Kolmogorov.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import (\n",
    "    norm, binom, expon, t, chi2, pareto, ttest_ind, ttest_1samp,\n",
    "    sem, beta, kstwobign, randint, kstest, shapiro, jarque_bera,\n",
    ")\n",
    "from statsmodels.stats.diagnostic import lilliefors\n",
    "from statsmodels.stats.proportion import proportion_confint\n",
    "from tqdm.notebook import tqdm\n",
    "import numpy as numpy\n",
    "from seaborn import distplot\n",
    "from matplotlib import pyplot\n",
    "import seaborn\n",
    "\n",
    "import sys\n",
    "sys.path.append('.')\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inverse_plot_colorscheme():\n",
    "    import cycler\n",
    "    def invert(color_to_convert): \n",
    "        table = str.maketrans('0123456789abcdef', 'fedcba9876543210')\n",
    "        return '#' + color_to_convert[1:].lower().translate(table).upper()\n",
    "    update_dict = {}\n",
    "    for key, value in pyplot.rcParams.items():\n",
    "        if value == 'black':\n",
    "            update_dict[key] = 'white'\n",
    "        elif value == 'white':\n",
    "            update_dict[key] = 'black'\n",
    "    \n",
    "    old_cycle = pyplot.rcParams['axes.prop_cycle']\n",
    "    new_cycle = []\n",
    "    for value in old_cycle:\n",
    "        new_cycle.append({\n",
    "            'color': invert(value['color'])\n",
    "        })\n",
    "    pyplot.rcParams.update(update_dict)\n",
    "    pyplot.rcParams['axes.prop_cycle'] = cycler.Cycler(new_cycle)\n",
    "    lec = pyplot.rcParams['legend.edgecolor']\n",
    "    lec = str(1 - float(lec))\n",
    "    pyplot.rcParams['legend.edgecolor'] = lec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "inverse_plot_colorscheme()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Лекция 8. Критерии согласия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Критерий согласия \n",
    "\n",
    "*или (goodness of fit)*\n",
    "\n",
    "> 📈 **Задача**\n",
    ">\n",
    "> Вы купили новый красивый игральный кубик и хотите проверить, правда ли, что все грани у него выпадают равновероятно? \n",
    "\n",
    "\n",
    "\n",
    "Пусть мы накидали кубик n раз, и у нас появилась выборка $X_1, X_2 \\dots X_n$. Как понять, честный ли кубик? Для этого нам помогут критерии согласия!\n",
    "\n",
    "Какую задачу они решают? Есть выборка $X_1, X_2 \\dots X_n$ из истинного распределения $\\mathcal{P}$. Мы хотим проверить, а совпадает ли $\\mathcal{P}$ с распределением $\\mathcal{P_0}$?\n",
    "   - Например, пусть распределение выпадений граней кубика $p_1, p_2, p_3, p_4, p_5, p_6$ (Это $\\mathcal{P}$). Нас интересует, а не равновероятны ли все грани, то есть $p_i = \\dfrac{1}{6}$ для любого i (Это $\\mathcal{P_0}$). А наша выборка $X_i$ &mdash; результат i-ого броска кубика. \n",
    "       - С точки зрения теории вероятности число выпадений каждой грани кубика при N бросках описывается [мультиномиальным распределением](https://ru.wikipedia.org/wiki/Мультиномиальное_распределение).\n",
    "\n",
    "То есть критерий согласия проверяет\n",
    "- $H_0: \\mathcal{P} = \\mathcal{P}_0\\ vs.\\ H_1: \\mathcal{P} \\neq \\mathcal{P}_0$.\n",
    "\n",
    "Но иногда нас интересует равенство не одному распределению $\\mathcal{P}_0$, а семейству распределений. Например, нас интересует, правда ли, что выборка $X_1, X_2 \\dots X_n$ из нормального распределения? Гипотеза выше проверила бы, что выборка $X$ из нормального распределения с фиксированными параметрами $\\mu, \\sigma^2$.\n",
    "\n",
    "Поэтому на самом деле есть **2 гипотезы у критерия согласия**:\n",
    "- *Простая*: $H_0: \\mathcal{P} = \\mathcal{P}_0\\ vs.\\ H_1: \\mathcal{P} \\neq \\mathcal{P}_0$\n",
    "- *Сложная*: $H_0: \\mathcal{P} \\in \\{\\mathcal{P}_{\\theta}| \\theta \\in \\Theta \\}$. То есть параметры не фиксированы.\n",
    "    - Для нормального распределения $ \\{\\mathcal{P}_{\\theta}| \\theta \\in \\Theta \\}$:\n",
    "        - $\\mathcal{P}$  &mdash; нормальное распределение, \n",
    "        - $\\theta$ это пара $(\\mu, \\sigma^2)$\n",
    "        - $\\Theta = (-\\infty, \\infty) \\times (0, \\infty)$ (декартово произведение двух множеств)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Критерий Колмогорова для простой гипотезы\n",
    "\n",
    "Сфокусируемся на простой гипотезе: $H_0: \\mathcal{P} = \\mathcal{P}_0\\ vs.\\ H_1: \\mathcal{P} \\neq \\mathcal{P}_0$. Но заметим, что эту запись можно изменить: вместо того, чтобы сравнивать сами распределения мы можем сравнивать функции распределения между собой. Так как [распределение однозначно задается своей функцией распределения](https://stats.stackexchange.com/questions/136658/why-does-a-cumulative-distribution-function-cdf-uniquely-define-a-distribution).\n",
    "\n",
    "Поэтому в дальнейшем мы будем писать, что критерий согласия проверяет $H_0: F = F_0\\ vs.\\ H_1: F \\neq F_0$, *где $F, F_0$ &mdash; функции распределения*.\n",
    "\n",
    "Ну а теперь закономерный вопрос: как проверять такую гипотезу? **Для этого нам надо придумать статистику и как она распределена при $H_0$**.\n",
    "\n",
    "\n",
    "\n",
    "**Шаг 1. Оцениваем CDF, или $F(x)$**\n",
    "\n",
    "Начнем издалека. Попробуем решить такую задачу: как аппроксимировать `cdf` выборки? Мы ее не знаем, но хотим как-то точно оценить. Что такое cdf по определению? Это вероятность получить такое или более маленькое значение случайной величины, $F(x) = P(X \\leq x)$. Тогда рассмотрим статистику по выборке:\n",
    "\n",
    "$$\\widehat{F_n}(x) = \\frac{1}{n}\\sum_i[X_i \\leqslant x]$$\n",
    "\n",
    "Она по смыслу должна оценивать $F(x)$. Назовем **$\\widehat{F_n}(x)$ &mdash; эмпирической функцией распределения**.\n",
    "\n",
    "Что можно про эту оценку сказать: **на бесконечности $\\widehat{F_n}(x) \\stackrel{p}{\\rightarrow} F(x)$**. ([сходимость по вероятности](https://tvims.nsu.ru/chernova/tv/lec/node53.html))\n",
    "\n",
    "---\n",
    "\n",
    "*Док-во*\n",
    "\n",
    "- $F(x) = P(X \\leq x) = 1 *  P(X \\leq x) + 0 * P(X > x) = \\mathbb{E} I\\{X \\leq x\\}$, где $I$ &mdash; функция индикатор. Она равна 1, если выполнено условие в скобках.\n",
    "- $\\widehat{F_n}(x) = \\frac{1}{n}\\sum_i[X_i \\leqslant x] = \\overline{I\\{X \\leq x\\}}$\n",
    "\n",
    "Тогда по усиленному закону больших чисел (УЗБЧ):\n",
    "\n",
    "$\\widehat{F_n}(x) = \\overline{I\\{X \\leq x\\}} \\stackrel{p}{\\rightarrow} \\mathbb{E} I\\{X \\leq x\\} = F(x)$. ч.т.д.\n",
    "\n",
    "---\n",
    "\n",
    "Давайте это визуализируем.\n",
    "\n",
    "- Возьмем некое распределение (например, экспоненциальное) и любую точку, например, 3.\n",
    "- Посчитаем в ней истинную $F(x)$.\n",
    "- Далее для разных n посчитаем $\\widehat{F_n}(x)$.\n",
    "- Построим график расстояния $\\widehat{F_n}(x) - F(x)$. Чем больше n, тем меньше должно быть расстояние."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_Fn(sample, x):\n",
    "    \"\"\"\n",
    "        Функция строит эмпирическую функцию распределения по sample для Fn(x).\n",
    "    \"\"\"\n",
    "    \n",
    "    return numpy.mean(sample <= x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "N = 5000\n",
    "n_array = numpy.arange(10, N, 10)\n",
    "# В качестве примера взяли экспоненциальное распределение\n",
    "X = expon().rvs(N)\n",
    "x = 3\n",
    "F_x = expon().cdf(x)\n",
    "\n",
    "delta = []\n",
    "for n in n_array:\n",
    "    # Считаем F_n_x по первым n сгенерированным точкам\n",
    "    F_n_x = calc_Fn(X[:n], x)\n",
    "    delta.append(F_n_x - F_x)\n",
    "\n",
    "\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title('Распределение $\\widehat{F_n}(x) - F(x)$, x фиксирован', fontsize=12)\n",
    "pyplot.plot(n_array, delta, c='yellow', label='$\\widehat{F_n}(x) - F({x})$')\n",
    "pyplot.plot(n_array, [0] * len(n_array), c='white', linewidth=3, label='0')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.xlabel('Размер выборки', fontsize=12)\n",
    "pyplot.ylabel('$\\delta$', fontsize=12)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что все так и есть!\n",
    "\n",
    "Но что происходит в совокупности для всех x? Как $F_n(x)$ приближает $F(x)$ в каждой точке x?\n",
    "\n",
    "> **Теорема Гливенко-Кантелли**\n",
    ">\n",
    "> Пусть $X_1, X_2 \\dots $ &mdash; выборка неограниченного размера из распределения с функцией распределения $F$. Тогда\n",
    "$$\n",
    "    D_n = \\underset{x \\in \\mathbb{R}}{\\sup} |\\widehat{F_n}(x) - F(x)| \\stackrel{p}{\\rightarrow} 0\n",
    "$$\n",
    "\n",
    "То есть наибольшая разница между нашей оценкой и истинной функцией распределения равна 0! Это еще более сильное утверждение чем то, что было выше: оно сразу говорит про $|\\widehat{F_n}(x) - F(x)|$, на всей числовой прямой, а не про одну точку, как мы вывели ранее.\n",
