matemagica-para-devs/estatística.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Aqui vamos rever os seguintes conceitos de estatística:\n",
    "\n",
    "* O que é uma distribuição?\n",
    "* Quais os tipos de distribuição existentes?\n",
    "* O que é a média, moda, mediana, desvio padrão?\n",
    "* Normalização de dados\n",
    "* Central Limit Theorem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## O que é uma distribuição?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "É uma representação dos valores em um conjunto de dados e a frequência com que ocorrem.\n",
    "\n",
    "Por exemplo, podemos jogar um par de dados e temos as seguintes possibilidades\n",
    "\n",
    "| Soma | Frequência |\n",
    "| ---- | ---------- |\n",
    "| 2    | 1          |\n",
    "| 3    | 1          |\n",
    "| 4    | 2          |\n",
    "| 5    | 2          |\n",
    "| 6    | 3          |\n",
    "| 7    | 3          |\n",
    "| 8    | 3          |\n",
    "| 9    | 2          |\n",
    "| 10   | 2          |\n",
    "| 11   | 1          |\n",
    "| 12   | 1          |\n",
    "\n",
    "Soma é a soma do número em cada dado. Por exemplo, se um dado caiu com 2 e o outro com 3, então soma = 5.\n",
    "\n",
    "Frequência é a quantidade de vezes que a soma pode ocorrer. Por exemplo, 12 só pode ocorrer se os dois dados caírem com 6.\n",
    "Da mesma forma, 6 pode ocorrer em caso dos dados caírem com os pares (3, 3), (4, 2) e (5, 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Em um \"gráfico\"\n",
    "\n",
    "|  - |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - |\n",
    "|----|----|----|----|----|----|----|----|----|----|----|\n",
    "|    |    |    |    | *  | *  | *  |    |    |    |    |\n",
    "|    |    | *  | *  | *  | *  | *  | *  | *  |    |    |\n",
    "| *  | *  | *  | *  | *  | *  | *  | *  | *  | *  | *  |\n",
    "| 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10 | 11 | 12 |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Quantas amostras até ter uma boa distribuição?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2e3e3ec5e48>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e3e3ec57f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 5\n",
    "x = np.random.random(size=N)\n",
    "sns.distplot(x, kde=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2e3e3f4f5f8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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g+CQnj+v5pyXo+1xS4f/6VNUTwKPA89akuslY6WUkLmZwRDDNho45yRnA5qr6wloWNkF9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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e3e5f6efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 5000\n",
