CH1/templates/13_sample_distribution_evaluation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as sts\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Дискретное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сгенерируем выборку объёма 100 из дискретного распределения с шестью равновероятными исходами."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample = np.random.choice([1,2,3,4,5,6], 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Представим теперь, что эта выборка была получена не искусственно, а путём подбрасывания симметричного шестигранного кубика 100 раз. Оценим вероятности выпадения каждой из сторон с помощью частот:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Число выпадений каждой из сторон:\n",
      "(Counter({1: 21, 5: 19, 3: 17, 4: 15, 2: 14, 6: 14}), '\\n')\n",
      "Вероятности выпадений каждой из сторон:\n",
      "{1: 0.21, 2: 0.14, 3: 0.17, 4: 0.15, 5: 0.19, 6: 0.14}\n"
     ]
    }
   ],
   "source": [
    "# посчитаем число выпадений каждой из сторон:\n",
    "from collections import Counter\n",
    "\n",
    "c = Counter()\n",
    "for s in sample:\n",
    "    c[s] += 1\n",
    "\n",
    "print(\"Число выпадений каждой из сторон:\")    \n",
    "print(c, '\\n')\n",
    "\n",
    "# теперь поделим на общее число подбрасываний и получим вероятности:\n",
    "print(\"Вероятности выпадений каждой из сторон:\")\n",
    "print({k: v/100.0 for k, v in c.items()})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Это и есть оценка функции вероятности дискретного распределения."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Непрерывное распределение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сгенерируем выборку объёма 100 из стандартного нормального распределения (с $\\mu$=0 и $\\sigma^2$=1):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "norm_rv = sts.norm(0, 1)\n",
    "sample = norm_rv.rvs(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Эмпирическая функция распределения для полученной выборки:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x99b95c0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GDQo5MAlVVbccTXiCMLN6wOfAqcBqYAFwobsviTnnRqC5u99oZq2BpcD+7l5Y7lpKEFIj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\nhIiIxKUEISIicSlBiIhIXEoQIiIS1/8HUZR+3JnaOBgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9897940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4,4,100)\n",
    "cdf = norm_rv.cdf(x)\n",
    "plt.plot(x, cdf, label='theoretical CDF')\n",
    "\n",
    "# для построения ECDF используем библиотеку statsmodels\n",
    "from statsmodels.distributions.empirical_distribution import ECDF\n",
    "ecdf = ECDF(sample)\n",
    "plt.step(ecdf.x, ecdf.y, label='ECDF')\n",
    "\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.xlabel('$x$')\n",
    "plt.legend(loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Гистограмма выборки:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x9aedcf8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x98a9ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(sample, normed=True)\n",
    "plt.ylabel('number of samples')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Попробуем задавать число карманов гистограммы вручную:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xa136dd8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa0b77b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(sample, bins=3, normed=True)\n",
    "plt.ylabel('number of samples')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xa2d9630>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xac329b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(sample, bins=40, normed=True)\n",
    "plt.ylabel('number of samples')\n",
    "plt.xlabel('$x$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Эмпирическая оценка плотности, построенная по выборке с помощью ядерного сглаживания:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xaf03f98>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XX4ZLL4WyQztJiU4hLDTM7ZB8Zvx4KF6Tbk9cGY+x5GF6jNdeg8svd5qs0uN6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\nxov8tc9jGTBIRLKA7cAs4KpWZeYDtwE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      "text/plain": [
       "<matplotlib.figure.Figure at 0xac4ee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# для построения используем библиотеку Pandas:\n",
    "df = pd.DataFrame(sample, columns=['KDE'])\n",
    "ax = df.plot(kind='density')\n",
    "\n",
    "# на том же графике построим теоретическую функцию распределения:\n",
    "x = np.linspace(-4,4,100)\n",
    "pdf = norm_rv.pdf(x)\n",
    "plt.plot(x, pdf, label='theoretical pdf', alpha=0.5)\n",
    "plt.legend()\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.xlabel('$x$')"
   ]
  }
 ],
 "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}