    "\n",
    "\n",
    "Время визуализации:\n",
    "- Генерируем выборку.\n",
    "- Считаем $F(x)$ в каждой точке x.\n",
    "- Считаем $\\widehat{F_n}(x)$ в каждой точке x.\n",
    "- Строим графики в зависимости от n."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(4)\n",
    "N = 1000\n",
    "n_array = [10, 100]\n",
    "X = expon().rvs(N)\n",
    "# В этот раз не одна точка, а числовая прямая\n",
    "x = numpy.linspace(0, 5, 1000)\n",
    "F_x = expon().cdf(x)\n",
    "\n",
    "\n",
    "pyplot.figure(figsize=(25, 8))\n",
    "\n",
    "\n",
    "for ind, n in enumerate(n_array):\n",
    "    F_n_x = numpy.array([calc_Fn(X[:n], x_dot) for x_dot in x])\n",
    "    \n",
    "    # Рисуем Dn на графике\n",
    "    # Считаем delta \n",
    "    delta = numpy.abs(F_n_x - F_x)\n",
    "    # Ищем индекс максимального значения\n",
    "    x_ind = numpy.argmax(delta)\n",
    "    # По индексу получаем точку x, при которой наибольшее расстояние\n",
    "    dn_x_dot = x[x_ind]\n",
    "    # Ищем нижнюю и верхнюю точки\n",
    "    down_bound = min(F_n_x[x_ind], F_x[x_ind])\n",
    "    up_bound = max(F_n_x[x_ind], F_x[x_ind])\n",
    "    \n",
    "    pyplot.subplot(1, 2, ind + 1)\n",
    "    pyplot.title('$\\widehat{F_n} - F$, ' + f'n={n}', fontsize=16)\n",
    "    pyplot.plot(x, F_x, color=\"orange\", label='F(x)')\n",
    "    pyplot.plot(x, F_n_x,color=\"blue\", label='$\\widehat{F_n}(x)$')\n",
    "    pyplot.vlines(dn_x_dot, down_bound, up_bound,\n",
    "               color='maroon', linestyle='-', linewidth=3, label='$D_n$')\n",
    "    pyplot.legend(fontsize=16)\n",
    "    pyplot.grid(linewidth=0.2)\n",
    "    pyplot.xlabel('x', fontsize=16)\n",
    "    pyplot.ylabel('Вероятность', fontsize=16)\n",
    "\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Чем больше n, тем более точно мы предсказываем $F(x)$ на вcей числовой прямой.\n",
    "\n",
    "**Итого** на шаге 1 мы получили оценку $F(x)$ по выборке, которая с ростом n становится все более точной. Но пока это не приблизило нас к критерию."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----\n",
    "\n",
    "**Шаг 2. Придумываем статистику критерия Колмогорова**\n",
    "\n",
    "Мы научились приближать $F(x)$. Теперь давайте подумаем, что значит, что $F = F_0$? Если это так, то \n",
    "    $$\\begin{align}\n",
    "        &\\forall x \\in \\mathbb{R}\\ F(x) = F_0(x) \\Leftrightarrow \\\\\n",
    "        &\\forall x \\in \\mathbb{R}\\ |F(x) - F_0(x)| = 0 \\Leftrightarrow \\\\\n",
    "        &\\underset{x \\in \\mathbb{R}}{\\sup} |F(x) - F_0(x)| = 0\n",
    "    \\end{align}\n",
    "    $$\n",
    "  \n",
    "Хм, что-то похожее на то, что мы считали в прошлом шаге... Давайте заменим $F(x)$ на оценку: эмпирическую функцию распределения. Тогда **статиcтика критерия будет** \n",
    "$$\n",
    "    D_n = \\underset{x \\in \\mathbb{R}}{\\sup} |\\widehat{F_n}(x) - F_0(x)|\n",
    "$$\n",
    "Именно ее предложил Колмогоров в свое время.\n",
    "\n",
    "Что мы знаем уже про эту оценку?\n",
    "- При $H_0: D_n \\stackrel{p}{\\rightarrow} 0$\n",
    "\n",
    "Но этого мало: с помощью этой информации критерий не построить. Нам не хватает распределения.\n",
    "\n",
    "-----\n",
    "\n",
    "**Шаг 3. Распределение статистики критерия Колмогорова**\n",
    "\n",
    "\n",
    "> Теорема Колмогорова\n",
    ">\n",
    "> Пусть выборка $X$ из непрерывного распределения. Тогда при $H_0$ $\\sqrt{n}D_n \\stackrel{d}{\\rightarrow} \\phi$, где $\\phi$ имеет распределение Колмогорова: $F_\\phi(x) = \\begin{equation*} \n",
    " \\begin{cases}\n",
    "  \\sum\\limits_{k=-\\infty}^ \\infty (-1)^k e^{-2k^2 x^2}, &\\text{ $ x > 0$}\\\\\n",
    "   0, &\\text{ $ x < 0$}\n",
    " \\end{cases}\n",
    "\\end{equation*}$\n",
    "\n",
    "То есть, с ростом n $D_n \\rightarrow 0$, а $\\sqrt{n}D_n \\rightarrow \\phi$.\n",
    "\n",
    "Давайте графически посмотрим, как распределена статистика Колмогорова, и как она ведет себя при малых n. Для этого мы:\n",
    "\n",
    "1. Сгенерируем 1000 экспериментов и в каждом из них посчитаем статистику $\\sqrt{n}D_n$.\n",
    "2. В каждом эксперименте сгенерируем выборку.\n",
    "3. Посчитаем статистику D. Вопрос состоит в том, в каких точках считать статистику? Точек $x$ бесконечно много, неужели проверять все?\n",
    "    - **На самом деле достаточно проверить лишь точки изменения $\\widehat{F_n}(x)$. А ее значения меняются лишь в точках реализации выборки $X$.**\n",
    "        - Почему именно в них? Из-за монотонности функций. Рассмотрим интервал $[X_{(i)}, X_{(i + 1)})$ &mdash; 2 подряд стоящие точки в выборке.\n",
    "            - $F(X_{(i)}) \\leq F(X_{(i + 1)})$\n",
    "            - $\\widehat{F_n} = C$ &mdash; константа на этом интервале.\n",
    "            - Тогда максимум либо в точке $X_{(i)}$, либо в $X_{(i + 1)} - \\text{eps}$. \n",
    "                - Но если распределение абсолютно непрерывно, то мы можем смотреть вместо $X_{(i + 1)} - \\text{eps}$ точку $X_{(i + 1)}$. Так как $F(X_{(i + 1)}) \\approx F(X_{(i + 1)} - \\text{eps})$.\n",
    "                - Максимальная дельта на интервале будет или $|F(X_{(i)}) - C|$ или $|F(X_{(i + 1)}) - C|$. Промежуточные точки смотреть бесполезно, как раз-таки из-за монотонности $F(X)$.\n",
    "                - Но в точке $X_{(i + 1)}$ надо брать значение $\\widehat{F_n}(X_{(i)})$, а не $\\widehat{F_n}(X_{(i + 1)})$. Потому что это распределение дискретно и $\\widehat{F_n}(X_{(i + 1)}) \\neq \\widehat{F_n}(X_{(i + 1)} - \\text{eps})$\n",
    "                    - ограничение - Дискрентные распределения. Там не надо проверять смещения. \n",
    "4. Построим гистограмму.\n",
    "5. Построим распределение Колмогорова. В Python за него отвечает [kstwobign](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstwobign.html#scipy.stats.kstwobign).\n",
    "6. Повторим аналогичное упражнение для разных размеров выборок"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_D_statistic(sample, cdf_func):\n",
    "    \"\"\"\n",
    "        Считаем статистику D для выборки. Не работает для дискретных распределений.\n",
    "        Параметры:\n",
    "            - sample: выборка\n",
    "            - cdf_func: функция построения cdf для F0\n",
    "            \n",
    "    \"\"\"\n",
    "    \n",
    "    # Сортируем выборку, чтобы получить интервалы X_i, X_i+1\n",
    "    sample = numpy.sort(sample)\n",
    "    # Считаем эмпирическую функцию распределения\n",
    "    F_n_x = numpy.array([calc_Fn(sample, x) for x in sample])\n",
    "    # Сдвигаем на 1 вправо, чтобы посчитать разницу в точке X_i+1\n",
    "    F_n_x_shifted = numpy.concatenate([[0], F_n_x[:-1]])\n",
    "    # Строим массив значений F(X)\n",
    "    F_x = cdf_func(sample)\n",
    "    \n",
    "    F_x_shifted = cdf_func(sample)\n",
    "    # Определяем максимальное расстояние в левых точках интервала X_i\n",
    "    left_interval_max = numpy.max(numpy.abs(F_x - F_n_x))\n",
    "    # Определяем максимальное расстояние в правых точках интервала X_i+1\n",
    "    right_interval_max = numpy.max(numpy.abs(F_x_shifted - F_n_x_shifted))\n",
    "    return max(left_interval_max, right_interval_max)"
   ]
  },
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\n",
      "text/plain": [
       "<Figure size 1800x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(8)\n",
    "n_array = [5, 100]\n",
    "distribution = expon()\n",
    "exp_size = 10000\n",
    "\n",
    "\n",
    "pyplot.figure(figsize=(25, 8))\n",
    "\n",
    "# Для разных размеров выборок построим графики\n",
    "for ind, n in tqdm(enumerate(n_array), total=len(n_array)):\n",
    "    \n",
    "    statistics = []\n",
    "    # Генерируем exp_size экспериментов\n",
    "    for i in tqdm(range(exp_size), leave=False):\n",
    "        X = distribution.rvs(n)\n",
    "        statistics.append(get_D_statistic(X, distribution.cdf) * numpy.sqrt(n))\n",
    "    \n",
    "\n",
    "    pyplot.subplot(1, 2, ind + 1)\n",
    "    pyplot.title(f'Визуализация распределения статистики Колмогорова, N={n}', fontsize=16)\n",
    "    distplot(statistics, label='$\\sqrt{n}D_n$')\n",
    "    x_array = numpy.linspace(0, numpy.max(statistics), 1000)\n",
    "    pyplot.plot(x_array, kstwobign.pdf(x_array), label='Распределение Колмогорова')\n",
    "    pyplot.legend(fontsize=16)\n",
    "    pyplot.grid(linewidth=0.2)\n",
    "    pyplot.xlabel('Значение статистики', fontsize=16)\n",