    "x = np.random.random(size=N)\n",
    "sns.distplot(x, kde=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Alguns tipos de distribuição"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Em uma distribuição uniforme, todos os valores tem \"a mesma probabilidade\" de ocorrer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2e3d46588d0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cc9n+3nFWVpdQ6MizuhSlVILk59lYU1uStStmNNzjsL/XS2udjtqVyjYb6krp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e3e6018588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "uniforme = np.random.uniform(size=N)\n",
    "sns.distplot(uniforme, kde=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Em uma distribuição normal (gaussiana) os valores mais próximos de $\\mu$ (média) com $\\pm \\sigma$ (desvio padrão) são mais frequentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2e3e70b6048>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Sh0H3CDdm2CwpmHHhT7sraevqntQTzcyfFkdeehwvbLdeSGb0WFIw48Lz28rJmRrF0txE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\nxhjTx5KCMcaYPv8fT5PJW89yejgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e3e70659e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "media = 5\n",
    "desvio_padrao = 2\n",
    "normal = np.random.normal(loc=media, scale=desvio_padrao, size=N)\n",
    "sns.distplot(normal, kde=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Em uma distribuição exponencial, os valores da calda são mais frequentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2e3e7098240>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9iLrG9Crw/U9P+GlzgQMn+54VoNrrh+rfhmqvH6p/G6q9frbB3Bs+dtLbsLiY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\nIhHy/wFSzJBaefI65wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e3e917ccf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta = 1.0 / 0.1\n",
    "exponencial = np.random.exponential(scale=beta, size=N)\n",
    "sns.distplot(exponencial, kde=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Medidas de tendência central: média, moda, mediana"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "Estas três medidas de tendência central indicam, como é de se esperar, onde é o centro de uma distribuição.\n",
    "Não é o caso de sempre ser exatamente o centro, mas a ideia é estar próximo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# vamos assumir um conjunto de dados aleatórios x com N amostras\n",
    "\n",
    "N = 1000\n",
    "x = np.random.random(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "A média é calculada conforme $\\bar{x} = \\frac{1}{N}\\sum_{i=1}^{N}x_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.521596074668\n",
