Rxbajq2oSz5E+ymf3G7DWdDjD9QZPLjlshCuvbS9WzRj0/NIzN4kV7bTc65khN9GKT0uweP+x/F4JJOR7Y4ye9Wz9Dt9kH9sOMjD3+yi9PAJZ4cohGglMsJ3AmeNLDT1NNon76B+s5hVA64jJ3Q4x+pUro82c310iMs2Y9PzSMzeJFe203Ou3GqELxxDMXhguOEODLdP5opNXzB78zwu7+DJP3+y8relO9l66LizQxRCOJBLFnyZ0nEswxUjMTzwNIFHLUz57DFm9KzlWK1K+je7eLvgACfqVGeHKIRwAJnScQJX+SqpWcpR58wEyz6Op07gXf/+fFVyhHB/T+4bEs5l4X7ODhFwnXy5A8mV7fScK5nSEedQOnTEkP4C9O5Huw+yuSfvbWYOa4+iwGPf7WHO2nKqT512dphCCDuRgt/GKb5+GCY/hnL9HfBzPlFzppF10UHGRbXnux1HmbxkJ+vKqpwdphDCDqTgizMnc0elYJjxMgSb8XztWW7bsJAXrgoj0NuDZ3/Yy4sr93JEmrEJ4dZcsuDLSVvnUC7qhmH6iyhjbkRbt5wer0zjxe6V/PmyENbuqWbSkp0s33m0wecgCCFcn5y0dQJ3OFmk7dyGmvMyHNiLMuQqykbewpwtJ9l66AQDO/mRNjicUL/WacbmDvlyFZIr2+k5V3LSVjSJEtELw2NZKKNvQCtcw0UZk5hVuZw7+5r4+UANk5fsZOm2w6iuPV4QQvwPKfiiUYq3N4aU2zDMnIcy6AoM3y7mD/P/j9nBO+hl9ua1vAPMyN3NvkppxiaEO2i1KZ2ysjK+/PJLqqqq6Nu3b4MPMG+ITOm4Dm33r6gfzYctm9A6dGTZlXcw/2h76lSNm/uGcF1vxzRjc9d8OYPkynZ6zlWL+uFnZ2dTWFiIyWQiMzOzfnlRURHz589HVVUSExMZO3bsBQNRVZXXX3+dtLQ0mwKXgu9aNE2DnwtQP1kAe3dREdyJNwf8hXVqeyLbezN5aEcign3s+p7unK/WJrmynZ5z1VjBN9qy8YgRI0hOTmbu3Ln1y1RVJScnhxkzZmA2m5k+fTqxsbGoqsrChQvP2j4tLQ2TyUR+fj6ffvopycnJLTgU4UyKokDfWAzRMbBlE+2Xf8lD37/AmpA+vNn7eqZ9eYJx0e1J7RuKl4fMGArhSmye0rFYLDz//PP1I/xt27bx0Ucf8eijjwKwePFiAFJSUi64r+eee47p06c3+LPc3Fxyc3MByMjI4NQp/c0PG41G6ur0c0376UMWjn/7GQeWfc3bIZezPDyWrv4ePDo6mj4dA1u8f73ly5EkV7bTc668vLwaXG7TCL8hFRUVmM3m+tdms5mSkpJG19+8eTPr1q2jrq6OAQMGNLpeUlISQUFBFBQUAOjyK5f+vkoaYORYAuPHMGXDGq5Y+iGvXTSKif/ayJhL2vPnfqG082z+aF9/+XIcyZXt9JyrFk3pNKShLwbKeZ6VGh0dTXR0dHPfTrgBxWhEGTSc2Ev6MvvNl3nvdFc+53LWlVVx35CO9O/oGs3YhGirmj3sMpvNWK3W+tdWq5Xg4GC7BBUbG8uECRPssi/R+pTAIPymPs49kUZmbsjGePgQTyzbw6try6k+Kc3YhHCWZhf8yMhIysvLsVgs1NXVsXr1amJjY+0SlLRWcH+KhweGP91Onz/fwktFcxi3byXLfj3CpCU7WLNHmrEJ4Qw2TelkZWVRXFxMVVUVEydOJDU1lYSEBMaPH8+sWbNQVZX4+Hi6dOni6HiFm1EGDMWnU1dunfccwwoKyB4ygYwf93J51wDuiQ0jqF2zZxWFEE0kvXScQM8nixqjnTyB+nYWdRvW8ln8RD4kAm+jwp0Dw4iPCDzv+Z+2mK/mklzZTs+5cqteOjKloz+Ktw+GCQ/imfAHxi3L5qWq7+gc4MXsNeU89X0ZlupaZ4cohO7JCN8J9DyyuBBN09C++RTt4/movfrwdfL9vFt8FFD4S/9QrukVhOF3o/22nK+mklzZTs+5cqsRvtAvRVEwjEpBuWsahl+3cM3HM3nlChOXhrbjjfwDPPrtbsoqTzo7TCF0ySULvkzp6J9hyFUYpjwBhw8RkjWdJ3rWMmVYR3YfPcnUL0r5eLOVOtWlv3wK4XZkSscJ9PxVsqm0sp2os5+GY1UoN93FkdhE3iywsHp3FT2CzzRjG9yrs+TLRvLZsp2ecyVTOsIlKZ0jMMx4CS6OQns3m6B3XuKhgSbSh19ExfE6pn1VymurSjl1WnV2qEK4PZcs+DKl07YopmAMU55EGXc72oY1qE9PZWjtXuaO6UF8hIl388uY+mUpxZYaZ4cqhFuTKR0n0PNXyZbSft2C+ubf4YgV5bpbUUalsOO4JxnfbsNyrJbRvYK4rX8ovp4ezg7VJclny3Z6zpVM6Qi3oEReiuHxLJT+Q9EWLUDNeoKBXsd45Q8RjLkkmKXbjnD/kp0U7qt2dqhCuB0p+MLlKL7+KBMeQrntXti5Dev9f8Z7yULu6mviuau74m008NT3ZWSt3keVNGMTwmYuWfBlDl8oioLhymQMz8zD54pEtC//hfr4vVy6u4iXr+lGah8zP5ZWct+SHazaXenscIVwCzKH7wR6njt0hJCQEA6u+RF14etQthN698Nw8z2U+oTy6tr9/FpxgmFd/LlnUDjt23gzNvls2U7PuZI5fOHWlIujMMx4CeWWCbBrO+pT99Mt9wNeuCqU2/uHkr/3GJOW7CD31yMNPpxHCCEFX7gRxcMDQ/wfMMx8DWVYAto3i1GeuI+x1T+TNbo73UzevLp2P08u28OBav09C1mIlmrVgn/ixAkefvjh+ufVCtEcSoAJw+2TMTzydzC1R3srk45vPMXMKI0Jg8LYcugE93+xk8+3VHBa2jMIUc+mCc/s7GwKCwsxmUxkZmbWLy8qKmL+/PmoqkpiYiJjx449737+/e9/M2zYsJZFLMR/KBG9MDzyItrKb9EWvQvPTCU5/g/EJqUyb1MlbxVYWLmriklDw+li8nZ2uEI4nU0Ff8SIESQnJzN37tz6ZaqqkpOTw4wZMzCbzUyfPp3Y2FhUVWXhwoVnbZ+WlsauXbvo3LkztbXS91zYj2LwQLkyGS0mDm3xe2jLlmAuWsdjEx/mx4iOvJV/gKlflnJjXzPjoswYDY0/aEUIvbOp4EdFRWGxWM5atn37dsLDwwkLCwMgLi6OvLw8UlJSSE9PP2cfmzdv5uTJk5SVleHl5cWAAQMwGOQUgrAPxT8Q5bZ70eISUN94Ae35dK68ZQL9xsTzZr6F9zceYvXuKiYN6UhPs4+zwxXCKZp9DVtFRQVms7n+tdlspqSkpNH1b775ZgCWL19OQEBAo8U+NzeX3NxcADIyMggJCWluiC7LaDTq8rgcpUn5CrkCtXcfjr70BKfemUOHsp08f8//saKsmr9//ysPfV3KzTGdGT+0C95G/bVnkM+W7dpirppd8Bu69O18zyX9zYgRI87786SkJIKCgupP7OrxOlk9X//rCM3Jl3bvIyiff8iJJf/kxLZieqel88robswvtPBeQRnLth1g0pCORIf5Oihq55DPlu30nCu7X4dvNpuxWq31r61WK8HBwc3dnRB2pRg8MFx3C4b7H4eKg6gz/4bf5jwmDQnn6cQunNbgkdzdvLZ+PzW10p5BtA3NLviRkZGUl5djsVioq6tj9erVxMbG2jM2IVpM6Rt7pt9+aDhq9rOozz3IZXs3Mvuarlx7aTBflRxh0pKd5O+VZmxC/2xqrZCVlUVxcTFVVVWYTCZSU1NJSEigsLCQBQsWoKoq8fHxjBs3zu4BSmsFYY98abW1aKty0b5ZDAf3Q4eOKCPHsu2SOOYUWNlz9BQjugdy58AOBPq4b3sG+WzZTs+5amxKxyV76eTn51NQUMCECROk4Au75ktTT8OGtahfLYLSEggwURc/hk8uupKPtxzF38uDu2PDuKJbgE3npFyNfLZsp+dcuVXB/19S8IUj8qVpGmzbjPr1IvgpH7pfzO7bpzPnp2q2V5xgcGd/Jg4Kw+zradf3dTT5bNlOz7lyq+Zp0h5ZOJqiKCiX9MHj/scx3PcI7N1F13kzeD7GmztiQikqP8bkJTv5Zrs0YxP6ISN8J9DzyMIRWiNf2vZi1FdngqcnhilPsj/oIuas28/PB2q4LMyX+4aEEx7g5dAY7EE+W7bTc65khC/EeSg9ozA8lAEGD9QXpxO+byvPJHbh3sHhlFhPMPmLnfz7F2nGJtybjPCdQM8jC0dozXxpFQdRs56Eg+UY7pqGMvByDtXUMm/dfvL3HaOXyYNJXWrp6m+AHpe43Ild+WzZTs+5kpO2LkTPHzRHaO18aceqUOfMhF+3QO9+UHUU7UgFK9tFkNPzWmqMPly/axkp5hq8/zwBJdB1bjiUz5bt9JwrmdIRwkaKXwCGB55GiUuAyqMQZMYwYChXDo3ilR5HGdYe/hlxNQ95DGXr87NQ1y6XE7vCLcgI3wn0PLJwBFfM1/qyKl5bu4/DJ07zxz0ruCmggna33oMSZL7wxg7kirlyVXrOlVuN8IVwdYM7B/DqtT1J6hnEv7texd98hrPpxRdRV+XKaF+4LCn4QjSTn5cH9w3txDOJXdDah/J41F+Zt7qM6vlz0OrkQT/C9UjBF6KFLgv345VrL2bspcHkdhrC/Qxi/bw30WqkIZtwLS5Z8OWkrXA33kYDdwwM4/lR3fH39+PZ9glkLviOI+X7nR2aEPXkpK0T6PlkkSO4W75qT2t88sNmPtqr4Hv6JHf18efKgRe3yjX77pYrZ9JzruSkrRCtxNND4aaEPmQO8SOs9igvbVWZ+flmDtXIvL5wrlYr+Js3b+bxxx/njTfeYPPmza31tkI4Tfde3cm4oR93WNew6YjKpE+38dXWClTX/lItdMymJz1kZ2dTWFiIyWQiMzOzfnlRURHz589HVVUSExMZO3Zso/tQFAUfHx9qa2vPevi5EHpmDGrPdRNuZtD815lX14N5+R6s2HqASfGRdHSDZmxCX2yawy8uLsbHx4e5c+fWF3xVVZkyZQozZszAbDYzffp0pkyZgqqqLFy48Kzt09LSCAgIwGAwcOTIEd555x3uv/9+mwKUOXyhh3xpmoZWsIZvctezoONV1Hl4cUt0ENf264SHwX5z+3rIVWvRc64am8O3aYQfFRWFxWI5a9n27dsJDw8nLCwMgLi4OPLy8khJSSE9Pb3Rffn7+1NbK3OZom1RFAUlNo5RfWMY+PkiXt/nwz+Ko1hZspFJib2IMPs6O0TRBjT74Z0VFRVnTc2YzWZKSkoaXX/dunVs3LiRY8eOkZyc3Oh6ubm55ObmApCRkUFISEhzQ3RZRqNRl8flKHrLV+jE+3lx906+XPAvXvPpx7SlpdzSxcAd1w7D29OjRfvWW64cqS3mqtkFv6GZoPNddjZkyBCGDBlywf0mJSURFBREQUEBgC6/cun5q6Qj6DJfvgHETRxP9NqVvF2wi3eVaJa//AWTLjZwyeWDUAzNK/y6zJWD6DlXdr8s02w2Y7Va619brVaCg12nTawQrk5RFIKGDeeBidcxI8xKjcGT9F2B5Mz9FzWrlqOdPu3sEIXONLvgR0ZGUl5ejsVioa6ujtWrVxMbG2uXoGJjY5kwYYJd9iWEq1OMRgYlXc6rN/djVNBJPm8/gKm/eFKU8SxaWamzwxM6YtNVOllZWRQXF1NVVYXJZCI1NZWEhAQKCwtZsGABqqoSHx/PuHHj7BJUfn4+BQUFTJgwQa7SEW0uXz/vr2buil3sO+VB0smd3HHr1fh72TbF09Zy1RJ6zlWLrtKZOnVqg8tjYmKIiYlpflRCiHP0CfcnK6U3H3yynH9r3Sj4bDtpQzoxpEuAs0MTbs4lWyvIlI5o67yNBm4f2ZeMDXMxnarm2R/38uLKvRw5Uefs0IQbc8mCL90yhQClfSg9L+7CC+tf5pboINbuqWbS5ztYvvOoPGRFNItLFpiWir4AABe6SURBVHwZ4QtxhiHhjxiPVXJD5UZeHt2dToFevLy6nGeWl3HwmNzAKJrGJQu+EOI/Lo6CzhFoy5bQJdCL50Z2466BHfj5QA2Tl+xk6bbD0oxN2MwlC75M6QhxhqIoKIljYO8u2PYzHgaFP17anlfHRNArxIfX8g7w6Le72Vt5ytmhCjfgkgVfpnSE+C9l8JXgH4C6bEn9sjB/L55K6MLkoeHsOnqSqV/uZNFmK3WqjPZF41yy4Ash/kvx8ka54mrYsA7N+t8mhoqikBQZxJwxPYjp5MeCooPc/V4eO3YfQKuVEb84V7N76TjS/954JYQAZcRotK8Xoy1fivKn28/6Wft2RtIHm1m5JZe3TkXzf9bjpOz5mOv3rsCrnQ/4+kFAIIbrx6NEXOykIxCuwCULfmxsrN3aNAihB4o5FAYMQVvxDdofb0Lx8q7/mVZxEHXOTOLKdjFkXDDZxzvxcbdE1nQfxqS6zVxybC/8XID2w1Ip+G2cTOkI4SYMCX+EY1Vo636oX6bt2Io6axocOoBh8mN0uvVOpqYM4on4zpxqF8gjHoN4e9AdHO87GG3zBrl+v42Tgi+Eu+gVDRd1Q1u2BE3TUNf9gPriI+DtgyH9BZS+A+tXjenkzytjIhjdK4glWw8zNegaipT2sG+3Ew9AOJtLFny5LFOIc525RPOPUFaK9saLaG9lQo9eGKb/HaVT13PW9/X04J5B4Tw3sitePt483e9uXllTTvVJabvcVrlkwZfLMoVomDL4KvD1R8tfiXLFSAwPPI0SEHjebaI6+JL1x0jGWfNZfiKQSUt2sGZ3VStFLFyJSxZ8IUTDFG9vDOOnotwxBeUvk1CMnjZt5+Vh4LbwkzxflE2QjwcZK/aS8eNeDh9vuBmbVryB0+l3oVUesWf4wsmk4AvhZpR+gzHEJZ73kaINbtcnhsiju3mxSwW39gshf281k5bsYNmOc5uxqbmfg9WCtnG9PUMXTtZqBV9VVT744APefvttli9f3lpvK4T4zcXR4OWFR/EGbugTQtbo7nQxeTN7TTlPfV+GpfpMMzbtSAVsLjzz35vynBmxsDObrsPPzs6msLAQk8lEZmZm/fKioiLmz5+PqqokJiYyduzYRveRn59PRUUF/v7+mM3mlkcuhGgSxdMLevVF+/lMMe9s8ubZkV1Zuu0I7xQdZPIXO/hL/w6M2vkDiqpC735QXIRWe+rMtsLt2VTwR4wYQXJyMnPnzq1fpqoqOTk5zJgxA7PZzPTp04mNjUVVVRYuXHjW9mlpaezbt49evXoxcuRIMjMz6du3r32PRAhxQUr0ALQP30I7uB8lNByDovCHS4IZdJE/2ev380b+AX48buK+XoPpcvU1qLOfgi2boK/cCKkHNhX8qKgoLBbLWcu2b99OeHg4YWFhAMTFxZGXl0dKSgrp6enn7KN9+/YYjWfezmBofCYpNzeX3NxcADIyMggJCbHtSNyI0WjU5XE5iuTLdhfKVd3wRKwfvoXfrhJ8e/epXx4SAq92C+eLHzfyal4Qf7voT4z36UxSOz/abf2JwPjk1gi/VbXFz1WzWytUVFScNTVjNpspKSlpdP0hQ4bw9ttvs2XLFnr37t3oeklJSQQFBVFQUACgy4cM6/nhyY4g+bLdhXKlefmCuQNV61ZQEzv8nJ8P3vgFrxSu4q2UZ3h93V6+iZ3CfT99Ss+DB5t8ktjV6flz1aKHmDekoVu0z/eB8Pb2Ji0tzaZ9Sy8dIRxDURSU6Bi09T+g1dWhGP9bArTaWrT1PxLcpz8Px3djze4qXl99mocuvo2UFSXcdHlPvDzkwj531uz/e2azGavVWv/aarUSHBxsl6DkTlshHEeJHgAnjsOOLWf/4Kc8OFaFEpcAwLCuAbya1JER+wv5ZI/K1C9L+cVS44SIhb00u+BHRkZSXl6OxWKhrq6O1atXy6hcCHdw6WXg4VF/tc5v1NXLIKg9RPWvXxYQ0p5JtZt4vPwLak9rTP92N2/k7aemVtozuCObpnSysrIoLi6mqqqKiRMnkpqaSkJCAuPHj2fWrFmoqkp8fDxdunSxS1AypSOE4yi+ftDjErTNG2DcXwDQKg/DT/koV6egGDzOXv+yQfT/9D1m//V23i89zRdbD7O+rJp7h4QT08nfGYcgmsmmgj916tQGl8fExBATE2PXgEAegCKEoynRMWifvodWeRglMBht3Y+gqvXTOWet228w2qfv4VNcwN1XjuKKbgHMWbufp74vIz4ikPEDwwj09mjgXYSrcckzMNI8TQjHUvqcGahpxUVomoa2KhcieqF0bOBb+kXdwNyh/q7b3qG+vDy6O6l9zPxYWsmkJTtYtbtSeu27AZcs+HLSVggH69IDAkzwcyHs2QF7dzU4uof/XNlz2SD4pQjt1EngTDO2P/cLJfOa7oT4evLCin1krNhLRQPN2LTaU2iFqx16OMI2LlnwZYQvhGMpBgNKVP8zI/yVuWA0ogy6svH1+w2GU6fgl01nLY8I9uHFUd24vX8oBXuPMenzHeT+euSs0b720XzUeRlo2zY77HiEbVyy4MsIX4hW0CcGqo6irfgapf9QFL/znIDt1Qe826FtOrd7podBYVy0mdl/iKBbkDevrt3PE8v2cKD6FACa9T936R8/5oijEE0gDzEXoo1SogagAdTVNTqdU7+upydED0DblIemaQ3eZHlRoBezRnbl65Ij/GPDQSYv2clt/UMZBcgpXdfgkiN8IYTjKYFB0DUSTMEQNeDC6/cbBEcqYPevja5jUBSu6RXMnDER9Anz5a0CCzMC4tnj28GeoYtmcsmCL1M6QrQOwx1TMNw3A8XjwmNwpW8sKIpND0UJ9fPksRGdeSCuI/s8ApgWO5V/WbyoU+VKHmdyyYIvJ22FaB1K5+4oERfbtm6A6cwNWzY+BUtRFEZEmJh99GuGHPqZhRYfpi0tpcR6vCUhixZwyYIvhHBNSr/BsHsHWoXtXSaDtJNMK17I9K41VJ48zUNf7+IfhRZO1qkOjFQ0RAq+EMJmymWDAdA2F15gzXMNCazj1TERJEWaWPxLBVO+3MnmA9KMrTW5ZMGXOXwhXFSH8DP/Vlc2a3N/Lw/uG9KRZxK7oGrwSO5uXlsvzdhai1yWKYRodZeF+/HKHyJ4f+NBPt9ymPV7q7l3cDixF0kzNkdyyRG+EEL/fIwG7hwYxvOjuuHraeCZ5WW8vGoflSfObc8g7EMKvhDCqS4JacfL13Tnxr5mVuyqZNKSnawolWZsjtBqUzq//PILK1asQFVVysrKmDlzZmu9tRDCxXl6GLjlslDiugTw6tr9/H3VPn7c5c/EQWGYfT2dHZ5u2FTws7OzKSwsxGQykZmZWb+8qKiI+fPno6oqiYmJjB07ttF99O7dm969e7N+/XoiIyNbHrkQwj00YaTePdiHF0Z14/OtFby/8RCTl+zkrzEdGBlp0t1D1J3BpoI/YsQIkpOTmTt3bv0yVVXJyclhxowZmM1mpk+fTmxsLKqqsnDhwrO2T0tLw2QyAbBy5UomTpxox0MQQrgH2wq2h0FhbG8zQzoHMGdtOXPX7WdFaSX3DgmnY4CXg2PUN5sKflRUFBaL5axl27dvJzw8nLCwMADi4uLIy8sjJSWF9PT0Bvdz6NAhfH198fX1bWHYQgg90zZvIOzoYZ5Jiufb7UeZX2jh/i92cmu/UMZcEoyHQUb7zdHsOfyKigrMZnP9a7PZTElJyXm3WbZsGfHx8eddJzc3l9zcXAAyMjIICQlpboguy2g06vK4HEXyZTtH50o7dRIL4Ofri5+N73PYy4tTQGBgAN42bnMg6wkAwq5N5c+hoYzs04W/f7+dtwstrN1bw/Ski+kR4tfMozijLX6uml3wGzqDfqE5ttTU1AvuNykpiaCgIAoKCoAz3wr0JiQkRJfH5SiSL9s5Olda7Zke98dqajhu4/ucrq0FoLKyEqWJsf12LAbgwWEdGNqpHW/mH+CODzZwQ3QIf4o24+nRvNG+nj9XnTp1anB5sy/LNJvNWK3W+tdWq5Xg4ODm7k4IIc5LURSu7B7InDERxHUN5IOfDjFtaSnbDkkzNls1u+BHRkZSXl6OxWKhrq6O1atX2+3uWOmWKYRojMnHyLTLO/HoVRdRfeo0D3+zi/nSjM0mNk3pZGVlUVxcTFVVFRMnTiQ1NZWEhATGjx/PrFmzUFWV+Ph4unRp4In3zZCfn09BQYEUfSFEowZ3DiC6gy8LNhzk018qWLunivuGhHNZeMvm9vXMpoI/derUBpfHxMQQExNj14CEEG7ARe6C9fPy4N4h4QzvHsCctft57Ls9jOoZxO0DQvHzkgcr/p40TxNCNIFrXg7ZN+xMM7aFmw7x2ZYK8vZWkzY4jMGdA5wdmktxyV460h5ZCNFU3kYDd8R04IVR3Qjw9mDWD3vJXLmPo9KMrZ6M8IUQunKxuR2Zyd35pNjKRz8fYsP+Y9w9sANXdg90SnsGdd0PcOokSv+hKAGBrf7+/8slC74QQkecMN/v6aFwU9+Q/zRjK+el1eX8WFrJxMHhhPq1bjM27f3X4PgxtPeyoVcflIFxKAOGoZha/zJ2mdIRQrSS1h9ddw3yJuPqboyP6cCmAzVMXrKTr0oOo7bmHyFNhf5DUZL/BEesaO+/hvrgXzn9fDpq3orWiwMXHeHLlI4Qwl48DArX9W7PkM7+zF23n3nrD7CitJIZyf60a6UYlJAwDCm3oY29FfbtQStcjfbj12j/yoFBw1spChcd4QshhL2FB3jxdGIXJg0JZ+fhk/zl/Q0sKrZyWm290b6iKCgXdcXwx5tQLott9ekulyz4MqUjhHAERVEY2TOIV8dEMKRbEAs2HOShr3dReviEs0NrFS5Z8KW1ghDCkcy+njw3pjcPXtGJgzW1/G1pKQs3HaT2tL7bM7hkwRdCCEdTFIUrugUyZ0wPhncP5MOfrDywtJStOm7GJgVfCNFKXKMdw+8FenvwQFwnHh/RmeO1Kg9/vYucggOc0GEzNpcs+DKHL4SOuMmzaAde5M+rYyJIvjiIz7Yc5v4vdrJx/zFnh2VXLlnwZQ5fCOEMvp4eTBwczrNJXfFQ4PHv9vDq2nKqT512dmh24ZIFXwjh4lykW6ajRIf5kjU6gnFR7Vm24yiTluxk3Z4qZ4fVYlLwhRC2c4/ZGbvwNhq4fUAHXhzVnSAfD579cS8vrNjLkePu24yt1e60PXToEDk5OQQEBNCpUyfGjh3bWm8thBDN1tPsw9+Tu7Oo2MqHP1nZtP8Ydw4MY0SEc5qxtYRNBT87O5vCwkJMJhOZmZn1y4uKipg/fz6qqpKYmHjeIr5v3z5iYmIYOXIkc+bMaXnkQgj3oIPpH6NBIbVPCMO6BPDq2v1krSlnxa5K0pzQjK0lbCr4I0aMIDk5mblz59YvU1WVnJwcZsyYgdlsZvr06cTGxqKqKgsXLjxr+7S0NCIiIli8eDGrV6/myiuvtO9RCCHcgHuNhhvSxeTNcyO7srTkMO8WHWTSkp3cPiCU5IuDMLjBaN+mgh8VFYXFYjlr2fbt2wkPDycsLAyAuLg48vLySElJIT09/Zx9fPbZZ9xwww1ERUWRmZlJfHx8g++Vm5tLbm4uABkZGYSEhDTpgNyB0WjU5XE5iuTLdo7OlVZbiwXw8/PDz8b3OezlxSkgMDAQbxu3OfCffx15LC3J1V87hDKqb1ee/247r+cdYO3e46QnXUzX4HPbsVkUhXbtfAj43XtV+vhw0mBo1c92s+fwKyoqMJvN9a/NZjMlJSWNrt+/f38++ugjVq5cSWhoaKPrJSUlERQUREFBAXBm7l9vQkJCdHlcjiL5sp2jc6XV1QJw7Ngxjtv4PqdPnQKgsrISpYmxOfJYWporT+DRK8JYtsOHnEILf3mvkJsvC2Fs7/Z4GP472tc0jePHT3Dyd++lnjiBpqoOOcZOnTo1uLzZBV9rYF7ufCcwunbtyrRp02zat7RHFkK4A0VRSIwMIqaTP6/n7eedooOs2l3J5KEdiQj2cXZ452j2ZZlmsxmr1Vr/2mq1Ehxsnye4yJ22Qgh3EtzOSPqVnXl4eCesNXVMW1rKe0UHOeVizdiaXfAjIyMpLy/HYrFQV1fH6tWrZVQuhGjT4rqeacZ2VUQgH2228sCXpWzx6+LssOrZNKWTlZVFcXExVVVVTJw4kdTUVBISEhg/fjyzZs1CVVXi4+Pp0sU+ByZTOkIIdxXg7cGUYZ0Y3i2Q7HX7ebTPeEaf3s9ttSrtPH83xm7lS1ZtKvhTp05tcHlMTAwxMTF2DQjOTOkUFBRIPx0hhNuK6eTPK2MieGf2e3zRcQh5X+zg3iEdGdDR7z9rtP5lnC7ZWkGapwkh9MDX04O7S79klscmPD0MPLlsD7PXlFN90jnN2Fyy4MtJWyH0yP3vuG2uKEMVWaO7c320meU7jzJpyQ7W0Pjl6Y7Sar10mkLm8IXQETe4A7U1eHkYuK1/KJd3DeCVteW8cKIvQyM8mXi8juB2rVOKZYQvhGgCKd4t1aP9mWZst6q/UmDqyaQlO/ju1yMN3ttkby5Z8GUOXwgd0UHzNHszGhT+xC5e+uUtupq8eWXtfp78vowD1acc+r4uWfCFEHok3w5+76KTFcwa2ZUJg8LYcvA493+xkyVbK1Ad9EfSJQu+TOkIIdoKg6Iwulcwc8ZEEBXqy5v5FqZ/s5u9lfYf7ctJWyGEcAGhfp48Ht+Z5TsrWVB0kNMOGOW7ZMEXQoi2SFEU4nuYuKJbAJ4e9p+AcckpHSGEaMscUezBRQu+zOELIYT9ueSUjszhCyGE/bnkCF8IIYT9ScEXQog2Qgq+EEK0EVLwhRCijZCCL4RoumbdFCQ9dc7Ryn2GFK01WrQJIYRwOrcY4Tfnmnxbtznfeo39rKHlv192vtfp6ek2xdYcessVOC5fzb3Xw5btHJWr3y9rrVw1Fos9trnQOrbmpaHlevs9bE6u/pfHk08++WRTgnKWTp06OWyb863X2M8aWv77ZY29zs3NJSkpyabYmkNPuQLH5qs5ubJ1O0fl6vfLWitXjcVij20utI6teWloud5+D5uTq9/IlI4TpKenk5GR4eww3Ibky3aSK9u1xVy5xZSO3jhyVKFHki/bSa5s1xZzJSN8IYRoI2SEL4QQbYQUfCGEaCOk4AshRBvhku2R25oDBw6waNEiampqmDZtmrPDcWnr16+nsLCQyspKRo0aRb9+/ZwdkksrKyvjyy+/pKqqir59+3L11Vc7OySXduLECZ544glSU1MZOHCgs8OxOzlp6yDZ2dkUFhZiMpnIzMysX15UVMT8+fNRVZXExETGjh1b/7PMzMw2WfCbk6vq6mreffdd0tLSnBGyUzUnX6qq8vrrr7e5fDU1Vx9++CHe3t506dJFlwVfpnQcZMSIETzyyCNnLVNVlZycHB555BFefvllVq1aRVlZmZMidB3NydWiRYsYNWpUa4fqEpqar/z8fB5//HH69u3rjHCdqim52rRpE507dyYoKMhJ0TqeFHwHiYqKwt/f/6xl27dvJzw8nLCwMIxGI3FxceTl5TkpQtfRlFxpmsZ7771H//796dGjh5Midq6mfrZiY2OZOXMmK1ascEa4TtWUXG3evJmSkhJWrlzJd999h6qqToracWQOvxVVVFRgNpvrX5vNZkpKSqiqquKDDz6gtLSUxYsXk5KS4sQoXUNjuVq6dCk//fQTNTU17N+/X+ak/6OxfG3evJl169ZRV1fHgAEDnBih62gsV3feeScAy5cvJyAgAINBf+NhKfitqKHTJYqiEBAQwD333OOEiFxXY7kaPXo0o0ePdkJErq2xfEVHRxMdHe2EiFxXY7n6zYgRI1oxmtalvz9hLsxsNmO1WutfW61WgoODnRiR65JcNY3ky3ZtOVdS8FtRZGQk5eXlWCwW6urqWL16NbGxsc4OyyVJrppG8mW7tpwruSzTQbKysiguLqaqqgqTyURqaioJCQkUFhayYMECVFUlPj6ecePGOTtUp5NcNY3ky3aSq7NJwRdCiDZCpnSEEKKNkIIvhBBthBR8IYRoI6TgCyFEGyEFXwgh2ggp+EII0UZIwRdCiDZCCr4QQrQRUvCFEKKN+H9Sy7pvv9GRkgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start = np.amin(data_powerlaw2)\n",