    "    pyplot.ylabel('Плотность', fontsize=16)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы видим, что даже несмотря на то, что метод асимптотический, распределение Колмогорова достаточно хорошо приближает $\\sqrt{n}D_n$ даже при малых размерах выборок. Но есть небольшой сдвиг в большую сторону, что хорошо, так как критерий будет ошибаться меньше, чем в $\\alpha$% случаев. Но для малых размеров выборок были теоретически изобретены поправки, чтобы распределение описывало и эти случаи.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Какой будет критическая область у этого критерия? Мы будем отвергать гипотезу только в случае, если $D_n$ очень большое. А значит нас интересует лишь правая область распределения Колмогорова.\n",
    "\n",
    "### Критерий Колмогорова\n",
    "\n",
    "$H_0: F=F_0\\ vs.\\ H_1: F \\neq F_0$. **Важно помнить, что критерий работает для непрерывных распределений!**\n",
    "- Статистика $D_n = \\underset{x \\in \\mathbb{R}}{\\sup} |\\widehat{F_n}(x) - F_0(x)|$\n",
    "- При достаточно большом размере выборки $\\sqrt{n} D_n \\sim \\phi$, где $\\phi$ имеет распределение Колмогорова (по теореме Колмогорова-Смирнова)\n",
    "- критерий: $\\left\\{\\sqrt{n} D_n \\geq u_{1 - \\alpha} \\right\\}$, где $u_{1 - \\alpha}$ &mdash; $1 - \\alpha$ квантиль распределения Колмогорова\n",
    "    - `p-value = 1 - kstwobign.cdf(d)`, где d &mdash; реализация статистики $\\sqrt{n}D(X)$, `kstwobign` &mdash; функция распределения Колмогорова."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Критерий Колмогорова есть в библиотеке stats**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `scipy.stats.kstest` &mdash; [библиотека](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html) для критерия Колмогорова, Колмогорова-Смирнова."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В качестве cdf можно строкой указать распределение из scipy.stats. В таком случае аргументы распределения подаются на вход отдельно через args: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.6972\n"
     ]
    }
   ],
   "source": [
    "sample = norm(0.10, 0.04).rvs(10)\n",
    "\n",
    "\n",
    "Dn, p = kstest(rvs=sample, cdf='norm', args=(0.10, 0.04))\n",
    "print(f'p-value: {p:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Можно указать cdf в виде lambda-функции от $x$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.6972\n"
     ]
    }
   ],
   "source": [
    "Dn, p = kstest(rvs=sample, cdf=lambda x: norm.cdf(x, loc=0.10, scale=0.04))\n",
    "print(f'p-value: {p:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.6972\n"
     ]
    }
   ],
   "source": [
    "# для модников\n",
    "from typing import Callable\n",
    "\n",
    "def norm_cdf_closure(loc: float, scale: float) -> Callable:\n",
    "    \"\"\"Можно самостоятельно написать функцию\"\"\"\n",
    "    def inner_norm_cdf(x):\n",
    "        return norm.cdf(x=x, loc=loc, scale=scale)\n",
    "    return inner_norm_cdf\n",
    "\n",
    "# вместо 'norm' можно в явном виде указать любую функцию распределения\n",
    "Dn, p = kstest(sample, norm_cdf_closure(loc=0.10, scale=0.04))\n",
    "print(f'p-value: {p:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Можно заметить, что вне зависимости от варианта программы, результат совпадает 😊 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Проверка критерия\n",
    "\n",
    "Теперь давайте проверим с помощью Монте-Карло, как работает критерий на практике, а не с помощью визуализаций:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_kstest(dist, sample_size, N_exps=10000, to_print=True):\n",
    "    \"\"\"\n",
    "        Функция для проверки критерия Колмогорова\n",
    "        Возвращает доверительный интервал для FPR, если флаг to_print = False. Иначе печатает результат.\n",
    "    \n",
    "        Параметры:\n",
    "            - dist: Распределение выборки\n",
    "            - sample_size: размер выборки\n",
    "            - N_exps: число экспериментов, по которым потом считается FPR\n",
    "            - to_print: печатать результат или нет. Если нет, то функция возвращает дов. интервал для FPR.\n",
    "    \"\"\"\n",
    "    \n",
    "    numpy.random.seed(35)\n",
    "    bad_cnt=0\n",
    "    alpha=0.05\n",
    "\n",
    "    for i in tqdm(range(N_exps)):\n",
    "        # Генерирую выборку\n",
    "        sample = dist.rvs(sample_size)\n",
    "\n",
    "        # Запускаю критерий и считаю p-value\n",
    "        pvalue = kstest(sample, cdf=dist.cdf).pvalue\n",
    "\n",
    "        # Проверяю, что pvalue < alpha\n",
    "        bad_cnt += (pvalue < alpha)\n",
    "\n",
    "    if to_print:\n",
    "        print(f\"FPR: {round(bad_cnt / N_exps, 4)}\")\n",
    "        print(f\"CI={proportion_confint(count = bad_cnt, nobs = N_exps, alpha=0.05, method='wilson')}\")\n",
    "    else:\n",
    "        return proportion_confint(count = bad_cnt, nobs = N_exps, alpha=0.05, method='wilson')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Проверим критерий для экспоненциального распределения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "df31c4791f9247e0a831f5c26644d76c",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FPR: 0.0478\n",
      "CI=(0.043789399861243195, 0.05215788826519671)\n"
     ]
    }
   ],
   "source": [
    "check_kstest(expon(scale=10), sample_size=5, N_exps=10000, to_print=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "А что будет, если мы воспользуемся критерием Колмогорова для дискретных распределений?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4479b4089dbd433389df5f03045530f6",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FPR: 1.0\n",
      "CI=(0.9996160016293234, 1.0)\n"
     ]
    }
   ],
   "source": [
    "check_kstest(randint(1, 7), sample_size=100, N_exps=10000, to_print=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Он всегда отвергает гипотезу. Хотя она верна. **Поэтому не стоит использовать этот критерий для дискретных распределений!**\n",
    "\n",
    "**Итого, мы НЕ умеем решать задачу для дискретных распределений, но умеем для непрерывных!**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Проверка сложных гипотез про нормальное распределение\n",
    "\n",
    "\n",
    "Все предыдущие рассуждения мы вели для проверки простой гипотезы. Давайте разберемся, как проверять сложную гипотезу, но пока только для нормального распределения.\n",
    "\n",
    "\n",
    "> 📈 **Задача**\n",
    ">\n",
    "> Мы нашли в интернете доказательство, что отношение 2 независимых случайных величин из разных нормальных распределений &mdash; это нормальное распределение, в случае, если знаменатель \"маловероятно будет близ 0\" ([ссылка](https://link.springer.com/article/10.1007/s00362-012-0429-2)). Как это проверить на практике? \n",
    "\n",
    "**Идея**\n",
    "- Насимулируем выборку отношений большого размера.\n",
    "- На этой выборке проверим гипотезу $H_0:$ выборка из нормального распределения.\n",
    "- Так мы проверим работоспособность критерия на каком-то случайном примере.\n",
    "\n",
    "\n",
    "### Критерий Колмогорова для проверки сложных гипотез про нормальное распределение\n",
    "\n",
    "\n",
    "Но как проверить сложную гипотезу? Первая идея: давайте оценим параметры $\\mu, \\sigma^2$ по выборке. Похожее мы делали в t-test и там это сработало.\n",
    "- $\\widehat{\\mu} = \\overline X$\n",
    "- $\\widehat{\\sigma^2} =S^2 = \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}}(X_i - \\overline X)^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimated_params_kstest(sample):\n",
    "    \"\"\"Придуманный критерий\"\"\"\n",
    "    \n",
    "    mu = numpy.mean(sample)\n",
    "    sigma = numpy.std(sample, ddof=1)\n",
    "    dist = norm(loc=mu, scale=sigma)\n",
    "    return kstest(sample, cdf=dist.cdf).pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Проверим на практике критерий:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7997544280263768"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 1000\n",
    "num = norm(loc=100, scale=10).rvs(N)\n",
    "den = norm(loc= -1000, scale=25).rvs(N)\n",
    "\n",
    "sample = num / den\n",
    "estimated_params_kstest(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "На первый взгляд, все выглядит неплохо, но это впечатление обманчиво. Ведь по-настоящему критерии проверяются через Монте-Карло! И сначала на простом примере, где точно верна $H_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_criterion(criterion, sample_size, N_exps=10000, to_print=True):\n",
    "    \"\"\"\n",
    "        Функция для проверки придуманного критерия\n",
    "        Возвращает доверительный интервал для FPR, если флаг to_print = False. Иначе печатает результат.\n",
    "    \"\"\"\n",
    "    \n",
    "    numpy.random.seed(42)\n",
    "    bad_cnt=0\n",
    "    alpha=0.05\n",
    "\n",
    "    for i in tqdm(range(N_exps)):\n",
    "        # Генерирую выборку\n",
    "        sample = norm(loc=100, scale=10).rvs(sample_size)\n",
    "\n",
    "        # Запускаю критерий и считаю p-value\n",
    "        pvalue = criterion(sample)\n",
    "\n",
