{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<center>\n",
    "\n",
    "# R для тервера и матстата\n",
    "## Максимальное правдоподобие\n",
    "\n",
    "<center>\n",
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars/sem_4/M_MPlain_grande.png\" height=\"200\" width=\"350\"> \n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Данный ноутбук является конспектом по курсу «R для теории вероятностей и математической статистики» (РАНХиГС, 2019). Автор ноутбука - [вот этот парень по имени Филипп.](https://vk.com/ppilif) Если у вас для него есть деньги, слава или женщины, он от этого всего не откажется. Ноутбук распространяется на условиях лицензии [Creative Commons Attribution-Share Alike 4.0.](https://creativecommons.org/licenses/by-sa/4.0/) При использовании обязательно упоминание автора курса и аффилиации. При наличии технической возможности необходимо также указать активную гиперссылку на [страницу курса.](https://fulyankin.github.io/R_probability/) На ней можно найти другие материалы. Фрагменты кода, включенные в этот notebook, публикуются как [общественное достояние.](https://creativecommons.org/publicdomain/zero/1.0/)\n",
    "\n",
    "-------------------------------\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "В прошлый раз мы с вами поговорили точечные оценки, их свойства и доверительные интервалы. Также мы немного вспомнили метод моментов, который помогает эти самые точечные оценки получать. Сегодня мы во всех подробностях обсудим другой метод получения точечных оценок, __метод максимального правдоподобия.__\n",
    "\n",
    "Метод максимального правдоподобия — это основная лошадка современной статистики. Функция правдоподобия встречается абсолютно во всех областях от эконометрики и байесовской статистики до нейронных сетей и рекомендательных систем. Из-за этого очень важно как следует понять как она устроена. В этой тетрадке именно этим мы и займёмся. Итак, сегодня в программе: \n",
    "\n",
    "* Что такое метод максимального правдоподобия, вырабатываем интуицию \n",
    "* Решаем задачу про конфеты и смотрим на свойства оценок максимального правдоподобия \n",
    "* Из метода максимального правдоподобия на нас неожиданно выпрыгивает информация Фишера, разбираемся с тем почему эта штука называется информацией Фишера\n",
    "* Решаем несколько задачек\n",
    "* Строим тест отношения правдоподобий __(НЕ ПУТАТЬ С ЛЕММОЙ Неймана-Пирсона из ваших лекций, где тоже фигурировало отношение правдоподобий! Это разные вещи!)__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "library(\"ggplot2\")  # Пакет для красивых графиков \n",
    "library(\"grid\")     # Пакет для субплотов\n",
    "\n",
    "# Отрегулируем размер картинок, которые будут выдаваться в нашей тетрадке\n",
    "library('repr')\n",
    "options(repr.plot.width=4, repr.plot.height=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# В этом блоке написаны несколько функций, которые рисуют красивые картинки для проверки гипотез.\n",
    "# Можно не обращать на них внимание :) \n",
    "\n",
    "# Область, которую надо будет закрасить на графике \n",
    "limitRange <- function(fun, min, max) {\n",
    "    function(x) {\n",
    "        y <- fun(x)\n",
    "        y[x < min  |  x > max] <- NA\n",
    "        return(y)\n",
    "    }\n",
    "}\n",
    "\n",
    "\n",
    "# Эта страшная функция нужна для карсивых картинок для хи-квадрат распределения\n",
    "chi_stat_picture <- function(chi_stat, n, alpha =0.05, alternative = 'two-sided'){\n",
    "    # Опции для размеров графика\n",
    "    options(repr.plot.width=6, repr.plot.height=3)\n",
    "    \n",
    "    # Какие области надо закрасить (зависит от алтиернативы)\n",
    "    if(alternative == 'two-sided'){\n",
    "        chi_crit1 <- qchisq(1-(alpha/2), df=n)\n",
    "        chi_crit2 <- qchisq(alpha/2, df=n)\n",
    "        dlimit_left  <- limitRange(function(x) dchisq(x, df=n), 0, chi_crit2) \n",
    "        dlimit_right <- limitRange(function(x) dchisq(x, df=n), chi_crit1, Inf) \n",
    "        }\n",
    "    if(alternative == 'less'){\n",
    "        chi_crit2 <- qchisq(alpha,df=n)\n",
    "        dlimit_left  <- limitRange(function(x) dchisq(x, df=n), 0, chi_crit2)\n",
    "        dlimit_right <- limitRange(function(x) dchisq(x, df=n), Inf, Inf)        \n",
    "    }\n",
    "    if(alternative == 'greater'){\n",
    "        chi_crit1 <- qchisq(1 - alpha,df=n)\n",
    "        dlimit_left  <- limitRange(function(x) dchisq(x, df=n), 0, 0)\n",
    "        dlimit_right <- limitRange(function(x) dchisq(x, df=n), chi_crit1, Inf)\n",
    "        }        \n",
    "      \n",
    "    # Основная картинка\n",
    "    p <- ggplot(data.frame(x=c(0, qchisq(1-(alpha/2), df=n) + 2)), aes(x = x))+\n",
    "       stat_function(fun=dchisq, args = list(df=n)) +  # вся функция \n",
    "       stat_function(fun=dlimit_left, geom=\"area\",  fill=\"blue\", alpha=0.2) +\n",
    "       stat_function(fun=dlimit_right, geom=\"area\", fill=\"blue\", alpha=0.2) +\n",
    "       geom_point(aes(x=chi_stat,y=0), color=\"red\", size=2) +\n",
    "       geom_vline(xintercept = chi_stat, size=0.3, linetype=\"dashed\", color=\"red\") +\n",
    "       annotate(\"text\", label=round(chi_stat,2), x= chi_stat, y=0.2, parse=T, size=4, color=\"darkred\")\n",
    "    \n",
    "    # Рисуем критические точки \n",
    "    if(alternative == 'two-sided'){\n",
    "       p <- p + annotate(\"text\", label=round(chi_crit1,2), x=chi_crit1+0.1, y=-0.02, parse=T, size=4) + \n",
    "                annotate(\"text\", label=round(chi_crit2,2), x=chi_crit2-0.1, y=-0.02, parse=T, size=4)\n",
    "        }\n",
    "    if(alternative == 'less'){\n",
    "       p <- p + annotate(\"text\", label=round(chi_crit2,2), x=chi_crit2-0.1, y=-0.02, parse=T, size=4)\n",
    "        }\n",
    "    if(alternative == 'greater'){\n",
    "       p <- p + annotate(\"text\", label=round(chi_crit1,2), x=chi_crit1+0.1, y=-0.02, parse=T, size=4)\n",
    "        }      \n",
    "    \n",
    "    # Немного заключительных настроек, связанных с темой и вывод на экран \n",
    "    p <- p + theme(\n",
    "             axis.text.x = element_blank(),\n",
    "             axis.text.y = element_blank(),\n",
    "             axis.ticks = element_blank(),\n",
    "             axis.title.x = element_blank(),\n",
    "             axis.title.y = element_blank()\n",
    "            )\n",
    "    \n",
    "    return(p)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 5. Аварии на угольных шахтах  \n",
    "\n",
    "В [табличке](https://yadi.sk/i/wIFZJJ3X3VdPow) лежат данные о количестве крупных аварий на английских угольных шахтах. Хочется оценить интенсивность этих аварий. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>X</th><th scope=col>year</th><th scope=col>count</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1   </td><td>1851</td><td>4   </td></tr>\n",
       "\t<tr><td>2   </td><td>1852</td><td>5   </td></tr>\n",
       "\t<tr><td>3   </td><td>1853</td><td>4   </td></tr>\n",
       "\t<tr><td>4   </td><td>1854</td><td>1   </td></tr>\n",
       "\t<tr><td>5   </td><td>1855</td><td>0   </td></tr>\n",
       "\t<tr><td>6   </td><td>1856</td><td>4   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " X & year & count\\\\\n",
       "\\hline\n",
       "\t 1    & 1851 & 4   \\\\\n",
       "\t 2    & 1852 & 5   \\\\\n",
       "\t 3    & 1853 & 4   \\\\\n",
       "\t 4    & 1854 & 1   \\\\\n",
       "\t 5    & 1855 & 0   \\\\\n",
       "\t 6    & 1856 & 4   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| X | year | count |\n",
       "|---|---|---|\n",
       "| 1    | 1851 | 4    |\n",
       "| 2    | 1852 | 5    |\n",
       "| 3    | 1853 | 4    |\n",
       "| 4    | 1854 | 1    |\n",
       "| 5    | 1855 | 0    |\n",
       "| 6    | 1856 | 4    |\n",
       "\n"
      ],
      "text/plain": [
       "  X year count\n",
       "1 1 1851 4    \n",
       "2 2 1852 5    \n",
       "3 3 1853 4    \n",
       "4 4 1854 1    \n",
       "5 5 1855 0    \n",