    "finish = np.amax(data_powerlaw2)\n",
    "bins = np.logspace(np.log10(start), np.log10(finish), 50)\n",
    "h, b = np.histogram(data_powerlaw2, bins=bins, density=True)\n",
    "plt.loglog(b[:-1], h, label='data')\n",
    "plt.loglog(b[:-1], stats.pareto.pdf(b[:-1], 2 - 1, loc=0, scale=3))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vejamos agora como as estatísticas dos dados sorteados variam de um sorteio para outro, para diferentes distribuições."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_std_lognormal(m, s):\n",
    "    m2 = m * m\n",
    "    s2 = s * s\n",
    "    mean = np.log(m2 / np.sqrt(m2 + s2))\n",
    "    std = np.sqrt(np.log(m2 + s2)-2*np.log(m))\n",
    "    return mean, std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inf_sup_uniform(m, s):\n",
    "    a = m - np.sqrt(3)*s\n",
    "    b = a + np.sqrt(12)*s\n",
    "    return a, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def xini_powerlaw(m, g):\n",
    "    return (g - 2)/(g - 1)*m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Usando μ=10 e σ=3 para a gaussiana.\n",
      "Usando μ=2.2594962448735196 e σ=0.2935603792085227 para a lognormal\n",
      "Usando valor inicial 4.803847577293368 e final 15.196152422706632 para a distribuição uniforme\n",
      "Usando x0=0.9090909090909098 para lei de potência com γ=2.1\n",
      "Usando x0=4.7368421052631575 para lei de potência com γ=2.9\n"
     ]
    }
   ],
   "source": [
    "μ = 10\n",
    "σ = 3\n",
    "print(f\"Usando μ={μ} e σ={σ} para a gaussiana.\")\n",
    "μ_log, σ_log = mean_std_lognormal(μ, σ)\n",
    "print(f\"Usando μ={μ_log} e σ={σ_log} para a lognormal\")\n",
    "inf_uni, sup_uni = inf_sup_uniform(μ, σ)\n",
    "print(f\"Usando valor inicial {inf_uni} e final {sup_uni} para a distribuição uniforme\")\n",
    "γ1 = 2.1\n",
    "x0_1 = xini_powerlaw(μ, γ1)\n",
    "print(f\"Usando x0={x0_1} para lei de potência com γ={γ1}\")\n",
    "γ2 = 2.9\n",
    "x0_2 = xini_powerlaw(μ, γ2)\n",
    "print(f\"Usando x0={x0_2} para lei de potência com γ={γ2}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avaliando o quanto as médias e desvios variam de um sorteio para outro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def some_stats(data):\n",
    "    return np.mean(data), np.std(data, ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_size = 10000\n",
    "repetitions = 20\n",
    "mean_uni  = np.zeros(repetitions)\n",
    "std_uni   = np.zeros(repetitions)\n",
    "mean_norm = np.zeros(repetitions)\n",
    "std_norm  = np.zeros(repetitions)\n",
    "mean_log  = np.zeros(repetitions)\n",
    "std_log   = np.zeros(repetitions)\n",
    "mean_pow2 = np.zeros(repetitions)\n",
    "std_pow2  = np.zeros(repetitions)\n",
    "mean_pow3 = np.zeros(repetitions)\n",
    "std_pow3 = np.zeros(repetitions)\n",
    "for i in range(repetitions):\n",
    "    mean_uni[i], std_uni[i]   = some_stats((sup_uni - inf_uni)*generator.random(size=sample_size) + inf_uni)\n",
