7.1. Случайные величины.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as sts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Нормальное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вот так можно сгенерировать выборку из нормально распределённой случайной величины с параметрами $\\mu=2.0$ и $\\sigma=0.5$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.63825032,  2.36681347,  2.2736246 ,  0.96846104,  1.69283345,\n",
       "        2.66821477,  2.03735172,  1.91286173,  2.35722552,  2.56316467])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu = 2.0\n",
    "sigma = 0.5\n",
    "\n",
    "# зададим нормально распределенную случайную величину\n",
    "norm_rv = sts.norm(loc=mu, scale=sigma)\n",
    "\n",
    "# сгенерируем 10 значений\n",
    "norm_rv.rvs(size=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Параметр ```loc``` задаёт $\\mu$, ```scale``` — среднеквадратичное отклонение $\\sigma$, ```size``` — размер выборки. Имя параметра ```size``` при вызове функции ```rvs``` можно не писать.\n",
    "\n",
    "Следующая функция возвращает значение функции распределения нормальной случайной величины в точке, соответствующей её аргументу:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97724986805182079"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm_rv.cdf(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим график функции распределения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1099979d0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QCxjs7v2a843zQUVDkuC118I4xrJlusiSpEPB1mk0xt0/AqaZ2UfN+fsipeTGG2HIEBUM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\nIiI5U9EQEZGc/T/8jXopBBpjUAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1060a62d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,4,100)\n",
    "cdf = norm_rv.cdf(x) # функция может принимать и вектор (x)\n",
    "plt.plot(x, cdf)\n",
    "plt.ylabel('$F(x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "А так можно вычислить значение функции плотности вероятности нормального распределения в заданной точке:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10798193302637613"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm_rv.pdf(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим график функции плотности вероятности:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109bd7550>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CDxQ4XtkaOTJ0OF5xRewkIhu1bRs2/Dr33DDxT+KLcabRBZjn7gvdvQYYA/St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\naIiISNb+P9iRaGiIFyX2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109857e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,4,100)\n",
    "pdf = norm_rv.pdf(x)\n",
    "plt.plot(x, pdf)\n",
    "\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Равномерное распределение на отрезке"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вот так можно сгенерировать выборку из случайной величины, имеющей равномерное распределение на отрезке $[a,b]$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.11558487,  3.091038  ,  3.56067633,  3.81123891,  2.55567793,\n",
       "        3.88254872,  2.35302308,  3.38520448,  3.74897612,  2.79752261])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 1\n",
    "b = 4\n",
    "\n",
    "# обратите внимание, что в этой функции задается левая граница и масштаб, а не левая и правая границы:\n",
    "uniform_rv = sts.uniform(a, b-a)\n",
    "\n",