       "6 6 1856 4    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = read.csv('/Users/fulyankin/Yandex.Disk.localized/R/R_prob_data/coal.csv', sep=',')\n",
    "head(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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       "[1] 112"
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GYfQAABBBBAwIAAAWwAnSYRQAABBBAg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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- df$count        # наша выборка \n",
    "length(x)            # размер выборки \n",
    "qplot(x, bins=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Судя по гистограмме уместно предположить, что число аварий имеет распределение Пуассона, $Poiss(\\lambda)$. Попробуем оценить параметр $\\lambda$ методом максимального правдоподобия. \n",
    "\n",
    "Вероятность значения: $$ P(X = k) = \\frac{e^{-\\lambda} \\lambda^k}{k!}$$\n",
    "\n",
    "Логарифмическое правдоподобие: $$ \\ln L = \\sum x_i \\ln \\lambda - n \\lambda$$\n",
    "\n",
    "Производная номер один: $$ \\frac{\\partial \\ln L}{\\partial \\lambda} =  \\frac{\\sum x_i}{\\lambda}  - n $$\n",
    "\n",
    "Оценка максимального правдоподобия: $$\\hat \\lambda^{ML} = \\bar x$$\n",
    "\n",
    "А теперь всё то эе самое, но в R!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "lnL <- function(lambda, x) {\n",
    "  n <- length(x)\n",
    "  answer <- -lambda*n+log(lambda)*sum(x)\n",
    "  return(answer)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "-112"
      ],
      "text/latex": [
       "-112"
      ],
      "text/markdown": [
       "-112"
      ],
      "text/plain": [
       "[1] -112"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "-188.39111148695"
      ],
      "text/latex": [
       "-188.39111148695"
      ],
      "text/markdown": [
       "-188.39111148695"
      ],
      "text/plain": [
       "[1] -188.3911"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Пара значений функции\n",
    "lnL(1, x)\n",
    "lnL(0.5, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Кстати говоря, можно было не делать все эти расчёты и вбить функцию правдоподобия вот так: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "-226.80879194192"
      ],
      "text/latex": [
       "-226.80879194192"
      ],
      "text/markdown": [
       "-226.80879194192"
      ],
      "text/plain": [
       "[1] -226.8088"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lnL_2 <- function(lambda, x) {\n",
    "  answer <- dpois(x = x, lambda = lambda)\n",
    "  return(sum(log(answer)))\n",
    "}\n",
    "\n",
    "lnL_2(1, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Точка на выходе получилась другой, потому что в ручном варианте мы избавились от всех лишних констант. Тут они остались. Если мы будем максимизировать `lnL_2` вместо `lnL`, мы получим тот же результат. Но таскать за собой константы не очень хочется. Иногда они портят процедуру сходимости, поэтому мы будем использовать ручной вариант. __В домашках, в тех местах, где сложно вбить функцию правдоподобия в явном виде (например, гамма-распределение), используйте вариант с `lnL_2`.__  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Давайте посмотрим как выглядит наша функция правдоподобия на картинке. Мы ещё никогда не смотрели на неё на реальной выборке. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Zo0acwXyGES5M+fX3744Qf18nPmzBm1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\nYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda = seq(0.1, 10, 0.1)\n",
    "likelihood = lnL(lambda, x)\n",
    "qplot(lambda, likelihood, geom='line')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Ещё давайте посмотрим небольшую гифку с тем, как эта функция правдоподобия накапливается из отдельных наблюдений.\n",
    "\n",
    "![Гифка](https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars_2019/gif_creator/animation_likelihood.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Давайте найдём оценку максимального правдоподобия. Пакет позволяет. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "--------------------------------------------\n",
       "Maximum Likelihood estimation\n",
       "Newton-Raphson maximisation, 4 iterations\n",
       "Return code 1: gradient close to zero\n",
       "Log-Likelihood: -89.04906 \n",
       "1  free parameters\n",
       "Estimates:\n",
       "     Estimate Std. error t value Pr(> t)    \n",
       "[1,]   1.7054     0.1234   13.82  <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "--------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result <- maxLik(lnL, start=2, x=x)\n",
    "summary(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.70535714285714"
      ],
      "text/latex": [
       "1.70535714285714"
      ],
      "text/markdown": [
       "1.70535714285714"
      ],
      "text/plain": [
       "[1] 1.705357"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# сверимся с теорией! Оценка получилась хорошей :) \n",
    "mean(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Вытащим оценку в отдельную переменную\n",
    "lambda_hat <- result$estimate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Оценка есть. Теперь хотим доверительный интервал. Сначала построим его вручную, чтобы закрепить теорию. Для этого нам нужна вторая производная :\n",
    "\n",
    "$$ \\frac{\\partial^2 \\ln L}{\\partial \\lambda^2} =  -\\frac{\\sum x_i}{\\lambda^2} $$\n",
    "\n",
    "В этой задачке только один параметр. Поэтому матрица гессе это только одна единственная производная. Давайте найдём оценку дисперсии для нашей $\\hat \\lambda$: \n",
    "\n",
    "$$\n",
    "- H = \\frac{\\sum x_i}{\\lambda^2}\n",
    "$$\n",
    "\n",
    "$$\n",
    "- E(H) =  \\frac{n}{\\lambda}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0152264030656858"
      ],
      "text/latex": [
       "0.0152264030656858"
      ],
      "text/markdown": [
       "0.0152264030656858"
      ],
      "text/plain": [
       "[1] 0.0152264"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Первая оценка: \n",
    "1/(sum(x)/lambda_hat^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0152264030634552"
      ],
      "text/latex": [
       "0.0152264030634552"
      ],
      "text/markdown": [
       "0.0152264030634552"
      ],
      "text/plain": [
       "[1] 0.0152264"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Вторая оценка: \n",
    "1/(length(x)/lambda_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "\t<tr><td>0.01523463</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{l}\n",
       "\t 0.01523463\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| 0.01523463 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]      \n",
       "[1,] 0.01523463"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Оценка из пакета: \n",
    "-1*1/result$hessian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Давайте попробуем воспользоваться этой оценкой. Мы с вами помним, что оценка максимального правдоподобия довольно няшная. Она имеет асимптотически нормальное распределение: \n",
    "\n",
    "$$\\hat \\lambda \\sim N(\\lambda, 0.015)$$\n",
    "\n",
    "Давайте построим для неё, отталкиваясь от этой информации доверительный интервал."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Параметр lambda с вероятностью 95% лежит между 1.463441 и 1.947273"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "\n",
    "z_alpha = qnorm(1 - alpha/2)\n",
    "\n",
    "se = sqrt(-1*1/result$hessian)\n",
    "\n",
    "lambda_left  = lambda_hat - z_alpha*se\n",
    "lambda_right = lambda_hat + z_alpha*se\n",
    "cat('Параметр lambda с вероятностью 95% лежит между',lambda_left, 'и',lambda_right)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Обратите внимание, что интервал получился довольно коротким. Это сигнализирует о высокой точности оценки. Давайте посмотрим с какой вероятностью в следующем году произойдёт какое количество катастроф, то есть построим прогноз для наших угольных шахт:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.18</li>\n",
       "\t<li>0.31</li>\n",
       "\t<li>0.26</li>\n",