    "    mean_norm[i], std_norm[i] = some_stats(generator.normal(μ, σ, size=sample_size))\n",
    "    mean_log[i], std_log[i]   = some_stats(generator.lognormal(μ_log, σ_log, size=sample_size))\n",
    "    mean_pow2[i], std_pow2[i] = some_stats((generator.pareto(γ1 - 1, size=sample_size) + 1) * x0_1)\n",
    "    mean_pow3[i], std_pow3[i] = some_stats((generator.pareto(γ2 - 1, size=sample_size) + 1) * x0_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(mean_uni, label='uniform')\n",
    "plt.plot(mean_norm, label='normal')\n",
    "plt.plot(mean_log, label='lognormal')\n",
    "plt.plot(mean_pow2, label=f'power law γ={γ1}')\n",
    "plt.plot(mean_pow3, label=f'power law γ={γ2}')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(std_uni, label='uniform')\n",
    "plt.plot(std_norm, label='normal')\n",
    "plt.plot(std_log, label='lognormal')\n",
    "plt.plot(std_pow2, label=f'power law γ={γ1}')\n",
    "plt.plot(std_pow3, label=f'power law γ={γ2}')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vejamos agora como a média e o desvio padrão variam com o número de amostras."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "sizes = [10, 25, 50, 100, 250, 500, 1000, 10000, 100000, 1000000]\n",
    "averages_uni = np.zeros_like(sizes, dtype=np.float)\n",
    "averages_norm = np.zeros_like(sizes, dtype=np.float)\n",
    "averages_log = np.zeros_like(sizes, dtype=np.float)\n",
    "averages_pow2 = np.zeros_like(sizes, dtype=np.float)\n",
    "averages_pow3 = np.zeros_like(sizes, dtype=np.float)\n",
    "for i, size in enumerate(sizes):\n",
    "    averages_uni[i]  = np.mean((sup_uni - inf_uni)*generator.random(size=size) + inf_uni)\n",
    "    averages_norm[i] = np.mean(generator.normal(μ, σ, size=size))\n",
    "    averages_log[i]  = np.mean(generator.lognormal(μ_log, σ_log, size=size))\n",
    "    averages_pow2[i] = np.mean((generator.pareto(γ1 - 1, size=size) + 1) * x0_1)\n",
    "    averages_pow3[i] = np.mean((generator.pareto(γ2 - 1, size=size) + 1) * x0_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sizes, averages_uni, label='uniform')\n",
    "plt.plot(sizes, averages_norm, label='normal')\n",
    "plt.plot(sizes, averages_log, label='lognormal')\n",
    "plt.plot(sizes, averages_pow2, label=f'power law, γ={γ1}')\n",
    "plt.plot(sizes, averages_pow3, label=f'power law, γ={γ2}')\n",
    "plt.xscale('log')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora vejamos o que acontece se escolhemos um $\\gamma$ menor do que 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "averages_pow15 = np.zeros_like(sizes, dtype=np.float)\n",
    "for i, size in enumerate(sizes):\n",
    "    averages_pow15[i] = np.mean((generator.pareto(1.5 - 1, size=size) + 1) * 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sizes, averages_pow15, label=f'power law, γ=1.5')\n",
    "plt.xscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para verificar melhor o que acontece com a média, vamos fazer algumas estatísticas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "averages_pow15 = np.zeros_like(sizes, dtype=np.float)\n",
    "std_pow15 = np.zeros_like(sizes, dtype=np.float)\n",
    "for i, size in enumerate(sizes):\n",
    "    avg_pow15 = np.zeros(100)\n",
    "    for j in range(20):\n",
    "        avg_pow15[j] = np.mean((generator.pareto(1.8 - 1, size=size) + 1) * 2)\n",
    "    averages_pow15[i] = np.mean(avg_pow15)\n",