    "        # Проверяю, что pvalue < alpha\n",
    "        bad_cnt += (pvalue < alpha)\n",
    "\n",
    "    if to_print:\n",
    "        print(f\"FPR: {round(bad_cnt / N_exps, 4)}\")\n",
    "        print(f\"CI={proportion_confint(count = bad_cnt, nobs = N_exps, alpha=0.05, method='wilson')}\")\n",
    "    else:\n",
    "        return proportion_confint(count = bad_cnt, nobs = N_exps, alpha=0.05, method='wilson')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bcbe78951670477184092de91ed1ac12",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FPR: 0.0\n",
      "CI=(0.0, 0.0003839983706765959)\n"
     ]
    }
   ],
   "source": [
    "check_criterion(estimated_params_kstest, sample_size=1000, N_exps=10000, to_print=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Коэффициент ложных срабатываний (FPR) равен нулю. Что это значит на практике? **Что где-то есть ошибка!**\n",
    "- В общем случае, если вы придумали критерий, и он дает FPR равный 0, значит это плохой критерий! Почему? Потому что он будет менее мощным чем другой критерий с уровнем значимости 5%!\n",
    "    - Значит, придуманный критерий плох!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы оценили параметры по нашей выборке, а потом подставили их в распределение. В этом случае произошло \"переобучение под данные\". Наши параметры всегда были подобраны идеально для полученной выборки, хотя на самом деле они другие!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100.24918964915919, 9.951902255273907)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample = norm(loc=100, scale=10).rvs(1000)\n",
    "mu = numpy.mean(sample)\n",
    "sigma = numpy.std(sample, ddof=1)\n",
    "mu, sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы видим, что они отличаются от истинного значения. Эти отличия и делают FPR около 0.\n",
    "\n",
    "Для того, чтобы решить эту проблему ученые  насемплировали статистику $D_n$ и с помощью метода Монте-Карло построили критические области для разных $\\alpha$ для этой статистики.\n",
    "И назвали новый критерий **критерием  Колмогорова с поправкой Лиллиефорса**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Критерий Колмогорова с поправкой Лиллиефорса в библиотеке statsmodels\n",
    " [statsmodels.stats.diagnostic.lilliefors](https://www.statsmodels.org/dev/generated/statsmodels.stats.diagnostic.lilliefors.html) — Критерий Лиллиефорса. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kolmogorov-Lilliefors' Dn statistic: 0.0148,\n",
      "p-value: 0.9103\n"
     ]
    }
   ],
   "source": [
    "Dn, p = lilliefors(sample, dist='norm', pvalmethod='table') \n",
    "print(f\"Kolmogorov-Lilliefors' Dn statistic: {Dn:.4f},\\np-value: {p:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Проверим критерий через Монте-Карло:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fc045977f98d4d3ab5e4e0a1790442ac",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FPR: 0.0384\n",
      "CI=(0.0348075417687003, 0.04234696552710831)\n"
     ]
    }
   ],
   "source": [
    "lilliefors_crierion = lambda sample: lilliefors(sample, dist='norm')[1]\n",
    "check_criterion(lilliefors_crierion, sample_size=1000, N_exps=10000, to_print=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FPR все также занижен, но он сильно больше, чем у придуманного нами ранее критерия. Поэтому он мощнее, а значит и лучше!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Проверим теперь: правда ли, что отношение нормальных величин распределено нормально?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kolmogorov-Lilliefors' Dn statistic: 0.0157,\n",
      "p-value: 0.8520\n"
     ]
    }
   ],
   "source": [
    "N = 1000\n",
    "num = norm(loc=100, scale=10).rvs(N)\n",
    "den = norm(loc= -1000, scale=25).rvs(N)\n",
    "\n",
    "sample = num / den\n",
    "Dn, p = lilliefors(sample, dist='norm', pvalmethod='table') \n",
    "print(f\"Kolmogorov-Lilliefors' Dn statistic: {Dn:.4f},\\np-value: {p:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Да, так оно и есть! А если бы знаменатель был близок к 0?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kolmogorov-Lilliefors' Dn statistic: 0.3789,\n",
      "p-value: 0.0010\n"
     ]
    }
   ],
   "source": [
    "N = 1000\n",
    "num = norm(loc=100, scale=10).rvs(N)\n",
    "den = norm(loc= -10, scale=25).rvs(N)\n",
    "\n",
    "sample = num / den\n",
    "Dn, p = lilliefors(sample, dist='norm', pvalmethod='table') \n",
    "print(f\"Kolmogorov-Lilliefors' Dn statistic: {Dn:.4f},\\np-value: {p:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В этом случае выборка не из номального распределения!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Итого, мы рассмотрели первый метод, а именно Критерий Колмогорова с поправкой Лиллиефорса.\n",
    "\n",
    "----\n",
    "\n",
    "### Критерий Шапиро-Уилка\n",
    "\n",
    "Также является критерием согласия для нормального распределения. И также, как критерий Лиллиефорса, он проверяет сложную гипотезу (когда параметры не оценены).\n",
    "У него логика такая же, как и в предыдущем случае: ученые придумали некую статистику и с помощью метода Монте-Карло оценили критические области для статистики при разных $\\alpha$.\n",
    "\n",
    "\n",
    "- `scipy.stats.shapiro` &mdash; [реализация в Python](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html)\n",
    "\n",
    "Проверим критерий:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "86cd442ce96445169cfecc0ddcc3d9ab",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/10000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FPR: 0.0523\n",
      "CI=(0.04810587403933279, 0.05683795810177102)\n"
     ]
    }
   ],
   "source": [
    "shapiro_criterion = lambda sample: shapiro(sample).pvalue\n",
    "check_criterion(shapiro_criterion, sample_size=1000, N_exps=10000, to_print=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FPR у него более точный, чем у критерия Колмогорова."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь же рассмотрим графический метод принадлежности нормальному распределению: Q–Q plot. Это будет не критерий, а именно визуализация.\n",
    "\n",
    "---\n",
    "\n",
    "### Q–Q plot\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Предположим, что у нас есть два нормальных распределения $\\mathcal{N}(\\mu, \\sigma^2)$ и $\\mathcal{N}(\\mu', \\sigma'^2)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.linspace(-5, 10, 1000)\n",
    "dist_params = {\n",
    "    \"1\": (0, 1),\n",
    "    \"2\": (4, 2)\n",
    "}\n",
    "colors = {\n",
    "    \"1\": 'orange',\n",
    "    \"2\": 'lime'\n",
    "}\n",
    "quantiles = {\n",
    "    \"1\": [0.1, 0.4],\n",
    "    \"2\": [0.1, 0.4],\n",
    "}\n",
    "\n",
    "pyplot.figure(figsize=(10, 7))\n",
    "pyplot.title('График двух нормальных распределений', fontsize=12)\n",
    "for index in dist_params:\n",
    "    params = dist_params[index]\n",
    "    mu, sigma = params\n",
    "    color = colors[index]\n",
    "    q_array = quantiles[index]\n",
    "    distr = norm(mu, sigma)\n",
    "    pyplot.plot(x, distr.pdf(x), label='$\\mathcal{N}$' + f'$({mu}, {sigma}^2)$', color=color)\n",
    "    for q in q_array:\n",
    "        dot_x = distr.ppf(q)\n",
    "        pyplot.scatter(dot_x, 0, linewidth=0.2, color=color)\n",
    "        pyplot.text(dot_x + 0.1, 0, \"$Q_{\" + str(q) + \"}$\", fontsize=12) \n",
    "\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Пусть $\\alpha, \\beta$ &mdash; разные квантили. Обозначим через $Q_{\\alpha}$ квантили рыжего графика, и $Q'_{\\alpha}$ квантили зеленого графика.\n",
    "Докажем, что $$\\frac {Q_{\\beta}-Q_{\\alpha}}{Q'_{\\beta}-Q'_{\\alpha}} =\\frac{\\sigma}{\\sigma'}, i=1, 2,..., 9 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Напомним пару необходимых для дальнейшего доказательства свойств для нормального распределения:\n",
    "> $\\xi_1 \\sim \\mathcal{N}(\\mu_1, \\sigma_1^2),\\ \\xi_2 \\sim \\mathcal{N}(\\mu_2, \\sigma_2^2) \\Rightarrow \\xi_1 + \\xi_2 \\sim \\mathcal{N}(\\mu_1 + \\mu_2, \\sigma_1^2 + \\sigma_2^2)$\n",
    ">\n",
    "> $a \\xi_1 \\sim \\mathcal{N}(a\\mu_1, a^2\\sigma_1^2)$,\n",
    ">\n",
    "> $a + \\xi_1 \\sim \\mathcal{N}(a + \\mu_1, \\sigma_1^2)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Используя свойства нормального распределения, указанные выше:\n",
    "\n",
    "- $\\mathcal{N}(\\mu,\\sigma^2).ppf(\\alpha) \\cdot b + a = \\mathcal{N}(\\mu \\cdot b +a, b^2 \\cdot \\sigma^2).ppf(\\alpha)$. Это также видно на графике\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Пусть \n",
    "- $\\sigma' =\\sigma \\cdot b,$ а $\\mu' = \\mu \\cdot b + a$. \n",
    "- Тогда $b=\\frac{\\sigma'}{\\sigma}$, и $a=\\mu'- \\mu \\cdot \\frac{\\sigma'}{\\sigma}$.\n",