       "\t<li>0.15</li>\n",
       "\t<li>0.06</li>\n",
       "\t<li>0.02</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.18\n",
       "\\item 0.31\n",
       "\\item 0.26\n",
       "\\item 0.15\n",
       "\\item 0.06\n",
       "\\item 0.02\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.18\n",
       "2. 0.31\n",
       "3. 0.26\n",
       "4. 0.15\n",
       "5. 0.06\n",
       "6. 0.02\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.18 0.31 0.26 0.15 0.06 0.02"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f <- 0:5\n",
    "round(exp(-lambda_hat)*lambda_hat^f/factorial(f),2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Вероятнее всего на шахте произойдёт две катастрофы. Надо быть готовым к этому. \n",
    "\n",
    "На практике распределение Пуассона часто используют во всемирной организации здравоохрания. У каждого вируса гриппа есть свои особенности и нельзя привить людей сразу от всех недугов. Поэтому с помощью распределения Пуассона пытаются прогнозировать какие разновидности гриппа будут самыми популярными. Вакцину для прививок специфицируют именно под эти разновидности. Ясное дело, что они оценивают на основе распределения Пуассона более сложные модели. Например, Пуассоновскую регрессию. __Если захотите со мной ещё факультативов, поговорим про неё в будущем.__ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Остался последний нюанс. Выше мы сказали, что если функция плотности $f(x \\mid \\theta)$ удовлетворяет условиям регулярности, то тогда для любой несмещённой оценки $\\hat \\theta$ выполняется:\n",
    "\n",
    "$$\n",
    "I(\\theta) =  E\\left( \\frac{\\partial^2 \\ln L}{\\partial \\theta^2}  \\right) = E\\left[ \\left( \\frac{\\partial \\ln L}{\\partial \\theta} \\right)^2  \\right],\n",
    "$$\n",
    "\n",
    "то есть вторая производная является ничем иным как информацией Фишера. Давайте убедимся в этом на примере распределения Пуассона. Для простоты будем считать, что у нас есть только одно наблюдение и \n",
    "\n",
    "$$\\ln L = \\ln f(x,\\lambda).$$ \n",
    "\n",
    "Если мы откроем семинары/лекции или ручками найдём информацию Фишера для распределения Пуассона, мы увидим, что:\n",
    "\n",
    "$$\n",
    "J(\\lambda) = \\frac{1}{\\lambda}\n",
    "$$\n",
    "\n",
    "Это совпадает с $-E(H)$ для одного наблюдения. __Остановитесь! И задумайтесь о том в чём смысл информации Фишера, при чём тут вторая производная и почему это информация.__ Если вы смогли ответить на эти вопросы, двигайтесь дальше. Если не смогли, то перечитайте начало блокнота. Если вы всё ещё ничего не поняли, пишите в лс :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 6. Задача про наркотики, сбор статистики"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 7. Тест отношения правдоподобий\n",
    "\n",
    "Метод максимального правдоподобия очень распространён. Он используется практически везде. Ещё одноим его полезным своством является то, что с его помощью можно проверять гипотезы. Можно просто брать и смотреть насколько они правдоподобны с точки зрения собранной выборки. \n",
    "\n",
    "Давайте посмотрим на ситуацию с шахтами. Нарисуем на картинке функцию правдоподобия, а также точку оптимума. Она будет красной. Кроме неё, нарисуем ещё одну синюю точку. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GnTpnL+/Hk7FJ1lJAFLEqAANqFZDh06JJcuXeL6rwnsmWVoBNKlSyezZs2S6tWr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\nQAImEPg/DVg1gATm3lwAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda = seq(0.1, 10, 0.1)\n",
    "likelihood = lnL(lambda, x)\n",
    "\n",
    "df_L = data.frame(lambda=lambda, likelihood = likelihood)\n",
    "\n",
    "ggplot(df_L, aes(x=lambda))+\n",
    "    geom_line(aes(y=likelihood)) +\n",
    "    geom_point(aes(x=lambda_hat ,y=lnL(lambda_hat, x)), color=\"red\", size=2) +\n",
    "    geom_point(aes(x=1 ,y=lnL(1, x)), color=\"blue\", size=2) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "По выборке мы получили в качестве оптимума красную точку. Любая оценка, полученная по выборке - случайная величина. А что, если наши данные просто так выпали, что оптимум в красной точке, а на самом деле он в синей, и $\\lambda = 1$.\n",
    "\n",
    "Тест отношения правдоподобий позволяе проверить гипотезы о любых ограничениях на параметры, заданные внутри модели. Нампример, в нашей ситуации гипотеза \n",
    "\n",
    "$$\n",
    "H_0: \\lambda = 1\n",
    "$$\n",
    "\n",
    "Накладывает ограничение на параметр $\\lambda$. Если значение правдоподобия в синей точке не очень сильно отличается от значения в красной точке, мы можем сказать, что данные не противоречат гипотезе и она не отвергается. Осталось только понять как будет распределено расстояние между правдоподобиями. Это же тоже случайные величины."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Оказыватеся, что это расстояние между правдоподобиями распределено как\n",
    "\n",
    "$$\n",
    "LR = 2\\cdot(\\ln L(\\hat \\theta_{ML}) - \\ln L(\\theta_0)) \\sim \\chi^2_q,\n",
    "$$\n",
    "\n",
    "где $q$ это количество ограничений. Проверка любой параметрической гипотезы благодаря методу максимального правдоподобия сводится к простому рецепту:\n",
    "\n",
    "1. Оцениваем модель без ограничений. \n",
    "2. Оцениваем модель с ограничением, которое на неё накладывает $H_0$.\n",
    "3. Смотрим как сильно отличаются правдоподобия. \n",
    "\n",
    "Этот рецепт называется __тестом отношения правдоподобий.__ Кстати говоря, этот тест хорош ещё и тем, что в случае простых гипотез, на его основе можно построить критерий максимальной мощности. Про это говорит лемма Неймана-Пирсона, которая была у вас в лекциях. Но о ней мы поговорим в другой раз.  Сейчас давайте попробуем воспользоваться тестом отношения правдоподобий и проверить гипотезу о том, что $\\lambda = 1$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Найдём наблюдаемое значение статистики:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "45.9018806790865"
      ],
      "text/latex": [
       "45.9018806790865"
      ],
      "text/markdown": [
       "45.9018806790865"
      ],
      "text/plain": [
       "[1] 45.90188"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_0 = 1\n",
    "LR_obs = 2*(lnL(lambda_hat, x) - lnL(lambda_0, x))\n",
    "LR_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь критическое значение. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "5.02388618731488"
      ],
      "text/latex": [
       "5.02388618731488"
      ],
      "text/markdown": [
       "5.02388618731488"
      ],
      "text/plain": [
       "[1] 5.023886"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "qchisq(1 - alpha/2, df = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим для этого добра картинку по аналогии с теми, которые были в тетрадке про гипотезы. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WQVAQQQQAABBBCwWCAQAXQyNdAmgGYwFYtLI1lDAAEEEEAAAQQcEHA6gDY3EfbU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\nNoH/D6HqKFt8yVk6AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chi_stat_picture(LR_obs, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Наблюдаемое значение статистики попадает глубоко в хвост. Получается, что расстояние между двумя правдоподобиями слишком большое, и гипотеза об ограничении отвергается. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 8. Толи нормальные толи равномерные весы "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Решим ещё одну задачку. Пусть Ира раздобыла два золотых слитка массой $m$ каждый (для неё это вообще не проблема, её отец же король, а она принцесса). Также она раздобыла весы, которые работают с погрешностью. \n",
    "\n",
    "Сначала Ира положила на весы первый золотой слиток и получила в результате взвешивания $m + \\varepsilon_1$, где $ \\varepsilon_1$ - случайная величина, ошибка первого взвешивания. Затем Ира положила на весы сразу оба слитка и получил в результате взвешивания $2m + \\varepsilon_2$, где $ \\varepsilon_2$ - случайная величина, ошибка второго взвешивания. Оказалось, что $y_1 = 60$, $y_2 = 110$.\n",
    "\n",