    "uniform_rv.rvs(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "А так — вычислять значения функций распределения и плотностей:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109bd7b50>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8HB54APbuNSUtDYMNQrWwYwfcdpu7pKVhcgahyjMlLfWXMwiNhKkpd0lLZXHMp8o6fBje\n9S5T0lJZbBCqJHdJS+WzQahy3CUtVYNDalWKKWlp8ExSq3ZMSUvD4V1MqpVM2LjRlLRUJTYIVcL4\nODz4oClpqUpsECqdKWmpmpxBqFSmpKXhcwahyjMlLVWbo0CVYnralLRUdTYIDd3MTJGONiUtVVsp\nDSIi1kbEkYg4GhE39fj8ByLiUEQcjIgvRMT5ZdSp/uukpDduNCUtVd3Qh9QRcRZwFLgceAI4AFyZ\nmUe6jvlVYF9mPhMRNwBjmXllj9dySF0jzzwDb3mLKWmpbIsdUpdxBnEp8HBmPpqZzwG7gHXdB2Tm\n3sx8pv3ug8DKIdeoPpubg6uvhpUrYds2m4NUB2XcxbQSeKzr/RmKprGQa4HPDbQiDVQnJf3UU8Ud\nS6akpXooo0H0+t2x53WiiHgPcDHwqwu92ObNm0+8PTY2xtjY2JlVp74bH4d9+6DVMiUtlaHVatFq\ntZb8dWXMIC4DNmfm2vb7HwIyMz8677g3A38EvCEzv7vAazmDqLjt2+EP/gAmJ2HFirKrkQQVfppr\nRLwA+DrFkPpJYD9wVWZOdx3zS8BngDWZ+cgpXssGUWGmpKVqquyQOjPngI3AvcAhYFdmTkfEzRHx\n9vZhHwNeDHwmIr4UEX857Dp1ZiYni5T0xITNQaorn8Wkvjt0CN70Jrj9doNwUhVV9gxCo81d0tLo\nsEGob2Zni6awaZMpaWkUeIlJfXH8eJGSXr3alLRUdZW9i6mfbBDVMDcH7343vPCF7pKW6sB9EBqK\nTNiwAb7/fdi1y+YgjRIbhM7Ili1FStpd0tLosUFo2bZvh09+0l3S0qhyBqFlMSUt1ZczCA1MJyXt\nLmlptDlS1JIcPgzr18Odd7pLWhp1NggtWndKes2asquRNGg2CC2Ku6Sl5nFIrdM6frw4Y3CXtDQa\nTFKrL+bm4IorioyDKWlpNHgXk85YJyX99NPukpaayAahBY2Pw/797pKWmsoGoZ46KenJSVPSUlM5\ng9DzmJKWRpszCC3L1BRcdx3s3m1zkJrOsaNOmJ4uUtI7d5qSlmSDUNvMTLEudOtWU9KSCjYIndgl\nbUpaUjeH1A3XSUmvXg3btpmSlprAJLVOy5S01EzexaRTyiwuKR07VtyxZHOQNJ8NoqHGx4td0qak\nJS3EBtFApqQlLYYziIYxJS3JGYSeZ3KySEm7S1rSYjiabIjOLumdO4tbWiXpdGwQDeAuaUnLYYMY\ncZ2U9IYNpqQlLY1D6hHmLmlJvZikbjhT0pIW4l1MDZYJmzaZkpZ0Zkr50RERayPiSEQcjYibenz+\nnIjYFREPR8QDEfGyMuqsq/FxeOABuOsuU9KSlm/oDSIizgL+GFgDXAhcFRGvmXfYtcD3MvMC4H8A\nHxtulfXTarWAkynpz32uuSnpzvdCfi+6+b1YujLOIC4FHs7MRzPzOWAXsG7eMeuA29tvfxa4fIj1\n1VKr1eLuu+HDH4Z77oEVK8quqDz+IDjJ78VJfi+WrowGsRJ4rOv9mfbHeh6TmXPAUxHxU8Mpr14y\n4ZFH4KGHipT0xIQpaUn9UcaQutfkfP6tSPOPiR7HAPAbv9GPkurp2Wfh4EH4sR8rLif9xV+4S1pS\n/wz9NteIuAzYnJlr2+9/CMjM/GjXMZ9rH7MvIl4APJmZP9PjtbzHVZKWoaq3uR4AXhURLweeBK4E\nrpp3zF8B7wP2AVcA9/V6ocX8D5QkLc/QG0RmzkXERuBeihnIrZk5HRE3Awcy86+BW4GdEfEw8F2K\nJiJJGqJaJ6klSYNT24zt6cJ2TRERt0bEtyPiK2XXUraIWBUR90XE4Yj4akS8v+yayhIR50bEvoj4\nUvt78ZGyaypbRJwVEQ9FxETZtZQpIv4+Ir7c/rex/5TH1vEMoh22O0qRj3iCYq5xZWYeKbWwEkTE\nrwD/CNyRmf+67HrKFBErgBWZeTAiXgL8HbCuif8uACLiRZn5g/aNHpPA+zPzlD8QRllEfAC4GHhp\nZr6j7HrKEhHfAC7OzNnTHVvXM4jFhO0aITPvB077f3QTZOa3MvNg++1/BKZ5fsamMTLzB+03z6WY\nN9bvt8E+iYhVwK8DO8qupQKCRf7sr2uDWEzYTg0WET8HXERxJ1wjtS+pfAn4FvCFzDxQdk0l+jjw\nQRrcJLsk8PmIOBARv3WqA+vaIBYTtlNDtS8vfRb4r+0ziUbKzB9m5i8Bq4DXRsS/KLumMkTE24Bv\nt88ug94/P5rk32Xmaoozqg3ty9Q91bVBzADdT3hdRTGLUMNFxNkUzWFnZt5ddj1VkJnHgBawtuRS\nyvLLwDva197/F/DGiLij5JpKk5nfav/3/wH/m+KSfU91bRAnwnYRcQ5FTqLJdyb4W9FJfwYczsw/\nKruQMkXEeRHxE+23fxx4M9DIYX1m/rfMfFlmvpLiZ8V9mXlN2XWVISJe1D7DJiJeDLwF+NpCx9ey\nQbQf4NcJ2x0CdmXmdLlVlSMiPgVMAa+OiH+IiN8su6ayRMQvA1cDb2rfwvdQRDT1t+Z/DvxNRByk\nmMN8PjP3lFyTyvezwP3t2dSDwF9l5r0LHVzL21wlSYNXyzMISdLg2SAkST3ZICRJPdkgJEk92SAk\nST3ZICRJPdkgJEk92SAkST3ZICRJPQ19J7U0ytrLef4j8EqKR9JfCtySmd8stTBpGTyDkPrr31A8\nTfYbFA9Q/AzwZKkVSctkg5D6KDMfysxngdcBezOzlZnPlF2XtBw2CKmPIuKSiPhp4MLM/GZEvL7s\nmqTlcgYh9ddaihWfUxHxTuA7JdcjLZuP+5Yk9eQlJklSTzYISVJPNghJUk82CElSTzYISVJPNghJ\nUk82CElSTzYISVJP/x8oGJTplRwa0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109cfe690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,5,100)\n",
    "cdf = uniform_rv.cdf(x)\n",
    "plt.plot(x, cdf)\n",
    "\n",
    "plt.ylabel('$F(x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109d393d0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kDZ5LVW0Mjp6z45Cmsz7aGRySBs+Oo43BIUlqYnD0nEtV0nTWRzuDQ9LguVTVxuDoOTsO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\nBockqYnBIUlq8v8BBprZ/BxK9cgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10996c090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,5,1000)\n",
    "pdf = uniform_rv.pdf(x)\n",
    "plt.plot(x, pdf)\n",
    "\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Распределение Бернулли"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Генерация выборок из распределения Бернулли с заданным параметром $p$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 1, 1, 0, 0, 0, 1, 1, 1])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bernoulli_rv = sts.bernoulli(0.7)\n",
    "\n",