    "- Продолжим наше равенство: $\\mathcal{N}(\\mu \\cdot b +a, b^2 \\cdot \\sigma^2).ppf(\\alpha) = \\mathcal{N}(\\mu', \\sigma'^2).ppf(\\alpha)$ \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Из этого следует, что :\n",
    "1. $Q_{\\alpha}\\cdot b +a = Q'_{\\alpha}$\n",
    "2. $Q_{\\beta}\\cdot b +a = Q'_{\\beta}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вычтем из первого равенства второе и получим:\n",
    "\n",
    "1. $Q_{\\beta} \\cdot b + a  - (Q_{\\alpha}\\cdot b + a) = Q'_{\\beta} - Q'_{\\alpha}$\n",
    "\n",
    "2. $Q_{\\beta}\\cdot b  - Q_{\\alpha}\\cdot b  = Q'_{\\beta} - Q'_{\\alpha} $\n",
    "\n",
    "3. $ b \\cdot(Q_{\\beta}  - Q_{\\alpha})  = Q'_{\\beta} - Q'_{\\alpha}$\n",
    "\n",
    "4. $\\frac{Q'_{\\beta} - Q'_{\\alpha}}{Q_{\\beta}  - Q_{\\alpha}} = b $, а т.к.  $b=\\frac{\\sigma'}{\\sigma}$\n",
    "\n",
    "5. $\\frac{Q'_{\\beta} - Q'_{\\alpha}}{Q_{\\beta}  - Q_{\\alpha}}  = \\frac{\\sigma'}{\\sigma} $ ч.т.д"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Итак, получается, что если разность соседних квантилей одного распределения поделить на разность таких же соседних квантилей другого распределения (одно получается из другого линейным преобразованием), то это всегда константа. Для чего же это может нам понадобиться? И тут мы переходим к Q-Q Plot.\n",
    "\n",
    "### Постановка задачи QQ-plot\n",
    "\n",
    "QQ-plot &mdash; метод, который позволяет визуализировать \"насколько хорошо\" данные описываются нормальным распределением. В отличие от критериев этот метод не говорит, что он отвергает или не отвергает нормальность данных, но позволяет визуально посмотреть, насколько данные нормальны! Уметь грамотно визуализировать данные &mdash; одна из основных задач аналитика, и QQ-плот это лучший метод для визуализации нормальности данных.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Визуализация QQ-плот**\n",
    "- Пусть распределение выборки &mdash; $\\mathcal{N}(\\mu, \\sigma^2)$.\n",
    "- Найдем квантили 2 распределений: $\\mathcal{N}(\\mu, \\sigma^2)$ и $\\mathcal{N}(0, 1)$. Их квантили будут соответственно $Q, Q'$.\n",
    "- Отложим квантили первого распределения по оси Y, а второго - по оси X.\n",
    "- Тогда выведенное выше правило утверждает, что все точки $(Q'_{\\alpha}, Q_{\\alpha})$ лежат на одной прямой.\n",
    "    -  Тангенс угла наклона этой прямой всегда один и тот же и равен $\\frac{\\sigma'}{\\sigma}$. \n",
    "    \n",
    "    \n",
    "Для визуализации угла наклона воспользуемся [функцией из matplotlib](https://matplotlib.org/stable/gallery/text_labels_and_annotations/angle_annotation.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Arc\n",
    "from matplotlib.transforms import IdentityTransform, TransformedBbox, Bbox\n",
    "\n",
    "\n",
    "class AngleAnnotation(Arc):\n",
    "    \"\"\"\n",
    "    Draws an arc between two vectors which appears circular in display space.\n",
    "    \"\"\"\n",
    "    def __init__(self, xy, p1, p2, size=75, unit=\"points\", ax=None,\n",
    "                 text=\"\", textposition=\"inside\", text_kw=None, **kwargs):\n",
    "        \"\"\"\n",
    "        Parameters\n",
    "        ----------\n",
    "        xy, p1, p2 : tuple or array of two floats\n",
    "            Center position and two points. Angle annotation is drawn between\n",
    "            the two vectors connecting *p1* and *p2* with *xy*, respectively.\n",
    "            Units are data coordinates.\n",
    "\n",
    "        size : float\n",
    "            Diameter of the angle annotation in units specified by *unit*.\n",
    "\n",
    "        unit : str\n",
    "            One of the following strings to specify the unit of *size*:\n",
    "\n",
    "            * \"pixels\": pixels\n",
    "            * \"points\": points, use points instead of pixels to not have a\n",
    "              dependence on the DPI\n",
    "            * \"axes width\", \"axes height\": relative units of Axes width, height\n",
    "            * \"axes min\", \"axes max\": minimum or maximum of relative Axes\n",
    "              width, height\n",
    "\n",
    "        ax : `matplotlib.axes.Axes`\n",
    "            The Axes to add the angle annotation to.\n",
    "\n",
    "        text : str\n",
    "            The text to mark the angle with.\n",
    "\n",
    "        textposition : {\"inside\", \"outside\", \"edge\"}\n",
    "            Whether to show the text in- or outside the arc. \"edge\" can be used\n",
    "            for custom positions anchored at the arc's edge.\n",
    "\n",
    "        text_kw : dict\n",
    "            Dictionary of arguments passed to the Annotation.\n",
    "\n",
    "        **kwargs\n",
    "            Further parameters are passed to `matplotlib.patches.Arc`. Use this\n",
    "            to specify, color, linewidth etc. of the arc.\n",
    "\n",
    "        \"\"\"\n",
    "        self.ax = ax or plt.gca()\n",
    "        self._xydata = xy  # in data coordinates\n",
    "        self.vec1 = p1\n",
    "        self.vec2 = p2\n",
    "        self.size = size\n",
    "        self.unit = unit\n",
    "        self.textposition = textposition\n",
    "\n",
    "        super().__init__(self._xydata, size, size, angle=0.0,\n",
    "                         theta1=self.theta1, theta2=self.theta2, **kwargs)\n",
    "\n",
    "        self.set_transform(IdentityTransform())\n",
    "        self.ax.add_patch(self)\n",
    "\n",
    "        self.kw = dict(ha=\"center\", va=\"center\",\n",
    "                       xycoords=IdentityTransform(),\n",
    "                       xytext=(0, 0), textcoords=\"offset points\",\n",
    "                       annotation_clip=True)\n",
    "        self.kw.update(text_kw or {})\n",
    "        self.text = ax.annotate(text, xy=self._center, **self.kw)\n",
    "\n",
    "    def get_size(self):\n",
    "        factor = 1.\n",
    "        if self.unit == \"points\":\n",
    "            factor = self.ax.figure.dpi / 72.\n",
    "        elif self.unit[:4] == \"axes\":\n",
    "            b = TransformedBbox(Bbox.unit(), self.ax.transAxes)\n",
    "            dic = {\"max\": max(b.width, b.height),\n",
    "                   \"min\": min(b.width, b.height),\n",
    "                   \"width\": b.width, \"height\": b.height}\n",
    "            factor = dic[self.unit[5:]]\n",
    "        return self.size * factor\n",
    "\n",
    "    def set_size(self, size):\n",
    "        self.size = size\n",
    "\n",
    "    def get_center_in_pixels(self):\n",
    "        \"\"\"return center in pixels\"\"\"\n",
    "        return self.ax.transData.transform(self._xydata)\n",
    "\n",
    "    def set_center(self, xy):\n",
    "        \"\"\"set center in data coordinates\"\"\"\n",
    "        self._xydata = xy\n",
    "\n",
    "    def get_theta(self, vec):\n",
    "        vec_in_pixels = self.ax.transData.transform(vec) - self._center\n",
    "        return np.rad2deg(np.arctan2(vec_in_pixels[1], vec_in_pixels[0]))\n",
    "\n",
    "    def get_theta1(self):\n",
    "        return self.get_theta(self.vec1)\n",
    "\n",
    "    def get_theta2(self):\n",
    "        return self.get_theta(self.vec2)\n",
    "\n",
    "    def set_theta(self, angle):\n",
    "        pass\n",
    "\n",
    "    # Redefine attributes of the Arc to always give values in pixel space\n",
    "    _center = property(get_center_in_pixels, set_center)\n",
    "    theta1 = property(get_theta1, set_theta)\n",
    "    theta2 = property(get_theta2, set_theta)\n",
    "    width = property(get_size, set_size)\n",
    "    height = property(get_size, set_size)\n",
    "\n",
    "    # The following two methods are needed to update the text position.\n",
    "    def draw(self, renderer):\n",
    "        self.update_text()\n",
    "        super().draw(renderer)\n",
    "\n",
    "    def update_text(self):\n",
    "        c = self._center\n",
    "        s = self.get_size()\n",
    "        angle_span = (self.theta2 - self.theta1) % 360\n",
    "        angle = np.deg2rad(self.theta1 + angle_span / 2)\n",
    "        r = s / 2\n",
    "        if self.textposition == \"inside\":\n",
    "            r = s / np.interp(angle_span, [60, 90, 135, 180],\n",
    "                                          [3.3, 3.5, 3.8, 4])\n",
    "        self.text.xy = c + r * np.array([np.cos(angle), np.sin(angle)])\n",
    "        if self.textposition == \"outside\":\n",
    "            def R90(a, r, w, h):\n",
    "                if a < np.arctan(h/2/(r+w/2)):\n",
    "                    return np.sqrt((r+w/2)**2 + (np.tan(a)*(r+w/2))**2)\n",
    "                else:\n",
    "                    c = np.sqrt((w/2)**2+(h/2)**2)\n",
    "                    T = np.arcsin(c * np.cos(np.pi/2 - a + np.arcsin(h/2/c))/r)\n",