    "__a)__ Теперь Ира хочет с помощью метода максимального правдоподобия оценить вес слитка $m$ и погрешность весов $\\sigma$, если ошибки не зависят друг от друга и при этом \n",
    "\n",
    "$$\\varepsilon_i \\sim N(0,\\sigma^2)$$\n",
    "\n",
    "__b)__ Ира хочет $80\\%$ доверительные интревалы для обоих параметров \n",
    "\n",
    "__с)__ Ира хочет проверить гипотезу о том, что $m = 70$ с помощью статистики отношения правдоподобий. \n",
    "\n",
    "__d)__ А ещё у Иры есть такая гипотеза:  $\\mu = 60$, $\\sigma = 15$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Для начала осознаем как распределена выборка. \n",
    "\n",
    "\\begin{equation*}\n",
    "\\begin{aligned}\n",
    "& y_1 = m + \\varepsilon_1 \\sim N(m, \\sigma^2) \\\\\n",
    "& y_2 = 2m + \\varepsilon_2 \\sim N(2m, \\sigma^2)\n",
    "\\end{aligned}\n",
    "\\end{equation*}\n",
    "\n",
    "Выписываем функцию правдоподобия: \n",
    "\n",
    "$$\n",
    "L = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\cdot e^{-\\frac{(y_1 - m)^2}{2 \\sigma^2}} \\cdot \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\cdot e^{-\\frac{(y_2 - 2m)^2}{2 \\sigma^2}}\n",
    "$$\n",
    "\n",
    "Прологарифмируем: \n",
    "\n",
    "$$\n",
    "\\ln L \\propto - \\ln \\sigma^2 - \\frac{(y_1 -m)^2 + (y_2 - 2m)^2}{2 \\sigma^2}\n",
    "$$\n",
    "\n",
    "Значком $\\propto$ обычно обозначают равенство с точностью до константы. Мы, когда выписывали логарифм правдоподобия, избавились от лишних констант, которые никак не влияли на решение задачи. Вбиваем функцию в R. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "-3650.69314718056"
      ],
      "text/latex": [
       "-3650.69314718056"
      ],
      "text/markdown": [
       "-3650.69314718056"
      ],
      "text/plain": [
       "[1] -3650.693"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y <- c(60, 110)\n",
    "\n",
    "lnL <- function(th, y){\n",
    "    return(-log(th[2]) - ((y[1] - th[1])^2 + (y[2] - 2*th[1])^2)/(2*th[2]))\n",
    "}\n",
    "\n",
    "# все наши параметры в векторе th\n",
    "lnL(c(2,2), y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Находим оптимум:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”Warning message in log(th[2]):\n",
      "“созданы NaN”"
     ]
    },
    {
     "data": {
      "text/plain": [
       "--------------------------------------------\n",
       "Maximum Likelihood estimation\n",
       "Newton-Raphson maximisation, 21 iterations\n",
       "Return code 1: gradient close to zero\n",
       "Log-Likelihood: -3.302585 \n",
       "2  free parameters\n",
       "Estimates:\n",
       "     Estimate Std. error t value Pr(> t)    \n",
       "[1,]   56.000      1.414  39.600  <2e-16 ***\n",
       "[2,]   10.000      9.895   1.011   0.312    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "--------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result <- maxLik(lnL, start=c(2,4), y=y)\n",
    "summary(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "При желании можно свериться с ручными оценками: \n",
    "\n",
    "\\begin{equation*}\n",
    "\\begin{aligned}\n",
    "& \\hat m = \\frac{y_1 + 2 \\cdot y_2}{5} \\\\\n",
    "& \\hat \\sigma^2 = \\frac{1}{2} \\cdot((y_1 - \\hat m)^2 + (y_2 - 2 \\hat m)^2)\n",
    "\\end{aligned}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Давайте построим $80%$ доверительный интервал для $\\sigma^2$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Estimate</th><th scope=col>Std. error</th><th scope=col>t value</th><th scope=col>Pr(&gt; t)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>56.00000 </td><td>1.414151 </td><td>39.599740</td><td>0.0000000</td></tr>\n",
       "\t<tr><td> 9.99991 </td><td>9.894662 </td><td> 1.010637</td><td>0.3121903</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llll}\n",
       " Estimate & Std. error & t value & Pr(> t)\\\\\n",
       "\\hline\n",
       "\t 56.00000  & 1.414151  & 39.599740 & 0.0000000\\\\\n",
       "\t  9.99991  & 9.894662  &  1.010637 & 0.3121903\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| Estimate | Std. error | t value | Pr(> t) |\n",
       "|---|---|---|---|\n",
       "| 56.00000  | 1.414151  | 39.599740 | 0.0000000 |\n",
       "|  9.99991  | 9.894662  |  1.010637 | 0.3121903 |\n",
       "\n"
      ],
      "text/plain": [
       "     Estimate Std. error t value   Pr(> t)  \n",
       "[1,] 56.00000 1.414151   39.599740 0.0000000\n",
       "[2,]  9.99991 9.894662    1.010637 0.3121903"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "table <- summary(result)$estimate\n",
    "table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Параметр mu с вероятностью 95% лежит между -2.68061 и 22.68043 \n",
      "Длина интервала: 25.36104"
     ]
    }
   ],
   "source": [
    "alpha = 0.2\n",
    "z_alpha = qnorm(1 - alpha/2)\n",
    "left = table[2,1] -  z_alpha*table[2,2]\n",
    "right = table[2,1] +  z_alpha*table[2,2]\n",
    "cat('Параметр mu с вероятностью 95% лежит между', left, 'и',right, '\\n')\n",
    "cat('Длина интервала:', right - left)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Теперь проверим гипотезу, что $m = 70$. Для этого будем использовать статистику отношения правдоподобий. Зафиксируем значение $\\mu$ и найдём оптимальную оценку для $\\sigma$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "--------------------------------------------\n",
       "Maximum Likelihood estimation\n",
       "Newton-Raphson maximisation, 32 iterations\n",
       "Return code 1: gradient close to zero\n",
       "Log-Likelihood: -7.214608 \n",
       "1  free parameters\n",
       "Estimates:\n",
       "     Estimate Std. error t value Pr(> t)    \n",
       "[1,]   500.03      23.73   21.07  <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "--------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu0 = 70\n",
    "\n",
    "lnL_resricted <- function(th, y){\n",
    "    return(-log(th) - ((y[1] - mu0)^2 + (y[2] - 2*mu0)^2)/(2*th))\n",
    "}\n",
    "\n",
    "result_restricted <- maxLik(lnL_resricted, start=4, y=y)\n",
    "summary(result_restricted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь можем найти наблюдаемое значение статистики и сравнить его с критическим: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EAAAQQQiCbgdACdaBtoBaIru2jFhHUIIIAAAggggEAGBIqKxOuHOAMnSu4Uxcnt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\n6j8AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "LR_obs = 2*(lnL(result$estimate, y) - lnL_resricted(result_restricted$estimate, y))\n",
    "chi_stat_picture(LR_obs, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что гипотеза отвергается. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Пришло время завершающей гипотезы о том, что одновременно  $\\mu = 60$ и $\\sigma = 15$. В обычных параметрических критериях мы не обсуждали критерий, который мог бы протестировать сразу же два ограничения. Статистика отношения правдоподобий первый из них. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu0 = 60\n",
    "sigma0 = 70\n",
    "LR_obs = 2*(lnL(result$estimate, y) - lnL(c(mu0,sigma0), y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вспоминаем, что \n",
    "\n",
    "$$\n",
    "LR = 2\\cdot(\\ln L(\\hat \\theta_{ML}) - \\ln L(\\theta_0)) \\sim \\chi^2_q,\n",
    "$$\n",
    "\n",
