P03 - probability (statistics).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams.update({'font.size': 20})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Первый начальный момент: 121.500\n",
      "Он же математическое ожидание: 121.500\n",
      "Через параметры распределения: 121.500\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import expon\n",
    "\n",
    "λ = 0.4\n",
    "loc = 119.0\n",
    "# восстановим экспоненциальное распределение, полученное по данным\n",
    "ξ = expon(scale=1./λ, loc=loc)\n",
    "\n",
    "# построим график случайной величины\n",
    "plt.plot([ξ.pdf(i) for i in range(0, 151)], color='black')\n",
    "plt.show()\n",
    "\n",
    "# первый начальный момент - это оценка среднего значения случайно величины\n",
    "# для несмещённого экспоненциального распределения он рассчитывается как 1/λ\n",
    "# в нашем же примере нужно добавить смещение\n",
    "print(\"Первый начальный момент: {:.3f}\".format(ξ.moment(1)))\n",
    "print(\"Он же математическое ожидание: {:.3f}\".format(ξ.mean()))\n",
    "print(\"Через параметры распределения: {:.3f}\".format(1./λ + loc))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Вероятность ответа меньше чем за 125 мс: 90.928%\n",
      "Максимальное время ответа для 95% пользователей: 126.489 мс\n"
     ]
    }
   ],
   "source": [
    "prob125minus = ξ.cdf(125)\n",
    "max095time = ξ.ppf(0.95)\n",
    "print(\"Вероятность ответа меньше чем за 125 мс: {:.3f}%\".format(prob125minus * 100))\n",
    "print(\"Максимальное время ответа для 95% пользователей: {:.3f} мс\".format(max095time))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with open('data/times.log', 'r') as f:\n",
    "    # убираем сервисные строчки, приводим к числу и берём первые 100\n",
    "    data = [float(v) for v in f.readlines()[1:-4]][:100]\n",
    "\n",
    "bin_count = 6\n",
    "h = plt.hist(data, bin_count, color='black')\n",
    "plt.axis([0, 150, 0, 60])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Среднее выборочное = 121.21 мс\n",
      "Статистика 'доля ниже 125': 92.00%\n",
      "0.95-квантиль (95-процентиль): 126.00 мс\n"
     ]
    }
   ],
   "source": [
    "mean = sum(data) / len(data)\n",
    "print(\"Среднее выборочное = {:.2f} мс\".format(mean))\n",
    "\n",
    "prob125 = len(list(filter(lambda x: x < 125, data))) / len(data) \n",
    "perc95 = sorted(data)[int(0.95 * len(data))]\n",
    "\n",
    "print(\"Статистика 'доля ниже 125': {:.2f}%\".format(prob125 * 100))\n",
    "print(\"0.95-квантиль (95-процентиль): {:.2f} мс\".format(perc95))"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}