    "                    xy = r * np.array([np.cos(a + T), np.sin(a + T)])\n",
    "                    xy += np.array([w/2, h/2])\n",
    "                    return np.sqrt(np.sum(xy**2))\n",
    "\n",
    "            def R(a, r, w, h):\n",
    "                aa = (a % (np.pi/4))*((a % (np.pi/2)) <= np.pi/4) + \\\n",
    "                     (np.pi/4 - (a % (np.pi/4)))*((a % (np.pi/2)) >= np.pi/4)\n",
    "                return R90(aa, r, *[w, h][::int(np.sign(np.cos(2*a)))])\n",
    "\n",
    "            bbox = self.text.get_window_extent()\n",
    "            X = R(angle, r, bbox.width, bbox.height)\n",
    "            trans = self.ax.figure.dpi_scale_trans.inverted()\n",
    "            offs = trans.transform(((X-s/2), 0))[0] * 72\n",
    "            self.text.set_position([offs*np.cos(angle), offs*np.sin(angle)])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 5\n",
    "sigma = 10\n",
    "sample_distr = norm(loc=mu, scale=sigma)\n",
    "standart_distr = norm(loc=0, scale=1)\n",
    "quantiles = np.arange(0.001, 1, 0.1)\n",
    "quantle_xticks = [\"$Q_{\" + str(round(x, 2)) + \"}$\" for x in quantiles]\n",
    "quantle_yticks = [\"$Q'_{\" + str(round(x, 2)) + \"}$\" for x in quantiles]\n",
    "standart_q = standart_distr.ppf(quantiles)\n",
    "sample_q = sample_distr.ppf(quantiles)\n",
    "\n",
    "\n",
    "fig = pyplot.figure(figsize=(15, 10))\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "pyplot.title('QQ-Plot, визуализация на идеальных данных', fontsize=15)\n",
    "\n",
    "\n",
    "ax.plot(standart_q, sample_q, label=\"Прямая $(Q_{\\\\alpha}, Q'_{\\\\alpha})$\")\n",
    "for index in [1, 5]:\n",
    "    center = (standart_q[index], sample_q[index])\n",
    "    dot1 = (standart_q[index] + 1, sample_q[index])\n",
    "    dot2 = (standart_q[index + 1], sample_q[index + 1])\n",
    "    \n",
    "    label=\"\"\n",
    "    if index == 1:\n",
    "        label=\"$tan(\\phi) = \\dfrac{\\sigma'}{\\sigma}$\"\n",
    "    am1 = AngleAnnotation(center, dot1, dot2, ax=ax, size=250, text=r\"$\\phi$\", text_kw=dict(fontsize=16))\n",
    "    ax.plot(*zip(*[center, dot1]), color='white', label=label)\n",
    "\n",
    "\n",
    "pyplot.ylabel(\"Квантили $\\mathcal{N}(\\mu, \\sigma^2)$\", fontsize=15)\n",
    "pyplot.xlabel(\"Квантили $\\mathcal{N}(0, 1)$\", fontsize=15)\n",
    "pyplot.xticks(standart_q, quantle_xticks, fontsize=15)\n",
    "pyplot.yticks(sample_q, quantle_yticks, fontsize=15)\n",
    "pyplot.legend(fontsize=15)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Если отложить все отрезки с координатами $(Q_{0.i},Q'_{0.i});(Q_{0.i+0.1},Q'_{0.i+0.1})$, то можно заметить, что во всех случаях угол $\\phi_i$ будет одинаковым.  Давайте посмотрим, чему же равен угол $\\phi_i$.\n",
    "\n",
    "$$\\begin{align}\n",
    "   \\phi_i = arctg \\left({\\frac {Q'_{0.i+0.1}-Q'_{0.i}}{Q_{0.i+0.1}-Q_{0.i}}}\\right) = arctg \\left({\\frac{\\sigma'}{\\sigma}}\\right) = arctg(b) \n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Таким образом, можно сделать вывод: если построить график квантилей двух нормальных распределений, то это будет прямая. Это и будет Q-Q плот.\n",
    "\n",
    ">Замечание! Необязательно только для нормальных распределений Q–Q plot будет прямой. Для всех распределений, которые переводятся друг в друга линейными преобразованиями, графиком Q–Q plot будет прямая."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "Теперь давайте построим настоящий график QQ-plot для выборки. Для этого сделаем все то же самое, что и делали выше, только квантили получим по выборке.\n",
    "\n",
    "- Пусть у нас N точек в выборке.\n",
    "- Тогда оценка i-ой квантили &mdash; i значение в отсортированной выборке (вспоминаем эмпирическую функцию распределения из 1 части). $\\widehat{F_n}(x) = \\dfrac{1}{N}\\sum([X_i \\leq x])$.\n",
    "- Построим квантили стандартного нормального распределения.\n",
    "    - Для этого посчитаем квантиль в каждой точке $\\dfrac{i}{N},\\ i \\in \\{1, ...\\ N - 1\\}$\n",
    "- Отложим оценки квантилей первого распределения по оси Y, а истинные квантили второго распределения - по оси X.\n",
    "- Если график напоминает прямую, значит считаем, что это нормальное распределение.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_qq_plot(sample):\n",
    "    \"\"\"\n",
    "        Функция для отрисовки QQ-Plot.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Строим оценку квантилей\n",
    "    # Сортируем выборку\n",
    "    sample.sort()\n",
    "    # Сами значения и есть оценки квантили\n",
    "    sample_quantiles = sample[1:-1]\n",
    "    N = len(sample)\n",
    "\n",
    "    # Считаем N-2 точки квантилей стандартного нормального распределения (без +- бесконечности)\n",
    "    x = [i / N for i in range(1, N - 1)]\n",
    "    theoretical_quantiles = norm().ppf(x)\n",
    "    \n",
    "    # Визуализация\n",
    "    fig = pyplot.figure(figsize=(15, 10))\n",
    "    ax = fig.add_subplot(1,1,1)\n",
    "\n",
    "    ax.plot(theoretical_quantiles, sample_quantiles, 'k.', linewidth=1.0, color = 'green')\n",
    "\n",
    "    ax.set_xlabel('theoretical quantiles', fontsize=15)\n",
    "    ax.set_ylabel('sample quantiles', fontsize=15)\n",
    "    ax.set_title('QQ-Plot для выборки из нормального распределения', fontsize=15)\n",
    "    pyplot.grid(linewidth=0.2)\n",
    "    pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(102)\n",
    "sample = norm(loc=100, scale=1000).rvs(size=1000)\n",
    "my_qq_plot(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Можно заметить, что наш график очень напоминает прямую. Конечно, в данном случае мы взяли не совсем квантили, а выборочные квантили, но тем не менее, линейность довольно четко прослеживается."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----\n",
    "\n",
    "Давайте рассмотрим следующий пример. \n",
    "\n",
    "Допустим, мы захотели построить график загрузки нашего сайта в секундах. Мы взяли в наших логах последние 20 значений (в секундах) от разных пользователей, и построим график Q–Q plot для этой выборки."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample = [0.11, 0.07, 0.1, 0.09, 0.17, 0.14, 0.05, 0.05, 0.17, 0.07, 0.06, 0.06, 0.12, 0.12, 0.08, 0.15, 0.07, 0.06, 0.13, 0.17]\n",
    "my_qq_plot(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Заметим, что наш график уж совсем отдаленно напоминает прямую. Маловероятно, что наша выборка была получена из нормального распределения."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "Давайте посмотрим, а как будет вести себя наш график, если мы проверим на соответствие нормальному распределению другие распределения? Возьмем выборку из распределения Стьюдента с тремя степенями свободы и сравним его с нормальным распределением."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "numpy.random.seed(102)\n",
    "sample = t(df=3).rvs(size=1000)\n",
    "\n",
    "my_qq_plot(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Можно заметить, что в данном случае наш график не похож на линейную функцию. Можно сделать вывод: действительно, наша выборка была получена не из нормального распределения."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statsmodels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Перейдем к библиотечным вариантам построения Q–Q plot. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Statsmodels](https://www.statsmodels.org/stable/generated/statsmodels.graphics.gofplots.qqplot.html) — библиотека для Q–Q plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.gofplots import qqplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим выборку из распределения Стьюдента из Примера 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pyplot.figure(figsize=(10, 7))\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "\n",
    "qqplot(data=t(df=3).rvs(1000), line='s', ax=ax)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Далее рассмотрим нормальное распределение:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pyplot.figure(figsize=(10, 7))\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "\n",