    "где $q$ это количество ограничений. В нашей гипотезе сразу два ограничения. Поэтому число степеней свободы, $q=2$.  Давайте найдём наблюдаемое значение статистики и критическое. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NEQ92ZzBBBAAAEEEEAAgUgFHB9Ap0ofaHuh09LSZOLEiVKzZk2577775IsvvrAv\n8YgAAggggAACCCAQBwHHB9Cp1IXD1oe6devKX//6V9GyX3PNNbJ79277Eo8IIIAAAggggAAC\nMRZwfACdai3Qtj706NFD+vfvL99//72MHj3aruYRAQQQQAABBBBAIMYCjg+gU7EF2taJO+64\nQ4444giZOXMmQ9tZFB7jJ5CVKZKZEb/jcSQEEEAAAQSSRMDxAXSqtkBr/cnNzTU3EjK0XZK8\nm1LsNHaNHyuFQwanWKkpLgIIIIAAAiKuCaAzMz2tYSmYWrVqtX9oO52tsLS0NAUVKDICCCCA\nAAIIIBA/AccH0LYLh7bCpmqyQ9t9+OGHMmnSpFRloNwIIIAAAggggEBcBFwTQKdqC7TWEh3a\nbvLkyVKvXj158MEHZdGiRXGpPBwEAQQQQAABBBBIRYGw+z1Ur1494V4aONo+0LVq1ZJkOKdE\noWjZn332Wendu7cMHTpUFi9eLDrcXahJpwzPz89nlsNQ4fxsr7+OpHLd9EMT8ktaPzMyMuiq\nFLKc7x208YH66dsnlFfUUt/vOTk5oezGtj4E9G+8vt+pnz6AQlyt9VNnME7lX+yDISspKQlm\nMwk7gNYb2JIh2S4cGvQlyzklyqVnz55y5513ym233SbarWPevHmSnh76jwz6gUWKnoB6pnrd\njJ6mZ+CPFL3fIZqG3nlRP701eJ5sAhpE8/mZbFfF3edjG2YDlTLsAHrjxo2B8o756/rBbwu6\nY8cOSYZzinmhAxxg0KBBMn/+fLOMHDlSbrzxxgB7HPhy1apVpaCgQIL9Bnbg3vzPW0C/vNSu\nXVuKiopE66fbUsany0UqV5aSlkfFrWj6RVk97RfnuB3YpQfSX6n0M3Tbtm0uLWF8i5WXlyf7\n9u2T4uLi+B7YpUerU6eO+Vu0ZcsWl5YwvsXSLyLaAq2foSTfAvqlTeteoBR2AJ0MAZYW0v4h\n1WAlGc4pEHg8Xtf+0Keddpo88MADcuKJJ0rHjh1DOqyO5IFlSGQVbqwfVJr00Y2euc//XUoa\nNZQ9RzavsPyxWKmW1M/oyrq1fkZXKbjcqJ/BOQW7lXpSP4PVCrwdnoGNdItgf4UP/ff94I4f\nt61sCzR9ev5Hrq2eU6ZMMSuuvvpq+e233/73Is8QQAABBBBAAAEEIhJwfABtW6DpF3lgPejU\nqZPcdNNN8uuvv5qbCvWbJwkBBBBAAAEEEEAgcgHHB9C0QPuuBNddd5106dJF3nvvPXnooYd8\nb8grCCCAAAIIIIAAAkELuCaApgX64Guu/cIfeeQRqV+/vhkf+u233z54I9YggAACCCCAAAII\nhCTg+ADaduHQ8WFJBwtof+gnnnhC1EfHh/7xxx8P3og1CCCAAAIIIIAAAkELuCKA1jsmdUQO\nUsUC7dq1k7vuuku2b98uOsxdYWFhxRuyFoEQBAoHXCrFfXqHsAebIoAAAggg4A4BxwfQ2gea\nETgCV8bLLrtM+vbtKytWrJBhw4YF3oEtEAggUNKyhZQ2bRJgK15GAAEEEEDAfQKOD6C1Cwfd\nN4KrmPfee68cc8wxMnv2bHn66aeD24mtEEAAAQQQQAABBA4QcHwATQv0AdfT739ycnLkySef\nlOrVq8uYMWPkk08+8bs9LyKAAAIIIIAAAggcLOD4AFpboBmB4+AL62tNo0aNzCQrOjPeFVdc\nwfTnvqBYjwACCCCAAAII+BBwfABNC7SPK+tndbdu3WT48OEmeNYg2o6l7WcXXkIAAQQQQAAB\nBBD4r4DjA2j6QIdXl//yl79I7969TTeOESNGhJcJe6W2wL59Ip5fMkgIIIAAAgikmoDjA2ha\noMOrsjrs3+TJk6Vly5by4osvytSpU8PLiL1SVqDKyNGSO4V6k7IVgIIjgAACKSzg+ACaPtDh\n197KlSvL9OnTpWbNmnLnnXfKu+++G35m7IkAAggggAACCKSIgCsCaMaBDr+2NmzY0IzModN+\nX3XVVfLdd9+Fnxl7IoAAAggggAACKSDg6AC6tLTU0wWzhHGgI6yoHTp0kHvuuUd27Ngh5513\nnnmMMEt2RwABBBBAAAEEXCvg6ADajh5BC3Tk9fPiiy+WgQMHmhZoHZlDv5iQEEAAAQQQQAAB\nBA4WcHQArf2fNTEO9MEXNpw1Y8eOle7du8s777xj+kSHkwf7IIAAAggggAACbhdwRQBNC3R0\nqmlGRobMnDlTmjZtKk888YQ899xz0cmYXFwpsPe4Y6WkxZGuLBuFQgABBBBAwJ+AKwLorKws\nf2XktRAEatSoIc8//7yZ7vvWW281rdEh7M6mKSRQfOH5sqfHqSlUYoqKAAIIIIDA7wKuCKBp\ngY5udT788MPl6aefFm2RHjx4sKxYsSK6ByA3BBBAAAEEEEDAwQKuCKBpgY5+DdSROR566CEp\nKCiQSy+9VDZs2BD9g5AjAggggAACCCDgQAECaAdetHidsg5pN2zYMFm/fr1cdtllJpiO17E5\nDgIIIIAAAgggkKwCBNDJemWS5LxuuOEGueCCC+Srr74yE60wvF2SXBhOAwEEEEAAAQQSJuCK\nAJo+0LGtPxMmTJBOnTrJ22+/LbfffntsD0buCCCAAAIIIIBAkgs4OoC2E6nQBzq2tUx9n3rq\nKWnevLlMmzZNHnnkkdgekNwdIZAz7TmpNGeuI86Vk0QAAQQQQCCaApnhZpaenvjY23Yn0Bbo\nZDifcC2Tab+0tDRjWd7TDm93xhlnyPjx46VevXrSt2/fZDr1pDsXa2hNk+4EIzyhrJWrpKRR\nI9kXx88Ca2ltIywCu3sErCkYkQuoJZ6RO9oc8LQS0XlUT018fvr3tE7+t/JM4hdoA1+va0CV\n6GS7buTk5EgynE+iPaJxfJ3VsWrVqlJWVnZQdmo8d+5cOeWUU0T7Rh922GHSq1evg7ZjxYEC\nWk/dWD/TsrOlLDdXcuP4WaBDK2odrah+HqjO/4IVUE831s9gyx/N7bR+ZnveF5UrV45mtimd\nlwZ71M/oVAEbOGvMRPItYBtnfW/x+ythB9C//fZboLxj/vrWrVvNMbRSJMP5xLzAcTiAflDt\n3LlT9u3bV+HRGjRoIM8884z069dP/vSnP8nLL78s7dq1q3DbVF+p9VJb6ouLi2Xbtm2u46hS\nVCwlu3dLYRw/C6pVqyaFhYViu2+5DjXOBapfv77s3btXtmzZEucju/Nw+fn5xrOoqMidBYxz\nqfTzU4MZ/r5HBz4vL880Puz2fG6TfAvoF+FcT+NQoJT4fhiBztDP6/rBr4k+0H6QYvCS3lD4\nt7/9TfSPhI4RvXr16hgchSwRQAABBBBAAIHkFCCATs7rkvRn1adPH9MXWn8FuOiii5hoJemv\nGCeIAAIIIIAAAtESIICOlmQK5nP55ZfL9ddfLz///LPp0rF9+/YUVEjhImd5eoBlZqQwAEVH\nAAEEEEhVgbD7QCcDmO0HaW8mTIZzSrVzGD58uGzatElmzpxpZit84YUXuIEmRSrBrvFjU6Sk\nFBMBBBBAAIEDBRzdAm1vdKMP9IEXNd7/u/fee6V3797yySefyMCBA81Nc/E+B46HAAIIIIAA\nAgjES8DRAbRtgSaAjld1qfg4esfqo48+Kt26dZP3339fhgwZ4nMUj4pzYC0CCCCAAAIIIOAc\nAUcH0LRAJ09F0240Tz75pLRv317mzZtn+kaXlpYmzwlyJggggAACCCCAQJQEHB1A2xZo+kBH\nqTZEmI1OHvDss89KmzZtZPbs2TJixIgIc2R3BBBAAAEEEEAg+QQcHUDTAp18FUonEnj++efl\nyCOPlBkzZsidd96ZfCfJGSGAAAIIIIAAAhEIODqAti3Q9IGOoAbEYNeaNWvKSy+9JE2aNJHH\nHntMHnrooRgchSwTLZC5bLlkrPom0afB8RFAAAEEEIi7gKMDaFqg415fgj5g3bp1TRB96KGH\nyoQJE+Thhx8Oel82dIZAzouzpNL8Bc44Wc4SAQQQQACBKAo4OoC2LdD0gY5ijYhiVg0bNpSX\nX35ZDjnkENGh7iZPnhzF3MkKAQQQQAABBBBIjICjA+i9e/caNbpwJKbyBHPUpk2byqxZs6Re\nvXpyzz33yCOPPBLMbmyDAAIIIIAAAggkrYArAmhaoJO2fpkTa9asmQmitVvH+PHjZcqUKcl9\nwpwdAggggAACCCDgR8AVAXRmpqNnJPdzedzz0uGHH26C6Dp16si4cePMzYXuKR0lQQABBBBA\nAIFUEnBFAE0LtDOqbPPmzfcH0Tq83eOPP+6ME+csEUAAAQQQQAABLwFXBND0gfa6okn+9Igj\njjBBdO3atWXs2LF050jy6+Xv9AoHXCrFfXr724TXEEAAAQQQcKWAKwJoWqCdVTdtEG27czz4\n4IPOKgBnawRKWraQ0qZN0EAAAQQQQCDlBFwRQNMH2nn1VmcqfOWVV0THidYAWvtFkxBAAAEE\nEEAAAScIuCKApgXaCVXt4HPU0Tn++c9/SuPGjU1XjlGjRklZWdnBG7IGAQQQQAABBBBIIgFX\nBND0gU6iGhXiqehkKxpE6w2GzzzzjNx8881SWloaYi5sjgACCCCAAAIIxE/AFQE0LdDxqzCx\nOJLOVDh79mxp2bKlvPDCC3LttdeKnaY9FscjTwQQQAABBBBAIBIBRw+grFN5p6WlSUZGRiQG\n7JsEAjoqh85Y2K9fP9M3evfu3fLoo49KTk5OEpydO09Bu8usnjtX1i/9VNKzsqTBiSdIoy5d\nJDM7O6gCl3lmAl09b56sX7Y84P671q+Xb//1L9m25gfJrlpV6rY5Rpqffrp5/wZ1MDZCAAEE\nEEAgiQQcHUDrVN60PidRbYrwVGrUqCEvvfSSXHbZZfLGG2+YYHr69OmSn58fYc7sXpHAq5f2\nlx8WLJDs6tUlKzdXlv7tEWnQvr2cNf0ZE+RWtI/3ujkdT5Lvf/k54P6rXvmnvOXpmrOvsEiq\nevq7F2zcKCVFRVL/uHbyx+dnSjbX15uV5wgggAACDhBwdBcO/Zmf/s8OqGUhnKIGy9qNo2fP\nnrJ48WI599xzZdOmTSHkwKbBCKx56y0TPHe46Ua5YvmnMuiTJdJz0l/l5yVL5L3RYwJmoftr\n8HzSSV387r9j3c+e4HmYVDmkvlz4r1dl4OJFMvjz5XLidX+R9Z8ukw/uvCvgsdgAAQQQQACB\nZBNwdACtXThogU62KhX5+Wi3jaeeekr69u0rX3/9tZx11lny448/Rp4xOewXWPzgX6Wyp9vM\n8UOvMV020tLTpdUFF0iN5od7Aut39m/n64nun+e5Th07dvK7vwba+woL5ZhLLva0OB9nstMW\n5/Y3XC+5tWrJf95409chWI8AAggggEDSCjg6gKYFOmnrVcQnpv3aJ06cKEOGDDHBswbRK1as\niDhfMvhd4MI5r8klC946qL9zWlq6ZFerGpBJ9x/c5ywpPwZ7+f3rH3+8nHLvPdLygvMPyDOj\nUiXJqVFd9nqCa4YuPICG/yCAAAIIOEAg7D7QlStXTnjxbB9o/SOeDOeTcJAonIAGrtoCnCxD\nyd1zzz2io3SMHj3adOd48cUXpVOnTlEoaeyz0BtcNSVr/azi1ff4t9WrZdlTT8uW776THp6A\nN5j3U6Uq+VJWKUvSPJ8FvvZv4rkxUZfyaZ2nq8jW1d9Lk25dJS8vr/zLPv+vllo/ywfuPnfg\nhYAC+p4P5noHzIgNTJfCdM+vObqQIhfQz1C1pH5Gbqk50OU1OMdgG3XSPBs6duaKunXrmhvM\nvv/+++BU2MqxAtOmTZM///nP5gPgueeek/PPP7BF07EFS4ITf6pXb/n2v10pTr3jduk5dkxQ\nZ1Vy1VBJa3KYPPPugpD23+MZYWXqKafKz59+Ktd8tEgaelqpSQgggAACCCSDQLDdg8Nugd66\ndWvCy2kLWVxcLDrsGSlyAW0NLPKMkFBSUhJ5ZlHM4eyzz5Zsz/BqgwYNkgs8fXXvuusuueaa\na6J4hOhnpa0n1T0jXGg9LSgoiP4BopRjo65dpW7btvLVi3+Xd+6+R3bv3Cknjxop2i/aX8o8\nprWU1aopoey/Z9cumX1Zf1m75GPpNvoOyTv8cAnls0RbotSTccL9XZngX9ORb/SXvF2e60KK\nXCDXM5qNfnZqHSVFLqCfn/pr6I4dOyLPjBzM31Bl0JiJ5F8gmPvrwm6BXu8Z1zXRSWevO9zz\nB/ijjz7iDRali6F/UHd6AqhkDVA+++wzM8zd5s2bZcCAASaQTtafS/W86tWrJ4Wefr7btm2L\n0hWKXTb6Y9Rr/S+XNW+9LRe8MtszpN2JIR0s0P4Fv/4q/7z0Mtn01dfS+dYRcsK1Q0PKXzeu\nVq2a8SRACZmuwh3q169v/phu2bKlwtdZGZqAjiKkX0i0EYIUuYB+fuoXEv28J0UuoA1k+jlN\ng6N/S+3Wpj0cAiX/TUyB9k7w6/pHNJhvCQk+TQ4fRYG2npbSOXPm7J/6W1uk+TCIDrC2mLfp\nf5nJ7D/z54ecqb/9t3tGUfn7WX+U31Z9I394eGJYwXPIJ8QOCCCAAAIIxEjA0QE0o3DEqFYk\nebaNPZNxvPbaa9LeM+mHTrii/aFpoQj+ohVu2SpzBl0hi+67/6CdqjZqZNbt9fOTfqj7//bt\nt/LSH8+V4u3b5ZwXZkpL+q8f5M4KBBBAAAFnCTg2gNafyTTRAu2sChets9W+cToih/aN1m4d\nffr0ke88I0iQAgvk1qwhvyxdKkunPCo7f/nlgB1WvjzL/P/QE3133whl/727C+WfF18qez19\nwM+fPUsade58wPH4DwIIIIAAAk4UCPsmwkQX1gbQDMuS6CuRuOPrTYVTpkyRhg0byiOPPGKC\n6Mcee0y6d++euJNyyJFPum2kvHndDfKvgX+WtoMGSE3P/QTfvvqaLHviSWnoCXKPOueP+0uy\nznOPwdwh18hRni8rXceONuuD3f+Thx+WnT//LLVbtpTPn5m2P0/vJ93G3XXQeNTer/McAQQQ\nQACBZBNwfABNC3SyVan4no/2ux01apQ0a9ZMRowYIZdeeqmMGTPGDHkX3zNx1tF01sGyklJZ\nOG68CaT17NM9Yyy3HThAOo24RdTVppLiPbJ740ZPF4z/3QgZ7P7fzZ1rstm8cqXoUlE6eYwn\nKPd8GSIhgAACCCDgFAHHBtB2lAhaoJ1S1WJ7nhdddJE0bdrUBM533HGHfOvpdzt+/HgGjvfD\nfvSfLpRWfS8QvcFvn2dYoxqeLyE6Q2D5dJhnspPrf1lXfrUcV7RH2t59t2w65mif+/d//72D\n9mMFAggggAACThdwbB9oO4wVLdBOr4LRO/8OHTrIXE+L55FHHikzZswQDapDGWM4emfinJx0\nrOfqni8etVu0qDB49leSzBWrJPPHtWHv7y9vXkMAAQQQQCCZBRwbQNMHOpmrVeLOTUfo0GHu\nTj31VFm0aJGcccYZ3FyYuMvBkRFAAAEEEHClgOMDaFqgXVkvIypUlSpVZPr06XLllVfKDz/8\nIKeffrq8/vrrEeXJzggggAACCCCAgBVwfABNH2h7KXn0FtBZAEePHi0TJ040syrqhCv33Xef\nmRbWezueI4AAAggggAACoQo4PoCmBTrUS55a2/ft21deffVVadCggUyaNMlMA77dM6EHCQEE\nEEAAAQQQCFfAsQE0o3CEe8lTb782bdrIvHnzpFOnTrJgwQLp3bu3rFq1KvUgol3iLM8gPpkZ\n0c6V/BBAAAEEEEh6AccG0IzCkfR1K6lOsFatWvL3v/9dBg8ebPpF682FOh04KXyBXePHSuGQ\nweFnwJ4IIIAAAgg4VMCxATQt0A6tcQk87YyMDDPJis5aqOmqq64SHTPajuiSwFPj0AgggAAC\nCCDgIAHHBtC0QDuoliXZqZ5zzjnyr3/9y0y88uSTT8of//hHWbfu4IlCkuy0OR0EEEAAAQQQ\nSBIBxwbQtEAnSQ1y6Gm0atVK3njjDTnzzDNl+fLl0rNnT3nrrbccWhpOGwEEEEAAAQTiKeDY\nANr+7M4oHPGsLu46lo4X/fjjj8u4ceOkoKDAjNCh03+XlJS4q6CUBgEEEEAAAQSiKuDYANp2\n4WAc6KjWh5TMbODAgWaou4YNG4r2jz7//PNl/fr1KWlBoRFAAAEEEEAgsIBjA2jbhYMW6MAX\nmS0CC7Rt21befPNN05VjyZIlctppp5mh7wLvmbpbZC5bLhmrvkldAEqOAAIIIJCyAo4NoGmB\nTtk6G7OCV69eXZ555hkzUod26dCW6VtvvVWKiopidkwnZ5zz4iypNH+Bk4vAuSOAAAIIIBCW\ngGMDaFqgw7re7BRAIC0tzYwVPWfOHGnevLlMnz6diVcCmPEyAggggAACqSbg2ADa3kRIH+hU\nq7LxKW/r1q1NF45+/frJN998Y4LoadOmxefgHAUBBBBAAAEEklrA8QE0faCTun45+uQqV64s\nEyZMMCN1ZGdny8iRI6V///6yefNmR5eLk0cAAQQQQACByAQcH0DTAh1ZBWDvwAI6VrSOEd2+\nfXuZP3++dOvWTebOnRt4R7ZAAAEEEEAAAVcKOD6ApgXalfUy6QqlQ9z94x//kFGjRsnOnTvl\nz3/+s1x33XXmedKdLCeEAAIIIIAAAjEVcHwATQt0TOsHmXsJpKenyzXXXCOvv/66tGzZUl5+\n+WU55ZRTZNGiRV5bpc7TwgGXSnGf3qlTYEqKAAIIIIDAfwUcH0DTAk1djreATgOuQbQG07/8\n8ouZeGX06NFSWFgY71NJ6PFKWraQ0qZNEnoOHBwBBBBAAIFECKSVeVI4B7bDyIWzbzT2ufnm\nm2XSpEny0UcfyYknniilpaXRyDbl89BWViyDrwYLFy4040WvWbPGDHs3depU6dKly/4MMjMz\njSem+0kieqL1Uz+ywvzYiujYbtyZ+hndq0r9jK5nRkaGybCkpCS6GadobjpMqyY+P/1XAI1v\nc3Jy/G/keTUz4BY+Nti0aZOPV+Kzevv27eZA2gKtLX87duyIz4FdfpQaNWqYfr2J/oLkFOaj\njjrKzGA4fvx40WHutEvHgAEDTF/pKlWqSL169aS4uFi2bdvmlCIl9XlWq1bNvN/tREpJfbIO\nOLn69euLDgm6ZcsWB5xt8p9ifn6+8WTypehcK/381OCZkY+i45mXl2eC5927d0cnQ5fmol/c\nggmgHduFwwZ49IF2aQ12ULH0Q+nuu++W2bNnS5MmTcxsht27d5cPPvjAQaXgVBFAAAEEEEAg\nWAHHBtC2BYo+0MFearaLtUCHDh3k7bffNjMZrlu3Ti644AK58sor+XUk1vDkjwACCCCAQJwF\nHBtA0wId55rC4YISyM3NlTFjxshrr722v09027ZtRacGd13y9BPz/L7qumJRIAQQQAABBAIJ\nODaApgU60KXl9UQKHHfccaY1+rbbbjP99wYPHiyXXXaZaMu0W1KVkaMld8pUtxSHciCAAAII\nIBC0gGMDaFqgg77GbJggAZ3++6677pIlS5aYkWJ0NsOuXbuKjtTBXeUJuigcFgEEEEAAgSgI\nODaApgU6ClefLOIioJOuvPLKK3L//feL3vSqXTxOP/10+fzzz+NyfA6CAAIIIIAAAtEVcGwA\nTQt0dCsCucVWQMffvOSSS8zIHGeffbZ8+eWXJogePny4bN26NbYHJ3cEEEAAAQQQiKqAYwNo\nWqCjWg/ILE4CderUkUcffVRmzpxphrybMWOGnHTSSaKPTLYSp4vAYRBAAAEEEIhQwLEBNC3Q\nEV55dk+ogI4T/c4778gtt9wiOumCtkSfccYZdOtI6FXh4AgggAACCAQn4NgAWlugdbYYOzVl\ncMVlKwSSR0DHML/uuuvkvffek969e5vgWftGazD922+/Jc+J+jiTvccdKyUtjvTxKqsRQAAB\nBBBwr4BjA2htgWYWQvdWzFQqWcOGDeWpp56S559/Xpo2bWq6c3Tq1Ekee+wxsV2VktGj+MLz\nZU+PU5Px1DgnBBBAAAEEYirg2ABaAwsC6JjWDTKPs0C3bt1kwYIFcscdd5gj33nnnaLr5s2b\nF+cz4XAIIIAAAggg4E/AsQE0LdD+LiuvOVVAu3VcddVVsmjRIjNqx08//SQDBw6Uvn37ysqV\nK51aLM4bAQQQQAABVwk4NoDeu3cvLdCuqooUxlugVq1aZtzoN998Uzp37iwLFy6UHj16yM03\n3ywbNmzw3pTnCCCAAAIIIBBnAQLoOINzOARCEWjVqpW8/PLL8vTTT8thhx1m+klrQH3vvffK\nzp07Q8mKbRFAAAEEEEAgSgIE0FGCJBsEYinQq1cvM1rH3XffLZUrV5aHH35YOnbsaG4+1F9j\nSAgggAACCCAQPwHHBtDcRBi/SsKRkkMgMzNTLr/8clm8eLHccMMNUlhYKLfffrucfPLJ8uqr\nr0pZWVlcTzRn2nNSac7cuB6TgyGAAAIIIJAMAo4NoPUmQr3hioRAqgnk5eXJsGHD5KOPPjI3\nGq5du1aGDBli+khrn+l4pcwVqyRjzY/xOhzHQQABBBBAIGkEHBtAawu0tsiREEhVgbp165ob\nDd99910588wzZcWKFaaFuk+fPvLBBx+kKgvlRgABBBBAIOYCjgygS0tLzc/VtEDHvH5wAAcI\nNG/eXB5//HHR1ufTTjtNli1bJhdeeKFccMEFsnTpUgeUgFNEAAEEEEDAWQKODKDtTVO0QDur\nsnG2sRVo3bq1PPvss/Laa6+JzmT44YcfyllnnSX9+vWTTz75JLYHJ3cEEEAAAQRSSMDRATQt\n0ClUUylq0ALHH3+8zJo1S/7+97/LCSecINrF4+yzzzat0kuWLAk6HzZEAAEEEEAAgYoFHBlA\na/9nTbRAV3xRWYuACnTp0sWMzqGBdPv27U2/6HPOOcfMaqgjeUScsjz3IGRmRJwNGSCAAAII\nIOA0AUcG0DoChyZaoJ1W3TjfRAhoIP3KK6+YCVk6dOhgZjU899xzRYPpd955J+xT2jV+rBQO\nGRz2/uyIAAIIIICAUwUcGUDTAu3U6sZ5J1JAZzCcPXu2/OMf/5CTTjpJtDvHxRdfbIa/037T\nenMuCQEEEEAAAQQCCzgygKYFOvCFZQsEfAnoDIYvvfSSzJ07V3r37i1ff/21XHXVVabLx8yZ\nM8V+QfW1P+sRQAABBBBIdQFHBtB2FI6srKxUv36UH4GwBdq2bWumAn/vvffk/PPPl59++slM\n0HLiiSfK5MmTZdu2bWHnzY4IIIAAAgi4WSDsmUgSeQOf/anZ9oFOT0/nhsIo1dK0tDTJyODG\nsGhwar3UlOz1s2XLljJlyhQZOXKkeXz++eflnnvukUmTJpkh8K688ko57LDDokEScR62fiby\n8yfiQiRZBmqKZ3Quir7X9fMTz+h4at2kfkbHUnPR+llWVkb9DEBq/3YH2EzSPJhlgTZKttc/\n/fRT0aG6hg4dalrKku38OB8EnCywZcsWeeyxx8x7a8OGDSYg0JsOb7rpJjOah5PLxrkjgAAC\nCCDgT0C7MdoGWn/bhR1AFxQU+Ms3pq/pzU+nnnqqXHvttfLwww+Ldumg32Z0yLOzs42nbeWP\nTq6pmYu2nFSuXFm0z35xcbHjEPQ9pUPg6Xts5cqV5vz1i+vVV19tRvCo9NnnIpXzpOzolnEr\nm36olZSUmCVuB3XxgfLy8oxlUVGRi0sZv6Jp/dTPTnufTvyO7M4j6eentvEVFha6s4BxLpV2\ne1VP6qd/eH0P5+fn+9/I82rYXTh27NgRMPNYbVC+b6b+oU/k+cSqnInIt0aNGrJr1y7eYFHA\n15+B9A+AfsFzav3UCVh0NkOdjGXq1Kmi/aUHDhwoI0aMkNn1G0nTbl0l7Zabo6AVXBbVqlUz\nf0z5whycV6CtNIDWP6ZOrZ+Byhfv1/WPrr7f+UISHfnc3FzzBY/6GR1Pfb9rAL179+7oZOjS\nXLQbVkwD6ES6cRNhIvU5dqoJaEt69+7dzfLdd9/J008/bUbx+Hzj5/Lvr76U1b+slQEDBoje\nlEhCAAEEEEAgFQQcOQqH/fmBUThSoYpSxmQSOOKII8wNhsuXL5fjjjtO8qvkmwlaTj/9dOnV\nq5foDYi0biTTFeNcEEAAAQRiIeDIANr+fEsAHYsqQZ4IBBaoWrWqtGrZSq4aMkSmTZtmWqe/\n/PJLufnmm6Vdu3Zyxx13iLZWkxBAAAEEEHCjgCMDaLpwuLEqUiYnCmj3jp49e4pOwPLRRx/J\nNddcY4ZIevLJJ6Vr165y3nnnmZkP6RPqxKvLOSOAAAII+BIggPYlw3oEEAhJoHHjxjJq1CjR\nYSZ1IpYTTjjBBNU6Ws6xxx4rt912m6xYsSKkPNkYAQQQQACBZBQggE7Gq8I5IeAAgcIBl0px\nn94HnakOhagtz6+++qoZtWPw4MFmLGm9+fC0004z04fPmDGDkR8OkmMFAggggIBTBAignXKl\nOE8EkkygpGULKW3axO9Z6U2HY8aMkWXLlpnJWU4++WT5/PPPZfjw4WbUDu3yoUPkMe64X0Ze\nRAABBBBIMgEC6CS7IJwOAm4U0AkmdDzpF198UXQipBtvvFHq1Kkjr7zyipkuXCdo0enDV69e\n7cbiUyYEEEAAAZcJODqADmaqRZddL4qDgOMFGjVqZEbrWLx4scyaNUv69u1runNov2ltoe7d\nu7foTYibNm1yfFkpAAIIIICAOwUcHUBnZoY9kaI7ryalQsBBAjqCR6dOnWTixInyxRdfmMfO\nnTub5zoMnt542K9fPzOKR0FBgYNKxqkigAACCLhdwJERqJ1IhRZot1dPypcqAjrlubZE67J+\n/Xr55z//KbNnzzb9o7WPtE7pq8PlXXTRRdKlSxfR4JuEAAIIIIBAogQc2QJtJ1KhBTpR1Ybj\nIuAR2LdPpKQk6hT169eXIZ4JWubPny/vvPOO6DB4NWvWNKN6/OlPf5KjjjrKrHvrrbfEjgkf\n9ZMgQwQQQAABBPwIODKApgXazxXlJQTiJFBl5GjJnTI1pkfTYPnWW2+Vjz/+WF577TW5+uqr\npUqVKqZbx2WXXSZt2rQxNyQuWLBA7BfrmJ4QmSOAAAIIIOARcGQAbVudaIGmDiOQGgLaZUNH\n6njggQdMH2nt3tG/f38z66GO7HHJJZfIMcccI0OHDpXXX39dmPkwNeoFpUQAAQQSJeDIPtA2\ngKYPdKKqDcdFIHEC6enp0qFDB7OMGzfOzHb473//2wTOGljron2mTz31VDOihz5WrVo1cSfM\nkRFAAAEEXCfg6ACaFmjX1UcKhEBIAhkZGXLSSSeZ5e6775ZPPvlENJieO3euzJkzxyz6OaGj\nffzhD38wNyI2aNAgpGOwMQIIIIAAAuUFHB1A0wJd/nLyfwRSV0C7eZx44olmGTt2rOnqod05\n3njjDXn//ffNMmrUKNNvWkf00GnFtdsHI3qkbp2h5AgggEC4Ao4OoLOyssItN/shgIDLBfQG\nQ11uueUW+fHHH00gPW/ePHNDoo47PWHCBKlbt64JpLWbR9euXUWH0yMhgAACCCAQSIAAOpAQ\nryOAQIUCe487Vspq1qjwtWRbedhhh8ngwYPNsmXLFjM8ng6Dp2NMP//882bRX7Q6duwo3bt3\nN8sRRxyRbMXgfBBAAAEEkkTAkQG0Ha6KFugkqUWcRkoeOT4UAAAax0lEQVQKFF94viPLrWNK\nn3feeWbRITGXLl1qxpzWcaffe+89s4wZM0a0r7QNpnXyFh0+j4QAAggggIAKODKAtuNAE0BT\niRFAIBIBvcHQjuhx++23y9q1a03rtE7gsnDhQpkxY4ZZdLvjjjtOTj75ZLO0bdtW9AZGEgII\nIIBAago4MoC2w9gRQKdmpaXUCMRKoFGjRqITtOiinzM6qocG07osWbLELDoWdX5+vhn5Q1um\ndTn88MNjdUrkiwACCCCQhAIE0El4UTglBBBIvIB+Qdfh73TR0Ts2b95sRvL44IMPzKOO8KGL\npkMOOUQ6d+5sFh1Wr2HDhokvAGeAAAIIIBAzAQLomNGSMQIIuEmgdu3acu6555pFy/Xdd9+Z\nQPrDDz80k7n84x//MFOM62uNGzc2wbTelKhdRAioVYWEAAIIuEfA0QE0E6m4pyJSEgScJqCj\ndOgyaNAgKS0tla+++ko0mNa+09rd44UXXjCLlktvSLTBtD42bdrUacXlfBFAAAEEvAQcG0DT\n/9nrKvIUgQQI5Ex7Tkpr15I9fU5PwNGT65A6vbgdd3rIkCGiNzp//vnnpmV68eLFZuzpWbNm\niS6a6tSpIyeccIKZ9KV9+/Zy9NFHCw0CyXVNORsEEEDAnwABtD8dXkMAAZ8CmStWSUkj+vpW\nBGRH7dCRO4YOHSolJSXy9ddfiwbTNqDW6cZ10ZSbmyvt2rUzQfXxxx9vnlevXr2irFmHAAII\nIJAEAmEH0NWqVUvY6esfI530wI7Lqs8TeT4Jg4jBgbVlX13LyspikHtqZWmniFZTN9bPDM/7\nriwnRyrF8bNA3+va2qsBp9OSHbHDnve3334rixYtMgG1Pmr3D11sOvLII0Vbp3V6cn1s2bKl\nKbt9PVqPGuy7sX5GyyeUfPS9rkt2dnYou7GtDwH9DNXhIqmfPoBCXG1/5dI6SvItoF3ygklh\nB9CFhYXB5B+TbXQiFa0AxcXF5g+pBtSJPJ+YFDJBmeobTF3VlBSZgA303Fo/c0r2SZlnqLfi\nOH4WqKm+/+1QlpFdocTurUPmXXjhhWbRM9m0aZPp6qETu+jweZ999plokP3cc8+ZE83LyxMd\nf1pbqrVlWx8PPfTQiAqhU5frHws+PyNi3L+zBnzafcdO9rX/BZ6EJaBflKmfYdFVuFOOp8FD\nG8f0bzzJt4Bt/PK9xe+vhB1AJ/IDQo+tgZ79I6oBSiLPJxCyk17XDyt1tZPVOOnck+1cNdjT\npKZurJ+VSkrNF614lk3/oGr9jOcx41WvtJWtR48eZtFj6ntQu31oQL1s2TJZvnz5Qa3UdevW\nNUH1//3f/4ku2g9bRwsJJbm1foZiEK1tteWZADpammKCPQ343Ph+j55S8DlpwyOegb2CnSQr\n7AA68CnEbgv9A6qtMSQEEEDArQLaSGADYx3pQ9PWrVtNy7QG03Z58803RRebtFXaBtPHHHOM\ntG7dWjTQJiGAAAIIRE/AsQE0fXiiVwnICYGwBLI8Hx+ZTGcdll2YO9WoUUO6d+9uFpvFunXr\nzIgfX3zxxf5H70ledDsNoDWQ1oBal1atWslhhx1ms+ARAQQQQCBEAQLoEMHYHAEEfhfYNX4s\nFEkgoJO06HLGGWfsP5sff/xRvvzyy/2LjlG9YMECs9iNbJ9qDax1KnINqlu0aCHaL5qEAAII\nIOBfgADavw+vIoAAAo4T0NZlXfr06bP/3Dds2GAme9FgWvtW62JH/9i/keeJ7qcjfmgwbR+b\nNWtmRkPw3o7nCCCAQCoLODKA1ps06MKRytWWsiOAQKgChxxyiOhy2mmn7d81Pz9fPv30UzOU\nngbUK1eulFWrVsm8efPMYjfU4QObN28uRx11lOjwerro8yZNmsRkaD17XB4RQACBZBVwXABt\nR94ggE7WKsV5IYCAUwR0zPcOHTqYgNj7nLVftQbTunzzzTcmqF69erWsWLHCezMz3rG2Tttp\nze2jrmMs5AOo+A8CCLhMgADaZReU4iCAAAKRCth+1Tqsnk06XOiaNWvM2NQaVOui41R///33\nJtC22+mjDuGo41xr32pdtPXaPq9Xr573pjxHAAEEHCng2ADazqjjSHVOGgEEEHCYgI6NqoGw\nLqeffvr+s9fA+qeffpLvvvvugEUD6/I3LupOevOitlA3bdrUPNrn+v+aNWvuz5cnCCCAQDIL\nOC6AthN8aJ88EgIIJE4gc9lyKfOM2FDS4qjEnQRHTriABtYa/OrSs2fPA85n8+bNol0/dNGA\nWpf//Oc/psVaRwkpn6pWrWr6VWvfau9Fb2zU/tvBzhBWPl/+jwACCERbwHEBtJ2RiBboaFcF\n8kMgNIGcF2dJSaOGUkgAHRpcCm2tsyLqov2svZO2Wq9du9YE0xpQa9cQu+jNjDqmdfmkfaq1\nW0jjxo3NSCEaVNv/66MG3yQEEEAgXgKOC6BpgY5X1eA4CCCAQGwEtNXatjCfcsopBxxEP+P1\nJsYffvhh/6JdRHRsa120NbuipFOhayCti+3D7f2ok9CQEEAAgWgJOC6ApgU6WpeefBBAAIHk\nE9BfF21wXdHZ/fbbb/uDaQ2sNdjWR23R1hsbdZzripJOEKMBdYMGDfYvOu25Lrqufv36jBxS\nERzrEECgQgHHBdC0QFd4HVmJAAIIpIRArVq1RJd27dodVN7S0lLRCWM0mNbAWpeff/55/3Nd\nryOH+Ep6E6MG1BpM20X/b8fQ1nU69B8JAQQQcFwATQs0lRYBBBBAoCIBHT7Ptiq3b9++ok1k\ny5Yt8ssvv5jA2vtRn+virxVbM9RRRDSQ1uH4dNHgum7duuZRb6TUPt/anYQp0SvkZyUCrhFw\nXABNC7Rr6h4FQQABBOIuoK3MurRu3brCY5eVlYmOHrJ+/XoTUOujtmrbR32ui6++2DZTbanW\nwLr8UqdOHdFFA219TR+5Kd6q8YiAcwQcF0DTAu2cysWZulugcMClUpaT4+5CUrqUE9Ch8myQ\n26ZNG5/lLygoMIH0xo0b9z/a1m1tyd60aZP8+uuvZqQRn5n89wW9wVEDae/FBtm2y4p91NZt\nhvMLJMrrCMRewHEBNC3Qsa8UHAGBYARKWrYIZjO2QcCVAtqVw86uaAuYn58ve/fulaKiIrvK\nPLfBtAbb2rqt//d+rv/Xvto6GU2gpCOY2GDatqbro67z/r8G5broOrqTBFLldQRCF3BcAE0L\ndOgXmT0QQAABBBIjkOP5lcYOrxfoDAoLC0VHGbFBtj7qouvsoq3c+lzHzV65cmWgLM3rOoa2\nDairV69+0HNd571oK7duT+AdFC8bpaiA4wJo2wKdlZWVopeMYiOAAAIIuFEgNzd3/xjWwZRv\n9+7d5qZIG1Tbx61bt4ou+n/7XB816PZuHQ90DP07q8G0v0UnsLGLbqfP9VFb45kxOJAwrztZ\nwHEBtP48pokA2snVjnNHAAEEEIhUQFuIddHxrYNN2sq9bds2s2hQrc/toz7fvn27+b8+2u20\ni4lOwx5q0pZvDaRtgK3P7aLr9EZL+2jX6zp9ro8agNMKHqo628dLgAA6XtIcBwEEEEAAgQQL\naCu3LjoUXyhJx9jesWOHCbA1uNbF/t8+7ty5c/96Xaf/10fb5URHOKk41fOs1tdKPUuJ1/L7\n/7OzszzDB+Z4Auvfg2vtf64Btvdj+ecaeOu68ouWnaDcQ0yKWIAAOmJCMkAgRQU8Uy57hgMQ\n8dzUREIAAXcL6Bjbtp90OCXV4FlHLtGgeteuXSaw1uBan3/zTY7nsUi0S4puo63k+qhdNvV1\n3UfXbd2623Oz5U7P+gLPKezwLDbg9vdY0Wtlni8RlTxB+O/BtAbUvhb7hcMG3t7/97VO+72r\nF8ndAgTQ7r6+lA6BmAlUGTlaSho1lMJrh8TsGGSMAALuENCh97TVWJfyqVmzTCkp8XwZL5d0\nBBFt+dauJN5Ju3JqsK39uTWw1kX/r4/e6+xrus6u937U51u3FnrG+C6QPXt05BRdNnkWDbp9\nLdpC7us1u77M0800Q3Jysj2BebbnMce0+uujXTT4ts/to3Z5sc/to66zi+5jn9tH3U67utj/\ne06OFCcBAug4QXMYBNwikLlosVS5407J/OZbKfP8Uaw0/23Zef84KW3BsHZuucaUA4FkFvC+\nuTFa56mBenFxsQm0bcDt6/+63i66rX3u/agjhtn/b91a5BkrvNDz/0LP6e7yLLb1/H8B94FB\nue3Ooq8Hem5f//2xUqUsT0Cd5QmoszzB+O/BtwbYtj+5Bto6FKI+2vXez+06X49qr9vroy7e\n23mvs6/ZdW4cu5wAOlrvPvJBIAUEKo+7VypPedyUVNuLdMla+qnUPKW37Lx3nBRfdnEKKFBE\nBBBwm4B2ubDdM2JZNm09t4G1DbK919nn+lpFi31dH+3rdp12efFet3v3Hk+f9D2escmLPOuL\npaxMg/ednsUG5gcG378H697r/D0v/1pF/9d1v69XXw3ss7IyPTNvagCfJQ0aNDA3rNogW2fk\n1IBcHydMmCBNmjTx7J+8iQA6ea8NZ4ZAUgloy7MGz+V/aNX/60dk/ojbZO+p3aTU86FIQgAB\nBBA4WMAGixV1ZTl46+iu0eBUA2ztU66PGnjbxQbf+miDc/vcPnpvq891vX1NHzVPfSwpKTF5\neL+mz8svO3ZU90wo9Itnvealyx5PgXd7ljLPOf4+4lp0BaKbGwF0dD3JDQHXClQZfZfPstkg\nusodd8mOpx7zuR0vIIAAAuUF3PjzfvkyJsP/tRVY+0wnc9LgWwPtww8v31STfGcddgB9yCGH\nJKQ0elOB3gl86KGHSu3atc052LtnE3JCLjyo9m8iRU9AP7AS9X6JXik8g0t5JmHwl/TjLnvF\nypiXVX9mJUVPQFul3FA/oydCTvEW8Eys6AmafB01Q+rVq+XrRdaHIVCtWl4Ye8V3F0+I5wn2\n43tMezRtSQ8mpXmGltFfX0NO2nyfDEl/DtFvLHoDAClyAb25QC3DrBaRn4DLctD6qZ5aRx2f\nah4iabt0+KiKk/kgadZUZNUXFW8QhbXUzyggemXhqvrpVa5EPdUWPv3s5PMzOldA+8Jq0hZJ\nUuQCWj81ES/5t9T6FkxDTdgt0Js3b/Z/BnF4Vd9cderUMXfN6niSpMgFatSoYfpH8YEVuaV+\nWNWrV8/cMFJ+GKbIc49/DtWObiVZSz45qA+095kUnXC87IrhZ4NOEaxDUwXbQuB9bjw/WEAn\n09DGEJ3ymRS5gM6gp546MgMpcgH9/NTGh2SINyIvTeJz0Ell9MudDvlH8i2gDTXBBNCM9O3b\nkFcQQMBLYOf9d5v/VfSTlVnn+cKwa+ztXnvwFAEEEEAAAXcKEEC787pSKgSiLlB6RHPZ+eC9\nZvZBG0Tro3nu+ca+feY0kar5UT8uGSKAAAIIIJBsAgTQyXZFOB8Eklig+KILZcvSD6X4zNNl\nX+NGUtKkiRRd1Fc2f71c9nbtksRnzqkhgAACCCAQPYGw+0BHcgragf3jjz+W+fPnm5E0unTp\nIq1btw46S7v/22+/bQba7ty5c4UDbi9atEjW+Bg54Mwzz5SqVasGfUw2RACB3wVKPf1mdz7+\nCBwIIIDAQQKLFy+W1atXH7Tee8Xpp58uOqKWv/Tzzz/LM888Iz/++KM0bdpUNE5o1qxZhbu8\n++67osfVe6GOOOIIOf/880X7o5MQiKVA2KNwrF+/Pqzz2r59u/Ts2VN++eUXOeqoo2Tt2rVS\nUFAg999/v/Tr1y9gnt77t/BMHbxu3Tpz01tF+5911lmydOnSCvP84IMPPOMMHl7ha6m8kpsI\no3f17U2EetObG24ijJ5M+DlxE2H4dhXtqTcR6qxo3ERYkU7o67iJUGT48OEyY8YMv3hvvfWW\ntGrVyuc2H330kVx88cXmZsyWLVvKN998Y6affvjhh+Xss88+YL+hQ4fK7NmzzfjGetOhBtx1\n69aVF154QXRf0v8EuInwfxb+nulNhFqHAqW4t0CPHTvWBBNz586VY445xrxBBg8eLDfffLO0\na9dONCj2l7z3P/bYY823zHPOOeeg/fVO0xUrVki3bt1kxIgRB2XZsGHDg9axAgEEghfImfac\nlNauJXv6nB78TmyJAAKuFvjLX/4il1xyyUFlXLlypdxwww2mAS1QYHvnnXdKrVq1RANtbejS\nv+UDBw6Uq6++2sQJjRo1Mvlr4KyLBtX33Xef+VVZW6O1Me7666+XN95446DzYAUC0RKIax/o\nL774Ql588UXz84oGz5p0konx48eb59OmTTOPvv7xtf+DDz540P7adUOHaunYsaO0adPmoIXJ\nQnwpsx6B4AQyV6ySjDU/BrcxWyGAQEoIaONU+b+5GjA/9dRT0rhxY5k8ebL4m3lQu2Z+/vnn\ncsUVV8iRRx5pzLQ18M9//rMZgk0DZJu0m6YmDcxtl0xtNOvatat8+eWX/LJioXiMiUBcA2hb\n2fv06XNAYfTbpPaBnjdv3gHry//H1/6HHXbYQft//fXXZnd9I5MQQAABBBBAIDECkyZNkq++\n+kruueeegH2TTz31VNG/3/379z/gZPVndU02UNbn2gVJk3YF9U5bt2414/hqlwUSArESiGsA\nbW8ssJXeu1C6buPGjbJr1y7v1Qc8D2V/fbNq+uyzz0TfkPozUPfu3WXixInManSAKv9BAAEE\nEEAgNgIaDGsA3bt3b/M3OJij6L049ldi/SVZBxzQbh3a2KZ/x23S+5yqV69uum8sWLDA3BOl\n90Ppr9V/+tOf9udht+cRgWgKxLUPtJ0tsKK7b/VNoGnnzp1SpUqVCssYyv42gH7iiSdMAK0/\n6+hPP/rm0hFAZs6c6fdnpApPgJUIIIAAAgggELTAo48+amYTHDJkSND72A31b7aO2KE3umqf\naO3e4d0CrSNuvPnmm9KrV68D+l1rX+nbbrvNZsMjAjERiGsLtJ0euqIpErUvtCa7TUWlta8F\ns3/z5s3ltNNOM28u/fZ7++23mxsK9M2ob0q98YCEAAIIIIAAArER0NGH/v3vf5sulscff3zI\nB9HGtHHjxpkgWkfg0psDtW+zTdq6rTcX6khe5557rgwbNky0S6f2t9bGMx1MgIRArATiGkDX\nqVPHlMO2JHsXyq7z1fqs24ayv47W8eyzz8qhhx66/zCZmZlyyy23mP9rEE1CAIEIBLI8P2Bl\n/t4vMYJc2BUBBFwqMGvWLNN6fPnll4dVQg26r7vuOnnyySflX//6lxmN46677tqfl7YyaxCt\n3Tf+9re/mZsJ9V6pSy+9VEaPHu1zGNv9GfAEgQgE4hpAH3LIIeZUtYN/+aTfVDXA9Tf4eaT7\n6zGbeGZO06TjUJMQQCB8gV3jx0rhkMHhZ8CeCCDgagHtKqljt+tQs5Gm//u//xNd7IQpGkd8\n8sknZqhanWjFJh3hQ7twaNK+0yQEYiUQ1wBah7DRpN8YvZPOLKjjPOrA6hpE+0rB7v/bb7/J\njTfeaG5cKJ/Xhg0bzCqbV/nX+T8CCCCAAAIIRCbw008/mQlQtH9yRd0ufeWuk7DoTILlR9bQ\n7fUmQu3KuWfPHjNEncYOdkxo7/yKiorMf2ko81bhebQF4hpA6124erPgSy+9dEA5tDvFpk2b\n5IILLjhgffn/+NpfB1v33l9vUtQbCyZMmGDuyvXOR6cG1aRvahICCCCAAAIIRF/g22+/NZkG\nmjSl/JE1KNZuGI888sgBL/3666/y/vvvm2m9a9eubR61dVu7b9guoHaH559/3jxt27atXcUj\nAlEXyBjjSeHk6m+4OV/5ZWVliU5rrFNsakuwvgk+/PBDM4ugjgOtMwnZAdZ1Ks8zzzxTdMpw\nO2xN+f21T7Rud9VVV8nRRx+9f3/NQ7uCaBCtr2ur9t69e+Wxxx6TqVOnSo8ePcwxfZ1nKq/X\nlgL9dq8fYqTIBLQeap9+bTGxLSKR5cjeerOxepaUlIARBQH9nFRL/VwmRS6gQ6/pZ6e94T3y\nHJ2bg87roAGv/n3WG/t8JR3vWe9Z0tkEtT7qyBq678KFC0W7aeg6/TuuMxxqEK1/w/UXZP18\n1QlWtEHugw8+MF1FNm/eLA899JBoAN2sWTN54IEH/P6q7euc3Lq+UqVKpmgaD5F8C6Snp0sw\nY4j77i/hO++IXtGuFfqBrcGs9o/SpJOd6EgZetI26bA1Oi603nnrnSraX6f0Lr+/3kSgSYPy\nm266yTxXkCuvvJLhbYwG/yCAAAIIIBAbAdsC3aJFC78H2LJli/lbb78UV65c2QTAo0aNMvM2\n6NwNmnRkLQ2WO3fuvD+/vn37mgBZx4jWv+2aNLDWxjddZ0f32r8DTxCIokCaZ5iXsMZ50Zbh\nSJJ+Q9eJUfTbpY6UoZU+lKT763TdevOADrqu40dXlLQ1YN26daZVVb+RegfpFW2f6uusJS0o\nkdcErWv16tUzrXt6kywpcgH9yVZbS/VXElLkAjqBlTZWaBBDilxA/55p6x6/OEVuqTloAKyB\nuAbV+ou1v6T9nbXBrYlnoIBQ+lz7y9Ntr2kjooZ8OjkNybeAznqpv24ESnFvgbYnpN0qAn0z\ntdtW9Kj7a98q7cahY0D6ShrEcMOgLx3WIxC+QOay5VLm+cNW0uKo8DNhTwQQQMCHgH5hbteu\nnWjXjEBJG+K8h60NtD2vIxCpwP/6TESaE/sjgEBKCeS8OEsqzV+QUmWmsAgggAACCKgAATT1\nAAEEEEAAAQQQQACBEAQIoEPAYlMEEEAAAQQQQAABBAigqQMIIIAAAggggAACCIQgQAAdAhab\nIoAAAggggAACCCBAAE0dQAABBBBAAAEEEEAgBIGwx4EO4RhsigACLhQo07HXPeNlpnmGsiMh\ngAACCCCQSgIE0Kl0tSkrAggggAACCCCAQMQCdOGImJAMEEAAAQQQQAABBFJJgAA6la42ZUUA\nAQQQQAABBBCIWIAAOmJCMkAAAQQQQAABBBBIJQEC6FS62pQVAQQQQAABBBBAIGIBAuiICckA\nAQQQQAABBBBAIJUECKBT6WpTVgQQQAABBBBAAIGIBQigIyYkAwQQQAABBBBAAIFUEiCATqWr\nTVkRQAABBBBAAAEEIhYggI6YkAwQQAABBBBAAAEEUkmAADqVrjZlRQABBBBAAAEEEIhYgAA6\nYkIyQAABBBBAAAEEEEglAQLoVLralBUBBBBAAAEEEEAgYoH/B/gUxMYsLm8XAAAAAElFTkSu\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chi_stat_picture(LR_obs, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Гипотеза не отвергается."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. Киллер и тренд во времени.\n",
    "\n",
    "Помните в первой домашке мы изучали с помощью симуляций игру в Киллера. В послених пунктах домашки мы смотрели, насколько быстро игра протухнет, если интерес к ней падает. На экономе мы играли в киллера дважды. У нас есть немного статистике по игре. Целых два наблюдений. Время между смертями в перой игре и время между смертями во второй игре. Давайте подгрузим их. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": 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IBOQZFEgAABAgQIECBAIEtAAJ0lI50AAQIECBAgQIBAioAAOgVFEgECBAgQIECA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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "game_1 = read.csv('killer_time1.csv', sep = '\\t', dec=',')$hours_between_kill/24\n",
    "qplot(game_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n"
     ]
    },
    {
     "data": {
      "image/png": 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www7W+L0PP/wwoqMXFba1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\n0h4EEEAAAQQQQACBjAr8HyZ7BkQ7uc0QAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "game_2 = read.csv('killer_time2.csv', sep = '\\t', dec=',')$hours_between_kill/24\n",