      "0.521596074668\n",
      "0.521596074668\n"
     ]
    }
   ],
   "source": [
    "# existem algumas formas de calcular a média com python\n",
    "\n",
    "# um for padrão\n",
    "media = 0\n",
    "for i in range(N):\n",
    "    media += x[i]\n",
    "\n",
    "media = (1.0 / N) * media\n",
    "print(media)\n",
    "\n",
    "# utilizando a soma\n",
    "media = (1.0 / N) * sum(x)\n",
    "print(media)\n",
    "\n",
    "# utilizando a função mean\n",
    "media = np.mean(x)\n",
    "print(media)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "A mediana é o valor exatamente no centro do conjunto de dados. Portanto, 50% dos dados são menores que a mediana e 50% \n",
    "são maiores.\n",
    "\n",
    "Para um conjunto com tamanho ímpar, a mediana é definida como $\\hat{x} = x_{\\frac{N + 1}{2}}$ sendo que x é um conjunto\n",
    "ordenado.\n",
    "\n",
    "Para um conjunto de tamanho par, a mediana é definida como $\\hat{x} = \\frac{1}{2} * (x_{\\frac{N}{2}} + x_{\\frac{N}{2} - 1})$ sendo que x é um conjunto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.531223772005\n",
      "0.531223772005\n"
     ]
    }
   ],
   "source": [
    "# também existem algumas formas de encontrar a variância\n",
    "\n",
    "# ordenando e obtendo os valores\n",
    "s = sorted(x)\n",
    "mediana = (1.0 / 2) * (s[int(N / 2)] + s[int(N / 2) - 1])\n",
    "print(mediana)\n",
    "\n",
    "# função median\n",
    "mediana = np.median(x)\n",
    "print(mediana)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "A moda é simplesmente o valor mais frequente no conjunto de dados."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ModeResult(mode=array([ 0.0014021]), count=array([1]))\n"
     ]
    }
   ],
   "source": [
    "# aqui vamos direto ao ponto\n",
    "from scipy.stats import mode\n",
    "\n",
    "moda = mode(x)\n",
    "print(moda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# contando os valores únicos no conjunto de dados\n",
    "(unicos, quantidades) = np.unique(x, return_counts=True)\n",
    "unicos.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8 9\n",
      "[ 90  97  85  96 107  94  91 108 118 114]\n",
      "[ 0.0014021   0.10098917  0.20057625  0.30016333  0.3997504   0.49933748\n",
      "  0.59892456  0.69851163  0.79809871  0.89768579  0.99727286]\n"
     ]
    }
   ],
   "source": [
    "# separamos os valores em 10 conjuntos\n",
    "(quantidades, bins) = np.histogram(x, bins=10)\n",
    "\n",
    "# pegamos o índice com maior quantidade de valores\n",
    "indice = np.argmax(quantidades)\n",
    "\n",
    "print(indice, indice + 1)\n",