    "qqplot(norm(100, 2).rvs(1000), line='s', ax=ax)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь рассмотрим экспоненциальное распределение:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qo4ENgWeITZH7gAXAiyXUlaWJKBiqJEkdZyShCiJY/QA4roii1MAGRJDqAY4gAtYyoglnH3Ap5TfjzBquJEnqIAuAQ2lupAri1/hHccRqbG1CTPX1EFN/U4A/AqcTgepKYE1p1f05w5Ukqcs0G6wgQtVmxZSjIW1OLEbvIRanTyS6mZ9KBKrrqUXeVpMlXK0LfJJoTfsBYEdgJ2JKU5KkNtJL88HqJWK0SkXbllpTz72JnlC/A75BBKpbyiutKVnC1enATcSfE+AR4H8xXEmS2s73yBasnAYcKztRa+r5pvTcrcAXiEB1d0l1jUaWcLU98FdE3Ie4srGZyC9JUsl6gZ8A62R4rAvWi7Y7tRGqXdJz1wOfIrqk319SXXnJEq5WEj+N1Ri/PX/etV2SpBY0MFTVGxdwpKpI44C9qAWq7YkF6FcREfZsYlqsU2QJV18gVv9tDZwJ7Au8r8CaJEkahfnAPxArdiDbFjYLiY5Jyst44K3Utp3Zitg771Lg68C5wNLSqitWlnB1CXAz8BbiJ/SjRLSXJKnFzCd2bWv2SkCDVR4mAQcRYWoucX3li8Avgc8Si7WfLq26sVMvXO056HZ1X8Nt0uPmQiqSJGlEemk+WCV4JeDoTAUOIwLVMcDGROfxC4kF6RcTe+d1k3rh6p/q3JcQ4VSSpBYwH/gwzQerhbi+qnnrAUcRgerI9PZTxFRfHzHl1c2Ls+uFqwPHrApJkkaslwhW4xs9MJVQ2xvQKwKz2hg4lghUhxIjVo8D/0EEql8Dq8sqrsVkWXM1lfip3Y/4abyK2IxpRYF1SZKU0clkC1aGqma9mth2pkKMuEwClhAhoA+4FlhbWnWtK0u4OoOYPp2f3v5r4OfAXxRVlCRJ2W3b4P6EiAD/gqGqsa2pXeG3HxFb/0CsFeoDFpVXWtvIEq52BV4/4PblwF3FlCNJUjN6G9xvQ9AsdqDWg2qv9NztwJeJQHVHSXW1qyzhqtqG4fr09psxuEqSWsKPGH4Ru8Gqnl2pBard0nM3AicSXdL/UFJdnSBLuHoTMa26JL29DXAPEWoTav9NJEkaI1m2s1mMweqVZlELVK8lJkuvAT5GBKqHyiuto2QJV3ZWkyS1kF7g34DJdR6TACeNSTWtbDywD7U1VNsSV/RdDnwHOIe44k/5yhKuFhNXYG496PE2EZUkleB71A9WENdhdWf/qonAAUSYmge8hug5tZDYz+484E9lFdclsoSrrxB7Cd5HbWdLm4hKkkowH5je4DFrgQ+NQS2tYwrwdiJQHQtsQnRFv4hYkH4RETc1NrKEq78kNrBeWXAtkiTVkWV7m2ofq84ftZoGHEEEqqOB9Yl9+84nAtVCYl8/jb0s4eoOYCPgiYJrkSRpGL1EL/BGwWohnbyIfUNi/74eYkH0OsBS4L+IQHUZsKq06lSVJVydAtxChKyBWwUdW0hFkiS9bOBVgY32DXyOTrwGazowlwhUBxOrzR4hPpU+4GpgTWnVaShZwtW/A98gWi/Y5V6SNEYWELvYZdmMOaGT1lltQe0Kv/2BCcD9xFL+PuA31BZBq/VkCVcvAN8vuhBJkmpuJdooZg1WP6Dd11nNpNaDau/03F3Ezol9wG9LqkvNyxKuriKmBs/jldOCtmKQJBVgPs0Hq/ZcZ/U6aoHqjem5m4HPEU09f1dSXRqdLOGq+t/7LQPO2YpBklSQD9HJweqN1ALV69Jz1wKfJALVg+WUpRxlCVcHFl6FJEkvm5DhMe0TrMYRoxPVNVTbEQvQrwBOBc4GHi2tOhUhS7gCOArYBZg64NyX8y9HktSd5gMfpvGIVQKsAP6OVl5jNYFYiF7tkr4l0SzyV8DXgHOBJ0urTkXLEq5+BKxLjGD9BHgHcaGCJEk5yLJ4PSE6OL2PVg1Vk4lWCT3AHGBT4oqwBcSC9AuBZ0qrTmMpS7jah/ipvw34EvBPwMVFFiVJ6ga9wOlELMmyxmpKseWMwDpEZ60eornnhsCzwAVEoFpABCx1lyzhqto9/wWi9caTwOaFVSRJ6nDV/lWQLVRBK7XJXJ/YbqaH2H5mGvGLsS89foX7xXW7LOHqAmL7m28RV4gmwI+LLEqS1Gl6iVUm66e3s4YqiF87P8q9oma8ipjq6yE2SJ5CLEL/dyJQXQmsLq06tZos4eor6dc+ImhNJdu08dbAGcCrib8ZpxHNZSVJXWPgQvVmAlVVQqxKGfurAl9DbDtTAQ4gfmE+SFyj2Adch13SNbR64Wo28BDwWHr7vcTP2GLgi8BTDV57NdG242bif1VuAi4hGs5KkjpeM13WB0vS44eMZbDalri6r0IsOB4P3AN8kwhUds9WFuPr3Pev1KaN9we+ToxEPUOMQjXyKLWfw+eAu4mrUSVJHa2X+PUxkmCVpM99F9HQoPhg9VrgROBGYmTqn4kRgS8SPYh2JjqmG6yUVb2RqwnURqf+ighU1fV6tzb5PjOIprQ3DHHfB9OD6dOnN/mykqTWMh/4v4x8tGohcf1dsXaj1iV91/TcDcCniS7p9xVegTpZo3A1kZjeO5g0AGV43mDrEYHsY8QVqoOdlh4sW7bM6WtJalu9NB+sqv/sP0dse1NcD6u9qAWqHYC1xOa5xxNd0h8u7J3VbeqFpLOI7vzLiHYMV6XndyB7H7RJRLA6k/ifAUlSR+oF/oPswaoaqorbwmY8sC8RpnqIq6xWAZcRa6jOBZ4o5J3V7eqFq68BlxI9rRZS+5swnmx/E8YBPyXWWn1nFDVKklpaL7Ekt94y3qpiF6pPBA4iwtRc4nL1FcAviXVT5wNP5/6u0is1mt67fohzv8/42vsC7wFup7ZG6yTgoozPlyS1hR/R+NdJQjQCfS95T/1NJXpPVYBjgY2B54ntZvqIXzrLc31Hqb5m1k4162pGtqJRktQ25lNrDDqcaq+qPXJ71/WI7ugV4Kj09p+A84hAdQkxYiWVochwJUnqSL3AT4id9aDx/0c/Rx7BaiNi/74KcBgxYvU4sai3D/g1saZKKpvhSpLUhOrC9SzrqyAuOP/QiN9tM2LbmQqxlmoS0d36X4lAdQ1x1Z/USgxXkqSMmu1htZaRrLHailqX9P2IvkD3EldG9QGLcNsZtTbDlSSpgV5ii+KJNNdq4d1kDVbbU+tB9eb03B3AV4lAdXv2YqXSGa4kSUNodl3VQNVO6/WD1S7UAtXu6blFwGeJxohZL02XWo3hSpI0yALgUIrYwuZN1ALVTsTE4bXAx4lAtWQE7yi1GsOVJClVDVUwsi1sVgB/x8ARq3HAPkSg6iE2ml1NXNn3XeAc4LGRFyy1JMOVJImRj1YlxHjTjJfPTADeRoxOzSO2+XiJ6D31JaIX1VOjLVdqYYYrSRLNB6vqaFVMAU4GDiEC1RxgE6Ir+sXEgvQLiW5XUjcwXElSVxs4FZhVjFatywwOJwLV0cAGwDPE/n19xH5+L+ZYqdQuDFeS1JVuBXZLv88yYhUjVRvwNEfzMSqcweHAusAy4H+IQHUZsDL/YqW2YriSpK4yH/gwEaiyTQNO5wmO5RQqfJdDgMnAH4GfEYHqKmJLZknBcCVJXaG5KwG34BHmcjYV+ngbVzCBhAeA7xOB6gbski4Nx3AlSR2tF/g5sRdg/VA1gwfooZ8KfezDdQDcDZxCBKpbiy1U6hiGK0nqWI3bK+zM3S8Hqj25BYBb2IN/5ET6+Dq/G5tCpY5iuJKkjvQEMJ0/D1YJe3Dry4Hq9dwNwHW8hRP4Jv308AD3MlyHdUmNGa4kqaP8+dqqcaxlL35DhT566Gd77mcN47mS/fkhH+Yc5vAIWxE9q3YoqW6pcxiuJKmtDWypUDWOCaxmP66mQh/zOJuteISVTOJSDuYUPst5HMtSNiOWpd8GbDPmlUudynAlSW2nFzidaIoA1RGqSazkIC6jQh9zOYdNWcaLTGUBh3MiX+cCjuYZNqJ2nd9K4H0M3AtQ0ugZriSprVRHqiJQTeVFDuOXVOjjGM5nI57hOdbjAo6mjwoLOJzlrDfg+QnR9nOzsS9d6hKGK0lqGwuA3Vif5ziSi6jQx5FcxDRe4Ck25mzm0UeFX3EILzF1iOcnVPcClFQcw5UktbQYqXoVT3IM51PhWA5lIVNYyWO8mjN4L31UuIK3sZpJw7xGkh7vxilAqXiGK0lqKbXtaV7NY8zlHCqcwIFczkTWsJht+CEfpp8ermUf1jKhzmtV11bdBuxReOWSguFKklpCjFBtw2Lm8X0q9LEv1zCehN+zI9/iU/RR4SbexPBNQQdvSGOokspguJKk0jwIbMOO/D5t6vn3zGYRALfxBr7EF+ijwp3sQv2ta6qhyvVUUiswXEnSmLuYXdmCCj+jQj9v4A4AfsNsPsPX6aeHe9kx42tV+1Q5QiW1CsOVJI2RWUCFD1HhOHbkXtYyjqvZj4/yXc5mHg813cgzAZZgsJJai+FKkgoyHtgX6GEuPdzENjzEan7MZRzEtzmBc5nD47ymiVd0TZXUDgxXkpSjicABQIUjmctNvIbHWcHFLORQ/h9f4XyO4U+8qolXHBioDFNSOzBcSdIoTQHeDlSAY1mPV/E8z3MFF3EkfVS4iCN5nvWbeMWBgeoHwHF5liupYIYrSRqBacARRKA6inVZnxd4mg05j2Ppo8JCDmUF6zTxio5QSZ3CcCVJGW0EHA1U2JLDeJJ1WMETbMpZzKGPd3A5B7Lq5c2Um1FdmD4jz3IllcRwJUl1bArMIUaoDmYik1jNw8CP+QB9VLia/Rp0SW/E/f6kTmO4kqRBtgTmEYHqrcAE4D6245/poY93cCOzSRg/indwTZXUyQxXkgTMJMJUBXhLeu5O4Gt8gn7ezW/Zg/pd0hupBqpVwPtwA2WpcxmuJHWt11ELVNXl4zexNSfxf+inh3vYOT2bR6hyhErqFoYrSV1lT6CHCFTV6HQN8AnmcTbf4kG2I58wBbAGeC+OUkndxXAlqaONI6b5KkSomgmsBq7gtXyf4zmHuTzKFgMePRIDA5VX/UndznAlqeNMAPYnAtU8YAtgJXAJW/AVPs959PAk08lvhMqr/STVGK4kdYTJwMFEoJoDTAdeAC5md/o4gQs5mmfZkNEFqqoEeJFoJSpJr2S4ktS21iHGiypEc88NgWeB8zmCPv6OX3IYLzCNfAIV1EarHKmSNDzDlaS2sgFwFBGojgDWBZYBvwD6OJ1LeScrmUL+gQrclkZSFoYrSS1vE+BYIlAdQmyU/EfgdHakj1O5kgNZ8/I/Z45SSSqX4UpSS3oNtS7pbyP+sXoQOJW/p5+/4Tr2TrukFzFCBYYqSSNluJLUMral1oNqb2A88Dt24hv00E8PN7MnEaaKCFQ2+ZSUD8OVpFLtRC1QvSk9dyu784U0UN3FLuQXpsA1VJKKZriSNOZ2o7rtzAbswrMAXM+b+RQ9nM087mPHnN/RnlSSxo7hSlLhxgGzgQoH08OD7MB9rGE8V/FGjqPCOczlYbbO+V3dKFlSOQxXkgoxHtgPqPA2eriXrXiEVVzBpRzMN/gM5zKHpWyW87s65SepfIYrSbmZxPkcyEQq9DGXc9mMpbzIDfySw/gsp3ABR/M0G+f4jl7hJ6n1GK4kjcpUrudQHqVCP8fwHjbmaZ5jPS7kKPqocDFHsJz1cnq3wWHK0SlJrcdwJalJ81mP93AkF1OhnyM5mPVYzlNszLnMoY8Kl/B2XmJqTu9nuwRJ7cVwJamOBcChAGzMUxzD+VTo51BOYCov8Tib8R+8m356uJwDWc2kUb7f4JGpNcB7cTG6pHZiuJI0QC1MAWzG48zlNCr0cSCXM4nVLGFrfsSH6KPCtezDWiaM4v1cMyWp8xiupK7VC5wOTH7F2a15iHmcTYU+9uNqxpPwB3bgn/gk/fRwI7MZXVNPp/kkdTbDldTxbiXadg4lQtL23EuFPir0sRc3AnA7u/JlPk8/PdzOGxhZoBo8MgUGKkmdznAldYz5wIcZOgQNPpewC3e+HKh243YAbmQWJ3IK/fTwB147ghoGhinXS0nqToYrqS31Aj8B1hl0vt7oUsKbuOnlQPVa/sBaxnEN+/Ix/pmzmccSth1BLTbulKSBDFdSy6o3EkWd8zXjWcPeXEeFPnroZ1uWsJoJXM6BfIdPcDyIFpwAABC8SURBVC5zeIzNm6jJaT5JasRwJZVmuNGngZpf5zSRVbyNK9Iu6eewOY/xEpNZyKF8gS9xPsfwFJtkfLWBYco9+iQpC8OVNCaGG4UazVV3NVNYwSH8igp9HMt5bMJTLGddLuJI+qhwEUfyHBs0eJXBo1KGKUkaCcOVlJvRT+M1Y12WcwQXU6GPo7iQDXiOp9mQ8zmGfnr4JYfxIusOetZQ03pV9piSpDwYrqRh9QI/AtZv4jn5BqjBNuRpjuYCKvRxOAtYhxUsZTr/zV/RR4XLOIhVL/etSrBJpySNPcOVulijkSYa3Dc2prOUOZxLhT4O5lIms4pH2IKf8Pf008NVvJU1r+iSnuCUniSVx3ClNtELfA+YnvPrlh+ehrIFj7zcJX1/rmQCa7mfmXyP4+mnhxt4MwnjBzzDESlJahWGK2UwONgk1ELJcN8PdXuwRvcP1ppBKC8zuY8e+qnQz95cD8BdvI6T+Sz9HMWtfB/4p/SQJLWsJEmKPA5PkuSeJEnuTZLkxEaPv/HGG6uLRIY5ehN4IIE16dfeBo/P67UaPbbe/UPdl+Xc/CZuP5Eeg79fVefcUPetTmBteqwedC7xyO1Y+/KxM3cmn+PLyc3s8fIDboLkJEh2HvHPtoeHh4fHWBxJkiwaKs8UGawmJElyX5Ik2yVJMjlJkt8mSfL6kYer3gSeT3jFL6nnk5EFrGZeq9Fj690/1H0vJrAiw7nBgabRbY/WOtYOc6xJ9uDU5CuQ3DXgCddA8glIZlL+PxYeHh4eHtmO4cLVuCRJKMjewBeBw9Lbn02/njLcExYtWpTMnj17mHsfAGYMcf5BYGaTpTXzWo0eW+9+hrlP7amZvyu1NVDjgDcDFaAH2I7Yde8KoA84B/hjnmVKksZEkiQ3AbMGny9yzdWWwEMDbj9M/I4Z7IPpwfTp9RYrb9Pk+Xqaea1Gj82zLpWnUXB6DvgQWa++mwC8lQhU84i/DCuBXwFfA84Dlo2wUklSa2uFBe2npQfLli2r8xtuCUOPAi0ZwVs281qNHtvo/qHu0+jlOeK6FvgXRrs/3iTgYCJQzQE2BV4AFgD9wAXAM6N6B0lSOxjf+CEj9giw9YDbW6XnRugkYPmgc8vT80W+VqPH1rt/qPtWAC9lODc4PDS6PRaq08xrM3w/1O3BR6P7hzuWAu8ifnzzOCYy0mC1DjAX+Hla1cXAXwKXECFr0/TrmRisJKlrFLigfWKSJPcnSTJzwIL2XbxasN2uFlyV5PN5d86xPiTvhOR/IXmeWJC+DJKfQnIUJFNaoEYPDw8Pj+KPMha0AxwJfJdYgvIzYrnJsOovaJfK8yrgWGIU6u3AFOBR4Gxiyu8KYHVp1UmSylDGgnaAi9JDajuvJhajV4ADiL8si4EfEIHqOmJiU5KkgVphQbvUMrYh2iVUgH2IFVn3AN8kAtVN5ZUmSWoThit1vR2JMFWhNrb7W6JJWz9wZzllSZLalOFKXekN1ALVrum5G4BPE4HqvpLqkiS1P8OVusZsal3SdyTWS10FHE8sTH+4vNIkSR3EcKWONR7Yl1qg2hpYBVwGfAs4F3iitOokSZ3KcKWOMhE4kAhUc4kr/lYAvwQ+R3RJ/1Np1UmSuoHhSm1vKtF7qkL0otoYeB64kFg/dVF6W5KksWC4UluaRnSorQBHAesRI1LnEYFqITFiJUnSWDNcqW1sBBxDBKrDiBGrx4l9+/qBy4k1VZIklclwpZa2KbF2qgIcBEwCHgL+lQhUV2OXdElSazFcqeVsSa1L+n7ExpT3At8hAtWNxI6ZkiS1IsOVWsJ21Jp6vjk9dwfwVSJQ3VZSXZIkNctwpdK8nlqg2j09twj4LBGofl9SXZIkjYbhSmNqT2pNPXcm1ktdC3yc6JK+uLzSJEnKheFKhRoH7E0tUM0AVgO/Br4HnAM8VlJtkiQVwXCl3E0A3kYEqnnA5sBLwCXAl4DzgSdLq06SpGIZrpSLycAhRKCaA2wCLAcuJtZPXQg8W1p1kiSNHcOVRmxd4HAiUB0NbAA8Q4xM9RH7+b1YWnWSJJXDcKWmbEAEqQoRrNYFlgH/Q4xQXQqsLK06SZLKZ7hSQ5sQU30VYupvMvBH4GdEoLoSWFNadZIktRbDlYa0ObEYvUIsTp8APAB8nwhU12OXdEmShmK40stmUNt2Zp/03N3AKUSguqWcsiRJaiuGqy63E7UeVG9Kz90C/CMRqO4uqS5JktqV4aoL7U5t25nXp+euA04guqTfX1JdkiR1AsNVFxgH7EVthGp7YgH6lcAPiS7pj5RWnSRJncVw1aHGA2+l1iV9K6JFwqXA14FzgaWlVSdJUucyXHWQScBB1Lqkb0Y08VwAnAhcQDT5lCRJxTFctbmpwGFEoDoG2Ah4jghS/cT2M8tLq06SpO5juGpD6wFHEYHqSGAa8BSxGL2f2CD5pdKqkySpuxmu2sTGwLFEoHo7MWL1GHAGEah+DawuqzhJkvQyw1ULezUwlwhUBxL/sZYA/0IEqmuBtaVVJ0mShmK4ajFbU+uSvi9x1d/vgW8RgWpReaVJkqQMDFctYAdqTT1np+duA74M9AF3lFSXJElqnuGqJLtSC1RvSM/9hmiZ0A/8oaS6JEnS6BiuxtAsal3SX0usl7oa+BgRqB4qrzRJkpQTw1WBxgP7UAtU2xBX9F0GfIfYdubx0qqTJElFMFzlbCJwABGo5gKvAVYAC4HPA+cBfyqrOEmSVDjDVQ6mEL2nKkQvqlcBzwMXEdN9F6a3JUlS5zNcjdA04AgiUB0FrA88TYxM9QO/JEasJElSdzFcNWFDYv++CrGf3zrAE8BZRKC6DFhVWnWSJKkVGK4amE6tS/rBwCTgYeDHRKC6GlhTWnWSJKnVGK6GsCUwjwhUbwUmAPcD3yWaev4GSEqrTpIktTLDVWomtaaeb0nP3QmcTASq35ZUlyRJai9dHa5eR60H1RvTczcBJxFTfveUVJckSWpfXReu3kgtUL0uPXcN8EkiUD1YTlmSJKlDdHy4GkdM81UD1UxiAfqvgVOBs4FHyypOkiR1nI4MVxOA/YlANQ/YAlgJXAJ8FTgXeLK06iRJUifrmHA1mWiVUAHmEC0UXgAuJqb7LgCeLa06SZLULdo6XK0DHE4EqqOJJp/PAucTgWoBEbAkSZLGStuFq/WJIFUhtp9ZF1gG/IIIVL8ipgAlSZLK0Hbh6nhi3dSjwL8RPaiuwC7pkiSpNbRduPo34HLgOuySLkmSWk/bhatH0kOSJKkVjS+7AEmSpE5iuJIkScqR4UqSJClHhitJkqQcGa4kSZJyZLiSJEnKkeFKkiQpR4YrSZKkHBmuJEmScmS4kiRJypHhSpIkKUeGK0mSpBwZriRJknJkuJIkScqR4UqSJClH45IkKbuGgZYCi3N4nenAshxeR3/Oz7Y4frbF8bMthp9rcfxsi5PnZ7stsOngk60WrvKyCJhVdhEdys+2OH62xfGzLYafa3H8bItT+GfrtKAkSVKODFeSJEk56tRwdVrZBXQwP9vi+NkWx8+2GH6uxfGzLU7hn22nrrmSJEkqRaeOXEmSJJXCcCVJkpSjTg5XXwFuA24FFgJblFtOR/kW8Dvi8z0b2KjccjrKXwB3AmvxMuw8HA7cA9wLnFhyLZ3kZ8ATwB1lF9KBtgYuB+4i/i34aLnldJSpwG+A3xKf7ZeKeqNOXnO1AfBs+v3xwOuBD5VXTkc5FLgMWA18Iz33mfLK6SivI4LVvwInEP1YNDITgN8DbwceBm4EeolfWhqd/YHngTOAXUuupdNsnh43A+sDNwFz8ec2D+OAacTP7iTgaiK8Xp/3G3XyyNWzA76fBnRsiizBQiJYQfxQblViLZ3mbmKkRaO3FzFidT+wEvgvYE6pFXWOK4Gnyi6iQz1KBCuA54h/E7Ysr5yOkhDBCiJcTaKgbNDJ4Qrga8BDwLuAz5dcS6f6W+DisouQhrAl8fe/6mH8JaX2MgN4I3BDyXV0kgnEcqEngEso6LNt93D1K2LOf/BR/b/TzxHz12cCHymjwDbW6LOF+HxXE5+vssvy2UrqbusBfcDHeOVMjEZnDbAHMeOyFwVNa08s4kXH0CEZH3cmcBHwhQJr6TSNPtv3AUcDB+OUa7Oy/txqdB4h/ueqaqv0nNTqJhHB6kygv+RaOtXTxIUDh1PAhRntPnJVz44Dvp9DXN2mfBwOfBo4Fnih5Fqk4dxI/DswE5gMvBM4r9SKpMbGAT8l1lp9p+RaOs2m1K5uX4e42KWQbNDJVwv2ATsRV14tJq4U9P9a83EvMAV4Mr19PV6JmZd5wHziH4GnibUBh5VaUXs7Evgusc7iZ8Q6TI3eWcABwHTgcWJW4KdlFtRB9gOuAm4nfn8BnETMvmh0dgP+nfj3YDzwP8CXi3ijTg5XkiRJY66TpwUlSZLGnOFKkiQpR4YrSZKkHBmuJEmScmS4kiRJypHhStJAmxDtH24FHiPal9xKtIUY641j5xIbrld9mZE1YJ3B8E0CdyE2Ib8HuA/4EsX8u1jvz/JrYFYB7ympJIYrSQM9SWwNsQfwI+CfB9xeW+d5I1Vvl4jBgeTzxNZBeVmHaCr6daIn3huI7TA+muN7VBX9Z5HUQgxXkrKaAPwYuBNYSIQTgO2BBcBNRPPDndPzM4hRoduAS4Ft0vP/RgS3G4BvDvP8fYgdAL5FjJxtnz7vHelrzAauBX4L/AZYP32/q4Cb02OfBn+evwauSf8sELsNfAT4VHr7i8AJAx5/R/oeAOek9d4JfHDAY54nGpX+lmiu++oMf5aBDgWuS+v/X2J/OYgAeBfxWX67wZ9LUskMV5Ky2hH4ATGV9jRQSc+fBhwHvIkIIz9Mz88nuiHvRuyR9v0Br7UVETo+MczzryVGlT5FjJrdN+C5k4H/JkaYdiem114kdrl/O7An8FeD3m8ouxABaaD7iNC40Z8//BX+Nq13FnA8MZ0KMI0IVbsDVwIfaPBnGWg68I/pn2dPYBHx+WxCdO7fhfgsv9qgNkkla/eNmyWNnQeIkReIUDKDGFnZhxhlqZqSft0b6Em//zkxSlX1v8Tu9PWeP5ydgEeJvQMBnk2/TgNOJQLMGuC1DV5nNI4nAg/E5tA7ElOqK4EL0vM3EWEvq7cQU4fXpLcnE6NYzwAriO1lLhjw+pJalOFKUlYvDfh+DTHCM54Yxdqjyddann4d6fOH8nFin7vd09dd0eDxdwH7Dzq3HRGSngZW88rR/anp1wOI0aW9ianEXw+4bxVQ3VNsDc39GzsOuAToHeK+vYCDianEjwAHNfG6ksaY04KSRuNZYkTrL9Lb44hwAzEd9s70+3cR66Gaef5zxFqqwe4BNifWXZE+ZiKwITGitRZ4D7FGrJ4ziU1yq1ftrUNMJX4hvf0gMT1H+nVm+v2GwJ+IYLUzMeLUyHB/loGuB/YFdkhvTyNG39ZL3/MiIkDuPuSzJbUMw5Wk0XoX8HfEIu47gTnp+eOA9xOLsN/D8FfhDff8/yLWKd1CLAKvWkmsqZqfPucSYuToh8DfpOd2pjY6NpwXiYXmnwN+DywjpuTOTO/vA16V1vSR9DEQi+8nAncTC82vb/A+9f4sAy0F3gecRXxm16V/jvWJqcDbgKuJdViSWti4JEkaP0qSOt9c4DvAgcDikmuR1MYMV5IkSTlyWlCSJClHhitJkqQcGa4kSZJyZLiSJEnKkeFKkiQpR4YrSZKkHP1/T+MRvZMI7/UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pyplot.figure(figsize=(10, 7))\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "\n",
    "qqplot(data=expon.rvs(loc=0, scale=1 / 1, size=1000), line='q', ax=ax)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что совсем не похоже на нормальное распределение.\n",
    "\n",
    "Итак, Q–Q plot — это инструмент визуализации, который помогает нам в проверке сложной гипотезы принадлежности нормальному распределению. \n",
    "\n",
    "Плюсы метода:\n",
    "\n",
    "- Графически позволяет проиллюстрировать принадлежность выборки нормальному распределению; \n",
    "\n",
    "Минусы метода:\n",
    "\n",
    "- Нет никакого критерия. Непонятно, в какой момент график еще похож на прямую, а в какой нет?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "\n",
    "## Критерий согласия на практике: нужен ли он для t-test?\n",
    "\n",
    "\n",
    "В данной части лекции мы постараемся ответить на вопрос: могут ли помочь критерии согласия для t-test?\n",
    "\n",
    "Как мы уже знаем  из прошлых лекций, нормальность данных никогда не нужна была для t-test. Но не все об этом знают! Поэтому многие аналитики любят использовать такую процедуру:\n",
    "\n",
    "- Сначала мы проверяем данные на нормальность. \n",
    "- Если тест не отвергся мы считаем, что данные нормальны и t-test можно применять.\n",
    "    - А если отвергся, то t-test неприменим.\n",
    "    \n",
    "Давайте это проверим! Как именно? С помощью Монте-Карло! **Но только мы проверим \"наоборот\"**: мы будем запускать t-test только тогда, когда Шапиро отверг нормальность данных!\n",
    "\n",
    "В качестве распределения выборки возьмем экспоненциальное распределение."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Процент отвержений данных на нормальность:  100.0%\n",
      "FPR: 0.054\n",
      "CI=(0.04162131372306272, 0.06979215484605245)\n"
     ]
    }
   ],
   "source": [
    "numpy.random.seed(35)\n",
    "N_exps = 1000\n",
    "sample_size = 1000\n",
    "bad_cnt=0\n",
    "alpha=0.05\n",
    "\n",
    "mean=10\n",
    "dist = expon(scale = mean)\n",
    "sz = 0\n",
    "\n",
    "for i in range(N_exps):\n",
    "    # Генерирую выборку\n",
    "    sample = dist.rvs(sample_size)\n",
    "\n",
    "    # Проверяем выборку на нормальность\n",
    "    if shapiro(sample).pvalue > 0.05 :\n",
    "        continue\n",
    "        \n",
    "    # Мы попали сюда только тогда, когда отвергся критерий о нормальности данных\n",
    "    # Запускаю критерий и считаю p-value\n",
    "    pvalue = ttest_1samp(sample, popmean=mean).pvalue\n",
    "\n",
    "    # Проверяю, что pvalue < alpha\n",
    "    bad_cnt += (pvalue < alpha)\n",
    "    sz += 1\n",
    "\n",
    "print(f\"Процент отвержений данных на нормальность:  {round(sz/N_exps * 100, 0)}%\")\n",
    "print(f\"FPR: {round(bad_cnt / sz, 4)}\")\n",
    "print(f\"CI={proportion_confint(count = bad_cnt, nobs = sz, alpha=0.05, method='wilson')}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Что мы видим? Критерий все также ошибается в 5% случаев! Критерий Шапиро отверг нормальность, а t-test все равно работает! А значит мы показали, что критерий согласия бесполезен!\n",
    "\n",
    "----\n",
    "\n",
    "\n",
    "Но что, если выборка маленькая? В прошлый раз мы говорили, что нужно провести Монте-Карло.\n",
    "Но если вы не можете этого сделать? Например, у вас нет исторических данных, и выборка только начала собираться. Может ли помочь процедура описанная выше?\n",
    "\n",
    "\n",
    "**То есть в отличие от примера выше, мы будем проверять критерий на маленьких выборках!** Проверим ее на Монте-Карло. Для честности будем смотреть только те исходы, когда критерии согласия не отверглись."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Критерий согласия не отвергся для теста и контроля в 84.0% случаев\n",
      "FPR: 0.124\n",
      "CI=(0.11709147118543192, 0.1311964857651455)\n"
     ]
    }
   ],
   "source": [
    "numpy.random.seed(35)\n",
    "N_exps = 10000\n",
    "sample_size = 5\n",
    "bad_cnt=0\n",
    "alpha=0.05\n",
    "\n",
    "mean=10\n",
    "dist = expon(scale = mean)\n",
    "sz = 0\n",
    "\n",
    "for i in range(N_exps):\n",
    "    # Генерирую выборку\n",
    "    sample    = dist.rvs(sample_size)\n",
    "\n",
    "    # Проверяем выборку на нормальность\n",
    "    if shapiro(sample).pvalue < 0.05 :\n",
    "        # не идем дальше, если криетрий отвергся\n",
    "        continue\n",
    "        \n",
    "    # Запускаю критерий и считаю p-value\n",
    "    pvalue = ttest_1samp(sample, popmean=mean).pvalue\n",
    "\n",
    "    # Проверяю, что pvalue < alpha\n",
    "    bad_cnt += (pvalue < alpha)\n",
    "    sz += 1\n",
    "\n",
    "print(f\"Критерий согласия не отвергся для теста и контроля в {round(sz/N_exps * 100, 0)}% случаев\")\n",
    "print(f\"FPR: {round(bad_cnt / sz, 4)}\")\n",
    "print(f\"CI={proportion_confint(count = bad_cnt, nobs = sz, alpha=0.05, method='wilson')}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как мы видим, критерий согласия тут не помог.\n",
    "\n",
    "**Мораль:** критерии согласия никогда не нужны для t-test. В случае, если вы не можете запустить Монте-Карло, **то опираться на критерии согласия вы также не можете!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Итог\n",
    "\n",
    "На этом занятии мы рассмотрели с вами разные критерии согласия: \n",
    "- Простые критерии:\n",
    "    - В этом случае мы разобрали, как работает критерий Колмогорова.\n",
    "        - Узнали, что он не работает в случае дискретных распределений.\n",
    "- Сложные. Здесь мы разобрали разные критерии для проверки принадлежности нормальному распределению:\n",
    "    - Критерий Колмогорова с поправкой Лиллиефорса\n",
    "    - Критерий Шапиро-Уилка\n",
    "    - Метод для визуализации принадлежности QQ-plot.\n",
    "- А также показали, что критерии согласия могут быть **вредными для t-test**\n",
    "\t- в случае больших выборок при отвержении гипотезы о нормальности вы можете ошибочно отказаться от применения t-test, но t-test мы можем применять даже в случае не нормальных данных!\n",
    "\t- в случае маленьких выборок даже если гипотеза о нормальности НЕ отвергается, t-test применять все равно нельзя!"
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