    "    std_pow15[i] = np.std(avg_pow15, ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(sizes, averages_pow15, std_pow15, label=f'power law, γ=1.5')\n",
    "plt.xscale('log')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Teorema central do limite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primeiro, consideramos diversas variáveis aleatórias gaussianas, com média e desvio-padrão distintos e analisamos a distribuição da soma."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_var = 50 # 50 variáveis aleatórias\n",
    "sample_size = 10000 # 10000 amostras de cada variável\n",
    "results = np.zeros((num_var, sample_size))\n",
    "# Cria variáveis gaussianas com média e desvio-padrão aleatórios\n",
    "# As médias estão entre -3 e 3:\n",
    "averages = 6 * generator.random(size=num_var) - 3\n",
    "# Os desvios padrão estão entre 1 e 10\n",
    "deviations = 10 * generator.random(size=num_var)\n",
    "# Gera os valores aleatórios de cada variável\n",
    "for i in range(num_var):\n",
    "    results[i, :] = generator.normal(averages[i], deviations[i], size=sample_size)\n",
    "\n",
    "# Agora vamos somar os resultados de todas as variáveis, para cada amostragem:\n",
    "values = np.sum(results, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.956646594593954, 43.91149429132938)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "μ = np.mean(values)\n",
    "σ = np.std(values, ddof=1)\n",
    "μ, σ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.873560547239051"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minx = np.amin(values)\n",
    "maxx = np.amax(values)\n",
    "xvalues = np.linspace(minx, maxx, 50 + 1)\n",
    "plt.hist(values, bins=50, density=True, label='data');\n",
    "plt.plot(xvalues, stats.norm.pdf(xvalues, loc=μ, scale=σ), label=f'$G({μ:.2f}, {σ**2:.2f})$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Talvez não seja surpreendente que a soma de gaussianas seja uma gaussiana. Vamos então fazer algo similar mas partindo de distribuições uniformes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_var = 50 # 50 variáveis aleatórias\n",
    "sample_size = 10000 # 10000 amostras de cada variável\n",
    "results = np.zeros((num_var, sample_size))\n",
    "# Cria variáveis uniformes com início (entre 0 e 5) e final (entre 6 e 15) aleatórios\n",
    "starts = 5 * generator.random(size=num_var)\n",
    "ends = 9 * generator.random(size=num_var) + 6\n",
    "# Gera os valores aleatórios de cada variável\n",
    "for i in range(num_var):\n",
    "    results[i, :] = (ends[i] - starts[i]) * generator.random(size=sample_size) + starts[i]\n",
    "\n",
    "# Agora vamos somar os resultados de todas as variáveis, para cada amostragem:\n",
    "values = np.sum(results, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(322.1943341335076, 15.309794482658038)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "μ = np.mean(values)\n",
    "σ = np.std(values, ddof=1)\n",
    "μ, σ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "322.25171111069966"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minx = np.amin(values)\n",
    "maxx = np.amax(values)\n",
    "xvalues = np.linspace(minx, maxx, 50 + 1)\n",
    "plt.hist(values, bins=50, density=True, label='data');\n",
    "plt.plot(xvalues, stats.norm.pdf(xvalues, loc=μ, scale=σ), label=f'$G({μ:.2f}, {σ**2:.2f})$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mas o não há convergência se as distribuições originais não satisfazem as condições do teorema."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_var = 50 # 50 variáveis aleatórias\n",