    "print(quantidades)\n",
    "print(bins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Quanto a minha distribuição está espalhada?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "A variância e o desvio padrão ajudam a entender como os dados estão organizados.\n",
    "\n",
    "Principalmente se a distribuição seguir a forma de uma distribuição normal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "A variância é a média dos desvios em relação à média do conjunto.\n",
    "\n",
    "Calculamos a variância como: $x_\\text{var} = \\frac{1}{N}\\sum_{i=1}^{N}(x_i - \\bar{x})^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0840223445678\n",
      "0.0840223445678\n",
      "0.0840223445678\n"
     ]
    }
   ],
   "source": [
    "# usando um for\n",
    "media = x.mean()\n",
    "var = 0\n",
    "for xi in x:\n",
    "    var += (xi - media) ** 2\n",
    "var = (1 / N) * var\n",
    "print(var)\n",
    "\n",
    "# usando numpy\n",
    "var = np.square(x - x.mean()).mean()\n",
    "print(var)\n",
    "\n",
    "# usando a função var\n",
    "var = np.var(x)\n",
    "print(var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Como a variância mede o desvio da média em valores ao quadrado, para saber o desvio unitário precisamos calcular a \n",
    "$\\sqrt{\\text{var}}$.\n",
    "\n",
    "Essa medida é conhecida como o desvio padrão $\\sigma = \\sqrt{x_\\text{var}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.289866080402\n",
      "0.289866080402\n"
     ]
    }
   ],
   "source": [
    "# simplesmente a raiz quadrada de var\n",
    "std = np.sqrt(var)\n",
    "print(std)\n",
    "\n",
    "# ou usando std do numpy\n",
    "std = x.std()\n",
    "print(std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Normalização"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Supondo duas distribuições $x_1$ e $x_2$ com diferentes médias e desvios padrões, como podemos compará-las?\n",
    "\n",
    "Para isso, é necessário normalizá-las para que as duas tenham $\\mu = 0$ e $\\sigma = 1$.\n",
    "\n",
    "Dessa forma, as duas distribuições tem os valores no mesmo intervalo.\n",
    "\n",
    "A forma geral para normalizar uma distribuição é $x_i' = \\frac{x_i - \\bar{x}}{\\sigma_{x}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1 2.92957457083 3.08698871425\n",
      "x2 6.95478539486 1.0237278981\n"
     ]
    },
    {
     "data": {
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W1R7gWWBTZEI3xpxifARG+mJf0genB7CV9ONeOEm/EjgW8rwpuG46nwf+fTbHisitIlIv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\nWNI3xpgUYknfGGNSiCV9Y4xJIf8fwo48tV/JmzIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e3e91f2b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# duas distribuições\n",