    "bernoulli_rv.rvs(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция распределения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10b08a350>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Hlv7NdCHwtSWtaLQW7N9g2H98VV03zsJGoOW9eznwiiQ3DQ4LbxhbdYeupX9bgHcl2QN8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\nZoaGJKmZoSFJamZoSJKa/R+YlIlDTkHaDwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ae35650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-0.01,1,10)\n",
    "cdf = bernoulli_rv.cdf(x)\n",
    "plt.step(x, cdf)\n",
    "\n",
    "plt.ylabel('$F(x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Биномиальное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Генерация выборок из биномиального распределения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15, 15, 11, 10, 11, 16, 10, 16, 11, 15])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binomial_rv = sts.binom(20, 0.7)\n",
    "binomial_rv.rvs(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Первый аргумент функции binom — значение параметра $n$, второй — параметра $p$.\n",
    "\n",
    "Функция распределения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109e465d0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jqupOGPzBAj/ZcT2z7vVJbkrybnfprU+SJwHnAp8DHr+W7+eshsVqTuzT2vxCVT0TeDGD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10996c110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,20,21)\n",
    "cdf = binomial_rv.cdf(x)\n",
    "plt.step(x, cdf)\n",
    "\n",
    "plt.ylabel('$F(x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция вероятности ```pmf``` для дискретных случайных величин заменяет функцию плотности ```pdf```:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109e75310>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9t7C4OAvsBI4zMTHNoUM3GCYaKF5GXhpQU1PzHSECsJPFxVmmpuYbrEraGgaJVIOVlTVO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\nSZUYJJKkSv4/ChefA/LfeYgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109ea2290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,20,21)\n",
    "pmf = binomial_rv.pmf(x)\n",
    "plt.plot(x, pmf, 'o')\n",
    "\n",
    "plt.ylabel('$P(X=x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Посмотрим, как ведут себя биномиально распределенные величины при разных значениях параметров:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10a096ed0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BfcxrbAT3sKMQEcmaUFoWZjbJzN42s3fN7LZ2yl1mZs1mVp7N+ERE5EhZTxZm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109c13710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,45,46)\n",
    "for N in [20, 30]:\n",
    "    for p in [0.2, 0.7]:\n",
    "        rv = sts.binom(N, p)\n",
    "        cdf = rv.cdf(x)\n",
    "        plt.step(x, cdf, label=\"$N=%s, p=%s$\" % (N,p))\n",
    "plt.legend()\n",
    "plt.title(\"CDF (binomial)\")\n",
    "\n",
    "plt.ylabel('$F(X)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10a20b6d0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pVNdw4mF7O+AD3A/bdwEbgOtU9b0Axy4AXlLVpZ73GUCDqn4uIj2AtcDV/g/q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\nGGNMVCyRGGOMiYolEmOMMVH5f10uFIhEzP6fAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a192850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,45,46)\n",
    "symbols = iter(['o', 's', '^', '+'])\n",
    "for N in [20, 30]:\n",
    "    for p in [0.2, 0.8]:\n",
    "        rv = sts.binom(N, p)\n",
    "        pmf = rv.pmf(x)\n",
    "        plt.plot(x, pmf, next(symbols), label=\"$N=%s, p=%s$\" % (N,p))\n",
    "plt.legend()\n",
    "plt.title(\"PMF (binomial)\")\n",
    "\n",
    "plt.ylabel('$P(X=x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Распределение Пуассона"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Генерация выборок из распределения Пуассона с параметром $\\lambda$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 8, 4, 5, 4, 3, 6, 4, 4, 6])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson_rv = sts.poisson(5)\n",