    "sample_size = 10000 # 10000 amostras de cada variável\n",
    "results = np.zeros((num_var, sample_size))\n",
    "# Cria variáveis power law com γ entre 1.5 e 3.5 e x0 = 1\n",
    "gammas = 2 * generator.random(size=num_var) + 1.5\n",
    "# Gera os valores aleatórios de cada variável\n",
    "for i, γ in enumerate(gammas):\n",
    "    results[i, :] = generator.pareto(γ - 1, size=sample_size) + 1\n",
    "# Agora vamos somar os resultados de todas as variáveis, para cada amostragem:\n",
    "values = np.sum(results, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(56323.361838360404, 2160515.684937736)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "μ = np.mean(values)\n",
    "σ = np.std(values, ddof=1)\n",
    "μ, σ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "261.88245004975136"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minx = np.amin(values)\n",
    "maxx = np.amax(values)\n",
    "xvalues = np.linspace(minx, maxx, 50 + 1)\n",
    "plt.hist(values, bins=50, density=True, label='data');\n",
    "plt.plot(xvalues, stats.norm.pdf(xvalues, loc=μ, scale=σ), label=f'$G({μ:.2f}, {σ**2:.2f})$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.logspace(np.log10(minx), np.log10(maxx), 50)\n",
    "h, b = np.histogram(values, bins=bins, density=True)\n",
    "plt.loglog(b[:-1], h, label='data')\n",
    "plt.loglog(bins, stats.norm.pdf(bins, loc=μ, scale=σ), label=f'$G({μ:.2f}, {σ**2:.2f})$')\n",
    "plt.ylim(1e-10, 1e-2)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na verdade, só a presença de uma variável que não satisfaz as condições é suficiente para quebrar o teorema. No exemplo abaixo usamos 49 gaussianas e uma power-law com $\\gamma=1.5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_var = 50 # 50 variáveis aleatórias\n",
    "sample_size = 10000 # 10000 amostras de cada variável\n",
    "results = np.zeros((num_var, sample_size))\n",
    "# Cria variáveis gaussianas com média e desvio-padrão aleatórios\n",
    "# As médias estão entre -3 e 3:\n",
    "averages = 6 * generator.random(size=num_var) - 3\n",
    "# Os desvios padrão estão entre 1 e 10\n",
    "deviations = 10 * generator.random(size=num_var)\n",
    "# Gera os valores aleatórios de cada variável\n",
    "for i in range(num_var-1):\n",
    "    results[i, :] = generator.normal(averages[i], deviations[i], size=sample_size)\n",
    "results[-1, :] = generator.pareto(1.5 - 1, size=sample_size) + 1\n",
    "# Agora vamos somar os resultados de todas as variáveis, para cada amostragem:\n",
    "values = np.sum(results, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(16907.963032956523, 1117409.108604387)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "μ = np.mean(values)\n",
    "σ = np.std(values, ddof=1)\n",
    "μ, σ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.27781326055525"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minx = np.amin(values)\n",
    "maxx = np.amax(values)\n",
    "xvalues = np.linspace(minx, maxx, 50 + 1)\n",
    "plt.hist(values, bins=50, density=True, label='data');\n",
    "plt.plot(xvalues, stats.norm.pdf(xvalues, loc=μ, scale=σ), label=f'$G({μ:.2f}, {σ**2:.2f})$')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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