    "x1 = np.random.normal(loc=3, scale=3, size=N)\n",
    "x2 = np.random.normal(loc=7, scale=1, size=N)\n",
    "\n",
    "sns.distplot(x1, kde=True)\n",
    "sns.distplot(x2, kde=True)\n",
    "\n",
    "print('x1', x1.mean(), x1.std())\n",
    "print('x2', x2.mean(), x2.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1_prime -7.81597009336e-17 1.0\n",
      "x2_prime 2.16715534407e-16 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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e6t8XqEgRyROR1SJyw2mlM0PKtrI6clq3M8xXDelznI5jejLr04zwlRN3aDXF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e3e92ad518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1_prime = (x1 - x1.mean()) / x1.std()\n",
    "x2_prime = (x2 - x2.mean()) / x2.std()\n",
    "\n",
    "sns.distplot(x1_prime, kde=True)\n",
    "sns.distplot(x2_prime, kde=True)\n",
    "\n",
    "print('x1_prime', x1_prime.mean(), x1_prime.std())\n",
    "print('x2_prime', x2_prime.mean(), x2_prime.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1_prime -7.81597009336e-17 1.0\n",
      "x2_prime 2.16715534407e-16 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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e6t8XqEgRyROR1SJyw2mlM0PKtrI6clq3M8xXDelznI5jejLr04zwlRN3aDXF\n5fVOpzF9JJCiL93s09N4jyxVzQXuBH4uIuNOeAOR+/x/GPIqKipO46XNYLJiRwWfdL+PzxMFI6Y6\nHcf0ZNJ1+CISuNW9nMX5B5xOY/pIIEW/FMjstJ0BBHyRT1UP+v+7G1gOzOrmmBdUNVdVc1NSUgJ9\naTPIrNm+n2vd63CNnAHuMKfjmJ6EReGadjPXuvP4V/4OVE+nrWeCVSBFfx2QIyJjRCQcuB0IqBeO\niCSKSIT/cTIwD9ja27Bm8KppamN46VKiaIEMu7QzaMy6i3BamVnzHvn7q51OY/pAj0VfVduBh4Cl\nwDbgFVUtFJFFIrIAQETmiEgpcAvwvIgU+k+fDOSJSAGwDHhKVa3oh6DlReXc4lpGS8RwSBrjdBwT\nqFGz8KZM5lbPCv6Wb714hoKAlktU1SXAki77Hu/0eB0dl326nvcRMO0MM5ohoGDjWh53bcM35noQ\nGxM4aIjgnv1pZiz9Jk8WrKbtusmEue3fbzCzfz3T71ravYzZ+wrt4sGVeY7Tcczpmn4bPvFwVcs7\nLC+yjhaDnS2Mbvrd2h0HWMByjmReTVqELc4xWLy0puTjx+ePuIJbylZwz9v5VNQdP0nenedkDXQ0\ncwaspW/6XcWqP5EgjSRe/IDTUUwvFWXfRbw0Mq3in9Q1tzkdx5wBK/qmX6kqE0tf5WBYFhFjL3A6\njumlo4kzOBQ7lbvdSykoqXQ6jjkDVvRNvyou+JCpupPyCZ8C6W6cnxksdo37DGNdhwjf+5712R/E\nrOibftXy0a9o0nBGX/Y5p6OYM1SSdiU1nmRual3M/spGp+OYXrKib/pPbRkTyt9kZcxVJA63kdaD\nnbrC2Dn6Di50b+Hwro1OxzG9ZEXf9JvK936OW73Uzrrf6Simj+zNvpUWwjm/4s80t3mdjmN6wYq+\n6R9N1cRs/j3/9J3HJefOdTqN6SOt4cPYMmIhN8j77Csu7PkEE3Ss6Jt+oet+Q4S3kbXpnyYlLsLp\nOKYPlUy5H5+4mL3v1/jshu6gY4OzTN9ra6L9o2f40DuD2XMvcjqN6aVxJa+e9LktMedyXf0KXt34\nBzj32wOYypwpa+mbvpf/R8Kaj/IiC7hqaprTaUw/8KbPoQ0PaRUrnY5iTpMVfdO32prQ93/CJnJI\nmHwZsRH2YXIo0rBYVkddyMXetezbbj15BhMr+qZvrfkVUnuQJ1tvY+HM01lV0ww66WfTSAR1b33P\n6STmNFjRN32nsRLe/xlbYs5le+QMLppgffOHsujISN4Ov4KzqpdRu22Z03FMgKzom76z8sdoax2P\n1