    "poisson_rv.rvs(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10a1f9090>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PGva6ThZmZk1q8+bNLFiw4KBt8+fPZ8KECXR2dlIoVLY4Wi24GcrMrEbqvQY3wMKFC5kz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\nmaVysjAzs1ROFmZmlur/A3uWYt/izpXLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a2f7390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,30,31)\n",
    "for l in [1, 5, 10, 15]:\n",
    "    rv = sts.poisson(l)\n",
    "    cdf = rv.cdf(x)\n",
    "    plt.step(x, cdf, label=\"$\\lambda=%s$\" % l)\n",
    "plt.legend()\n",
    "plt.title(\"CDF (poisson)\")\n",
    "\n",
    "plt.ylabel('$F(x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10a0b9890>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Bi9LN26Smpqb5cSwWIxaLZVZSESlZzbWI7dsBOHv79oxqE53Nn0ri9riVlZVZXaMtvXv3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\niGRNQURERLL2/wEpuiuQUq1cqQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109fb3d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,30,31)\n",
    "\n",
    "symbols = iter(['o', 's', '^', '+'])\n",
    "for l in [1, 5, 10, 15]:\n",
    "    rv = sts.poisson(l)\n",
    "    pmf = rv.pmf(x)\n",
    "    plt.plot(x, pmf, next(symbols), label=\"$\\lambda=%s$\" % l)\n",
    "plt.legend()\n",
    "plt.title(\"PMF (poisson)\")\n",
    "\n",
    "plt.ylabel('$P(X=x)$')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Дискретное распределение общего вида"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Чтобы сгенерировать дискретную случайную величину общего вида, нужно задать множество её значений и соответствующих вероятностей и использовать функцию ```numpy.random.choice```:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5,  5, 12, 12, 12,  5, 12, 12,  5,  5])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elements = np.array([1, 5, 12])\n",
    "probabilities = [0.05, 0.7, 0.25]\n",
    "np.random.choice(elements, 10, p=probabilities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Другие распределения"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Существует большое количество других стандартных семейств распределений, многие из которых также можно генерировать в Питоне. \n",
    "Например, распределение хи-квадрат $\\chi^2_k$, имеющее наутральный параметр $k$, который называется числом степеней свободы:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10a654590>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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e/0c96denM+r7UV4t7AbDAnJzH2fs2NX06jXM0+ZIjhOOLbOXnp7OZDurpG3c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\nkAZ3pZSKQf8PUlIaJnuGrscAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a5a3110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,30,100)\n",
    "for k in [1, 2, 3, 4, 6, 9]:\n",
    "    rv = sts.chi2(k)\n",
    "    cdf = rv.cdf(x)\n",
    "    plt.plot(x, cdf, label=\"$k=%s$\" % k)\n",
    "plt.legend()\n",
    "plt.title(\"CDF ($\\chi^2_k$)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10a822a90>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PUUpx+6TbeWrDU8fvGDaM0+bOZe2f/kSCzcb4jRtZV1bWyeCFEKLn6/E993sz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a19eb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,30,100)\n",
    "for k in [1, 2, 3, 4, 6, 9]:\n",
    "    rv = sts.chi2(k)\n",
    "    pdf = rv.pdf(x)\n",
    "    plt.plot(x, pdf, label=\"$k=%s$\" % k)\n",
    "plt.legend()\n",
    "plt.title(\"PDF ($\\chi^2_k$)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Полный список функций SciPy для работы со всеми распределениями можно найти тут: http://docs.scipy.org/doc/scipy-0.14.0/reference/stats.html"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}