tzE9dNHEu6xH6+hTtLPZr9ctY4BAAAU+klEQVSm0LL46+C1idgGg4B+K0VkvogUiUixiDzazfMX\nicgGEWkXkZu7PHe3iOz0f93dV8FNkKnaC+v+i+1pC9jSns5d5452OpEZAKNilCXpXyGlaReNH/7K\n6TgmAD3eZRMRN/AMcCUdi6SvE5HFXZY9LAHuAb7R5dwk4DtALqDAev+5VX0T3wSFvN/Chv9GVfn6\ngYuZEttAzfv/xRqnc5kBcemCe1j+7Guct+LfYdatEDfC6UjmFAJp6c8FilV1t6q2Ai8DCzsfoKp7\nVXUT4Oty7tXAO6pa6S/07wDz+yC3CSbl2+DgRnalXsnW1hHMT7W/6aFkQlo8K8Z8HVd7M61vWZ/9\nYBdI0U8H9nfaLvXvC0RA54rIfSKSJyJ5FRW2HNug0toAm1+FmFR+0HADw8PayB1W73QqM8Buu+ZS\nnvdeT3jhK7DzXafjmFMIpOh3Nwl6oGOvAzpXVV9Q1VxVzU1JsR4fg8ryp6Cpkv3j7mB5RSxXplTh\ntmnzQ86ktHiKJj5AsWbgXfxlaK5xOpI5iUBGzpQCmZ22M4CDAb5+KXBJl3OXB3iuCXZlBbDqGcg6\nj+ePTCPcpVyeYr/sISfvtwB8NcPNI9vu47W678Afb4EZd5x4bO5nBzic6SqQlv46IEdExohIOHA7\nsDjA118KXCUiiSKSCFzl32cGu/ZWWPxliB5ORfZCXtsXxcKsZuI9Nt1uqBoX52X2uFH8qv162L+m\n416PCTo9Fn1VbQceoqNYbwNeUdVCEVkkIgsARGSOiJQCtwDPi0ih/9xK4Pt0/OFYByzy7zOD3fIn\nO1r61/+U/yhOpt0HD02y1ZRC3ZcnN/B7943sd41CN73ccc/HBJWAJkZR1SXAki77Hu/0eB0dl266\nO/dF4MUzyGic4P/I3q0jO2H1s5B1HvsOV/HyniTuGNvE6Fgvh+w+fEhLCFcentrCAxu/xGLf48jm\nV2H23bY+chCxIZPm9LQ2Qv4fISYZptzATwtjCHPBl62Vb/xuHdOMNz6T57kJyvLhwHqnI5lOrOib\nwKnC5legpRZmfZrC+hj+tj+Sz45vJDWq6xANE6rcAj+YVcePmxewNzwHtrwGjUedjmX8rOibwO37\nsKPlNvFaNCGLH22OISHMxxcnWivfHO/s5HbuHt/CXXUP0e6j49OhWsMgGFjRN4Gp2geFb0DqFBh3\nGX8piWTF4Qi+PLmBhHBbMs+c6JGz6nFHJ/JDvRsqd8Ou95yOZLCibwLR2gAbfgeR8TDzUxxo8vDd\njbHMTW7lszlNTqczQSrKAz/MreO/mi6iMOpsKHqzo8eXcZQta2ROTX0dH82ba2Hew/jCYvjGqnh8\nwE/m1NroW8OaPSfvhS3A1SnwqYr7+DD6G8T85T64bzmERQ1UPNOFtfTNqe18G8q3wtQbYFgWL+6M\nYlVFOI/PqCczxq7Rmp59KqOc2MhwvtH2RajYDu/aSltOsqJvTu5wIex4CzLmwOgLWH4onKc2x3LF\nyBZuzW52Op0ZJCJcylfGHOTd9pm8G7cQ1jwHu1c4HStkWdE33auvgI1/gIQMmHYL64+G8cCqBCYm\ntPPTubU21sacltHRLdyVUc5DFTdQE50Ff3uo45KhGXB2TT+EvbSmpNv9nvYGrl/1AmEqbEm9keKi\nNr5blMAwTxsPZ+1jW6nNr2NO39Up1eyPncEXdn6OP4d9D3n727DgP52OFXKspW+Opz7OK3iMqJYj\nFGfcxJbWNH6wI5Nwl49v5uwnIcwKvukdEXj65ukciJ3OS64FsOG/be59B1jRN8eZtvNZMsuXsS/t\nKv7eMpPv7cgi0u3j8Qn7SY2wha/NmUmMCefZT83myeZPciBsNLr4y9BU7XSskGJF33wss2wp03Y9\nz870G3i64Xqe3TuKSbFNPDlpL6MiW52OZ4aIGZnDePT6mdxf/wW07jAs/ZbTkUKKFX0DQGLNVs7b\n/P84GDedzx+5g39WDGd+SiWP5ewn1mNdM03fuuvc0YyZfgHPtV8P+f8DO99xOlLIsKJviGo+zMXr\nv0ytxHNT5QNUNME3xpXy2axyPNZLx/QDEeGpm6bx1vC72UUG7X+1JRYHSkBFX0Tmi0iRiBSLyKPd\nPB8hIn/2P79GRLL9+7NFpElE8v1fv+rb+OZMedobuXDdQ2hLHXc0/B/iktN5+PIc5tji5qafRYd7\n+OVnzuXbfAlpOEz7m990OlJI6LHLpoi4gWeAK+lY83adiCxW1a2dDvscUKWq40XkduCHwG3+53ap\n6sw+zm36gKiX6Wu/QWJdEV9o/7/kTDuH88YOR6wTvukn3XUTnjj7Ep5fez1fKvgflnnOoyz1Iu48\nJ8uBdKEhkH76c4FiVd0NICIvAwuBzkV/IfBd/+PXgF+KVY6gpj4fqR99j0m17/Nj9+c4a97NpCVE\nOh3LDHHjSl49cR/w95QLKTq6gdkbvsnOifeBO90WUe8ngVzeSQf2d9ou9e/r9hj/mro1wHD/c2NE\nZKOIrBCRC88wr+kDTa1e/vrcN7m89g3+GnkDyZd/xQq+cdT1I+v4ffRdRPvqid33L6fjDGmBFP3u\nWuxdJ1A/2TFlQJaqzgK+BrwkIvEnvIHIfSKSJyJ5FRW2yGp/Olrfwi/+8yk+WfEceTGX0HDxdwn3\n2P184ywRmD8mgpdc1zGpaQMlxVucjjRkBfLbXgpkdtrOAA6e7BgR8QAJQKWqtqjqUQBVXQ/sAiZ0\nfQNVfUFVc1U1NyUl5fS/CxOQspomnnzmeb5a91OqUuZQPO/HiMvtdCxjAAh3KSPHz2SbjiZ2+585\nXNb9NCHmzARS9NcBOSIyRkTCgduBxV2OWQzc7X98M/CeqqqIpPhvBCMiY4EcYHffRDenY9/RBr79\n7B9Y1PgE7YnjSLz3VXzuCKdjGXOchHDYm7GQGG2m5Dd3U9PY4nSkIafHou+/Rv8QsBTYBryiqoUi\nskhEFvgP+w0wXESK6biMc6xb50XAJhEpoOMG7/2qevIVF0y/2HukgUd+9So/bllEWFwy0ff+DaIS\nnY5lTLeShg1jf/aNzGnfwN9/9U1a2m2+p74U0CybqroEWNJl3+OdHjcDt3Rz3uvA62eY0ZyB/ZWN\nfPWFf/Bc2/eJi4rA89nFED/S6VjGnNL4s87lQOtRbjv4W37+37P5+mfvxOWyDoF9waZWHoKO9YWu\naWrjLyvy+LXvcZI8Tbw9+3cMf++vHx83zqmAxvREhPTP/Jq6n5/Lbfu+w6LXx/Cdm8+zMSR9wIr+\nEFXX3Mbr72/kOd8iRrprWD7nBarjJzG8erPT0Yzp0Zo9lezy1pE862kuW30PF216jE9VPcl10zOO\nK/w2iOv0WV+9IaihpZ1XP9jMf7Z/n2xXBStzf8mRRBsUbQafI4kz2TDlMS5z53NpyS95e+thVLv2\nGDenw4r+EFPT1MZrH27iZy3fZaKrlA/O/jnlw+c6HcuYXisefRtFWXfwBc8SRux6hbcKD1nhPwN2\neWcoyPstALVtwpdXevhJ09NMdu2nOPMWopvKuh36bkyw6/xzWx07juqYsTzZ8CKf3pXKyupR3JN5\nGNxJHQfYlA0Bs5b+EFHTKnxphZtHG37IJFcpO7NupTruhHFwxgxO4qI482ZaI5L4XfjTVB05xAv7\n0mi3pR5OmxX9IaCyRXh4RTuLmp5goruM4tG3UROX43QsY/qU1x3JtuxP4wuP5w8RP6S28jBfXJVA\nY7vTyQYXK/qDXGlVI48uq+eHzT8gy1ON+9z7qYm1zphmaGr3xPoLfxwvRT5F/aHd3LEikYo6G7kb\nKCv6g9j6fZV8/xfP8+O2JxgW7sMz78sw3Aq+GdrawuLYlv0ZfGGx/CnySabWfciNz33ItrJap6MN\nClb0B6k3Nuzn7V8/zjO+RURGxxFx4cMQP8rpWMYMiLawOArH3otr+Die9LzA/c0vcvOzH7C4oOtc\nkKYr670zyNQ0tvHk39Zx4dbv8Zh7Na051xE+9kIIs/nwTWjxuqNg7hdh61/51N6/MytyDw+8fC8F\n+8/j3+ZPsinDT8L+rwwiy4vK+fZPf8GD2+/mWvdavJd/l/A7/2gF34QulxvOuglueI7JrhLeiXwM\nXfUsn/zlSrYfsss93bGW/iCw5UANzy5Zx2Ul/8Ev3CtpSRiD68bfQfY8p6MZ46g1ezom7d2VdQtR\n5/+FuVsW8XjFH9hW9T4/+cXNuCdew7ycFNwusSkb/KzoBylVZd3eKl57v4DRO17kR553iPa00X7e\n14i49N+sdW9MF02RI1hx9i8ZXfYm04p+wX81/5j84r/wP3tvJm769YAVfQAJtuHMubm5mpeX53QM\nx+w50sA7hWUUrPkXc2rf5Vb3CqKklfZJC3g7+R5q4safcI6NuDWhblfW8TO7i6+N7AN/Z1LRcyS2\nHaJC41kXfxXpF32G6WdfiLiG3pVtEVmvqrk9HWctfQepKiWVjeTvr2bb7v1U7/iA7PqNXONay32u\ncrzh4eiUG5CLv0FYykRq1tjyccYEQl1h7Mm8kb3pn2BE+fsk7XiNK+veIOyfr1G5JJHa9IsYMfNq\norLnQtI4GIJ/BE4moJa+iMwH/gNwA79W1ae6PB8B/B44GzgK3Kaqe/3PPQZ8DvACX1HVpad6r6HS\n0j82p327z0ddczvVjW1ElyynpbkRb0s90lJHQvsRRlPGeDnABCnFJYoXF0ejxlCXdBZVcRPxuu0y\njjF9YcaIMPKLimkqK2KmdwuJUg9AqysSb1wGkcPSkLgREDsCYlJh3sOD6o9BoC39Hou+f43bHcCV\ndCyAvg64Q1W3djrmS8B0Vb1fRG4HPqmqt4nIFOBPwFxgFPAuMEFVT7r+2aAo+t42aKyksaacyiOH\nqas8TEPNEVpqj9DWUAVNVbQ3VBHlrSdG60iijkSpJ06ajnsZH0KNK4mmiGTaY9NoiMmiPioDnyvM\noW/MmKHrnDEdk7OpwoajLtbvqeRI+QEy2/Yw1bWXHDlw3O+o1x2Jb1g2nuSxSNJYSMzu+BqWBQmZ\nEB7tzDdyEn15eWcuUKyqu/0v/DKwENja6ZiFwHf9j18DfikdKx0sBF5W1RZgj38N3bnAqkC/kT6h\nCj4v+NrB1456W/G1NdPe2oy3paPl3dbcQHtTLd7GGtoaa/A2VqGNlWhjFa7mKsJaqghvrSKmvZoY\nbQAg2v/VWbu6aJAYGoii2R1NmyuSWk8mNZ4o3OGRuCNi0PA4Wj1xNIcnolbgjRkQx3r6HDMjGXT4\nSA40j2ZpQxS/qIukurGZ+LYjZHCYMe1ljC4/zOiKAka73iWC1uPOb/Ik0BSVRmt0Gt7oFIhNhZhU\n3DGJuKMT8UQPwxMZizsiBndkDJ7waFyeMMQTAS4PiAscWAkskKKfDuzvtF0KnHOyY1S1XURqgOH+\n/au7nJve67Sn0nAEfja1o8CjoIqiqNeLS47/NCN0XKdy9/CS9RpJNbHUaAzVkkCTZyxtUcNojxyO\nK2Y44fEpRCWkEF+7k6TYKJLjIogMjyBBhO17bP13Y4KdCGREtZIR1cplyTUA5GaPYH/DKPakPcbB\nmiYKqpspq26gveYQYXWlxDSWMqztECnNR0hrqWRkzV6SpYDh1OKR05v206uCDxeK4PG4cWXkwmeX\n9HziGQik6Hf3p6jrNaGTHRPIuYjIfcB9/s16ESkKIFegkoEjvTu1FijvwygnOINs/SpYc4Fl641g\nzQWWrYs34d4eW/8nyzU6kHcIpOiXApmdtjOArhNcHDumVEQ8QAJQGeC5qOoLwAuBBD5dIpIXyHUu\nJwRrtmDNBZatN4I1F1i23jjTXIHcml4H5IjIGBEJB24HFnc5ZjFwt//xzcB72nGHeDFwu4hEiMgY\nIAdY29uwxhhjzkyPLX3/NfqHgKV0XAZ/UVULRWQRkKeqi4HfAH/w36itpOMPA/7jXqHjpm878OCp\neu4YY4zpXwENzlLVJcCSLvse7/S4Gbil63n+554AnjiDjGeqXy4b9ZFgzRasucCy9Uaw5gLL1htn\nlCvopmEwxhjTfwbPcDNjjDFnLKSKvoh8Q0RURJKdznKMiHxfRDaJSL6IvC0iQbH8lYg8LSLb/dne\nEJFhTmc6RkRuEZFCEfGJiOO9K0RkvogUiUixiDzqdJ5jRORFESkXkS1OZ+lKRDJFZJmIbPP/Wz7s\ndCYAEYkUkbUiUuDP9T2nM3UlIm4R2Sgi/+jN+SFT9EUkk46pJIJt1rKnVXW6qs4E/gE83tMJA+Qd\n4CxVnU7HNByPOZynsy3AjcBKp4P4pyl5BrgGmALc4Z9+JBj8DpjvdIiTaAe+rqqTgXOBB4Pk/1sL\ncJmqzgBmAvNF5FyHM3X1MLCttyeHTNEHfgb8X7oZHOYkVe28vE8MQZJPVd9W1Xb/5mo6xlgEBVXd\npqp9OYDvTHw8TYmqtgLHpilxnKqupKM3XdBR1TJV3eB/XEdHEeuf0fqnQTvU+zfD/F9B8TsJICIZ\nwHXAr3v7GiFR9EVkAXBAVQucztIdEXlCRPYDnyJ4Wvqd3Qu86XSIINXdNCWOF6/BRESygVnAGmeT\ndPBfPsmnYzj+O6oaFLn8fk5H4/X05nvoZMjMpy8i7wJp3Tz1LeCbwFUDm+h/nSqbqv5NVb8FfMs/\nDfVDwHeCIZf/mG/R8VH8jwOR6XSyBYmAphox3RORWOB14KtdPvU6xj+WaKb/PtYbInKWqjp+X0RE\nrgfKVXW9iFzS29cZMkVfVa/obr+ITAPGAAUdE3+SAWwQkbmqesjJbN14CfgnA1T0e8olIncD1wOX\n6wD37T2N/2dOC2iqEXMiEQmjo+D/UVX/4nSerlS1WkSW03FfxPGiD8wDFojItUAkEC8i/6Oqd53O\niwz5yzuqullVU1U1W1Wz6fglnT1QBb8nIpLTaXMBsN2pLJ35F875N2CBqjY6nSeIBTJNienCP/X6\nb4BtqvpTp/McIyIpx3qqiUgUcAVB8jupqo+paoa/jt1Ox3Q3p1XwIQSK/iDwlIhsEZFNdFyCCoqu\na8AvgTjgHX930l85HegYEfmkiJQC5wH/FJFTrsbWn/w3u49NU7INeEVVC53K05mI/ImOtSsmikip\niHzO6UydzAM+DVzm//nK97dgnTYSWOb/fVxHxzX9XnWNDFY2ItcYY0KItfSNMSaEWNE3xpgQYkXf\nGGNCiBV9Y4wJIVb0jTEmhFjRN8aYEGJF3xhjQogVfWOMCSH/H+DtYRELONj6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e3e9264b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# usando o scikit-learn\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()\n",
    "\n",
    "scaler.fit(x1.reshape(-1, 1))\n",
    "x1_prime = scaler.transform(x1.reshape(-1, 1)).reshape(-1)\n",
    "\n",
    "x2_prime = scaler.fit_transform(x2.reshape(-1, 1)).reshape(-1)\n",
    "\n",
    "sns.distplot(x1_prime, kde=True)\n",
    "sns.distplot(x2_prime, kde=True)\n",
    "\n",
    "print('x1_prime', x1_prime.mean(), x1_prime.std())\n",
    "print('x2_prime', x2_prime.mean(), x2_prime.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}