    "qplot(game_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Предположим, что время между смертями имеет экспоненциальное распределение. Судя по гистограммам это похоже на правду. Можно даже гипотезу об этом проверить, при желании. На самом деле время между наступлением событий не всегда распределено экспоненциально. В домашке вы это увидите на примере гейзеров.\n",
    "\n",
    "Окей, давайте попробуем методом максимального правдоподобия оценить для одной из игр параметр $\\alpha$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "--------------------------------------------\n",
       "Maximum Likelihood estimation\n",
       "Newton-Raphson maximisation, 6 iterations\n",
       "Return code 1: gradient close to zero\n",
       "Log-Likelihood: -53.19531 \n",
       "1  free parameters\n",
       "Estimates:\n",
       "     Estimate Std. error t value  Pr(> t)    \n",
       "[1,]   0.6202     0.1034       6 1.97e-09 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "--------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lnL <- function(alpha, x) {\n",
    "  n <- length(x)\n",
    "  answer <- -alpha*sum(x)+log(alpha)*n\n",
    "  return(answer)\n",
    "}\n",
    "\n",
    "result <- maxLik(lnL, start=1, x=game_1)\n",
    "summary(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.620240758421918"
      ],
      "text/latex": [
       "0.620240758421918"
      ],
      "text/markdown": [
       "0.620240758421918"
      ],
      "text/plain": [
       "[1] 0.6202408"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "1/mean(game_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вроде бы совпало. Теперь давайте попробуем усложнить модель. Мы с вами говорили, что протухание в игре должно как-то зависеть от времени, прошедшего с её начала. При симуляциях в первой домашке, мы брали какие-то дискретные моменты времени, и изменяли в них значение $\\alpha$. Давайте сделаем умнее. Предположим, что $\\alpha$ это функция от времени, прошедшего с начала игры.\n",
    "\n",
    "Например, предположим, что затухание интереса к игре происходит линейно, то есть \n",
    "\n",
    "$$\n",
    "\\alpha = \\beta_0 + \\beta_1 \\cdot t.\n",
    "$$\n",
    "\n",
    "В таком случае $X_i \\sim Exp(\\beta_0 + \\beta_1 \\cdot t)$, и нам надо оценить параметры $\\beta_0$ и $\\beta_1$ вместо $\\alpha$. Вобьём функцию правдоподобия для такой ситуации. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>time</th><th scope=col>betwen_kill</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.249382 </td><td>0.2493820</td></tr>\n",
       "\t<tr><td>1.248449 </td><td>0.9990668</td></tr>\n",
       "\t<tr><td>2.317757 </td><td>1.0693085</td></tr>\n",
       "\t<tr><td>3.821953 </td><td>1.5041962</td></tr>\n",
       "\t<tr><td>3.997485 </td><td>0.1755315</td></tr>\n",
       "\t<tr><td>4.238015 </td><td>0.2405298</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " time & betwen\\_kill\\\\\n",
       "\\hline\n",
       "\t 0.249382  & 0.2493820\\\\\n",
       "\t 1.248449  & 0.9990668\\\\\n",
       "\t 2.317757  & 1.0693085\\\\\n",
       "\t 3.821953  & 1.5041962\\\\\n",
       "\t 3.997485  & 0.1755315\\\\\n",
       "\t 4.238015  & 0.2405298\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| time | betwen_kill |\n",
       "|---|---|\n",
       "| 0.249382  | 0.2493820 |\n",
       "| 1.248449  | 0.9990668 |\n",
       "| 2.317757  | 1.0693085 |\n",
       "| 3.821953  | 1.5041962 |\n",
       "| 3.997485  | 0.1755315 |\n",
       "| 4.238015  | 0.2405298 |\n",
       "\n"
      ],
      "text/plain": [
       "  time     betwen_kill\n",
       "1 0.249382 0.2493820  \n",
       "2 1.248449 0.9990668  \n",
       "3 2.317757 1.0693085  \n",
       "4 3.821953 1.5041962  \n",
       "5 3.997485 0.1755315  \n",
       "6 4.238015 0.2405298  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "betwen_kill = c(game_1, game_2)\n",
    "time = c(cumsum(game_1), cumsum(game_2))\n",
    "X = data.frame(time = time,  betwen_kill = betwen_kill)\n",
    "head(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "lnL <- function(beta, X) {\n",
    "  alpha = beta[1] + beta[2]*X$time\n",
    "  answer = sum(log(dexp(X$betwen_kill, rate = alpha)))\n",
    "  return(answer)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”"
     ]
    },
    {
     "data": {
      "text/plain": [
       "--------------------------------------------\n",
       "Maximum Likelihood estimation\n",
       "Newton-Raphson maximisation, 11 iterations\n",
       "Return code 1: gradient close to zero\n",
       "Log-Likelihood: -79.27675 \n",
       "2  free parameters\n",
       "Estimates:\n",
       "      Estimate Std. error t value  Pr(> t)    \n",
       "[1,]  0.904094   0.142894   6.327 2.50e-10 ***\n",
       "[2,] -0.013288   0.003077  -4.319 1.57e-05 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "--------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result <- maxLik(lnL, start=c(1, 1), X=X)\n",
    "summary(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KSSAAI6lTRJCwIQgAAEIAABCEAg7wnU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\nf9fJR1FYLp9rAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(X, aes(x=time))+\n",
    "      geom_point(aes(y=betwen_kill)) + \n",
    "      geom_line(aes(y=0.9 - 0.01*betwen_kill), col='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Можно попробовать более сложную гипотезу. Например, что \n",
    "\n",
    "$$\n",
    "\\alpha = \\beta_0 + \\beta_1 \\cdot e^{\\beta_2 \\cdot t}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”Warning message in dexp(X$betwen_kill, rate = alpha):\n",
      "“созданы NaN”"
     ]
    },
    {
     "data": {
      "text/plain": [
       "--------------------------------------------\n",
       "Maximum Likelihood estimation\n",
       "Newton-Raphson maximisation, 10 iterations\n",
       "Return code 1: gradient close to zero\n",
       "Log-Likelihood: -74.64443 \n",
       "3  free parameters\n",
       "Estimates:\n",
       "     Estimate Std. error t value Pr(> t)   \n",
       "[1,]  0.20592    0.08887   2.317 0.02050 * \n",
       "[2,]  1.69736    0.53791   3.155 0.00160 **\n",
       "[3,] -0.09203    0.03551  -2.591 0.00956 **\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "--------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lnL <- function(beta, X) {\n",
    "  alpha = beta[1] + beta[2]*exp(beta[3]*X$time)\n",
    "  answer = sum(log(dexp(X$betwen_kill, rate = alpha)))\n",
    "  return(answer)\n",
    "}\n",
    "\n",
    "result <- maxLik(lnL, start=c(1, 1, -2), X=X)\n",
    "summary(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AmQAAmQAAmQAAlEPQEK6KhvYp4gCZAA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DsMtnNN48aN037xixYtEriydOjQQdfTF0u/a578TgIk\nEIMEVOzffPWRWkX3GcRYPjZBxQ1fsUpS5n8sKQs+k7Q3Z+tPntovq8eVgig2CAnJRAIk4D0B\nCmjvWQVkT1iYYQm96667HPlBKEG0zpw5U1566SU94A7CzCxiIZxhVT3vvPMEVkuzSHVkFIAF\nCHiIOKsESzgGOsLlAJExIGDN1vHFixfrl4Phw4c7DodgRZ2/+eYbhzBG3fEy4BpFZNKkSXJA\nxc6E8MQgQ4hgOP2jLCP29dtvv13MAozCsO/TTz8tLVq00CHhHBUwLaBc1ANB+P1NEP1r1qyR\nDRs2aN9slOcaeQLWaFjmkQw+sOpD3GO9YTU31wH54hPohHoijCF6D9C2w4YNc/QgBLos5kcC\nJGBTAqoXL6dzR/05OvlhwaRDWkx/vljKvPq6/uQ2bCBZPbtrMZ3XpLFNT4TVIgH7EKCADkNb\nQEghagHEICy+p6lBHhDHsE7ecMMNDqFprhpEF4Rt165dzasDvty0aVPp1KmTjsBhtgTD+gy3\nEcRlxsQsVq4W2B+DJM0CGi8HsFRPmzZNh6fDgEC4J2AyF1efZIhm7PfLL7/o0H3wK+7YsaPD\nSo2ThW+zIUpdTx5WYfhsl2S5NVumXY/39juEuDuxi6gvGDTpmlAu3DkQWcXK1cV1/0B8Rz0Q\nsxoJL2SbN2/WLz///e9/dbzmP9UELvAhb9y4sX5hCUSZzIMESMDmBNS9XM/8pyzT6WpSjhQV\nNx1iOvnLr6Xss8/rD2aBzFQuHlnKZzq/XpH7nM3PjNUjgZASoIAOKe6iwjDw7T//+U/RihNL\nsMBaJQhWuE+EIiG+L/xyly1bpsUrBCsm9MB6JIQvc5cQ59k1wdoMIWeIOdftrt/hL+zOZxh+\n3xDzZnFvHI+BhBC2KM9KKOMFBDGog5m2b9/utnzUG6I1FAIaLi6whBvuKzhnYxm9HxDREPR4\n2YCLDFxyzG4owWTEvEmABGxCQMWzzup+hf4gMkjyZ4skdf4nkvTNd1Lu0Sn6k3NWK+0vnalc\nPZhIgASKCNhnireiOsX0ErrZrRJcPGD9DUWC2wQmPkF84hnKegy3B0wWYrgqwIIMkeqaYCWH\nZT2YCaHsrPzHIU7hnoDYyXAFcXWTQH3hq4yJWYKZEObPSryjTKz3NQygv3XFAE93lnq8fPzx\nxx86a7CEqxBmtoT/ORMJkEBsEkAUkay+feTw2zNl/7rVkv7oJMk+u70k/rhOyo1/WKq0PlvK\nKlHNRAIkUEiAAtpmvwQMdHMVf7ASQiAOUeHlQpng73zBBRcUc7W45ZZbdH1cXSVQb8R2DmZq\noELSwc0Dgw5hOcV/1OOqq66SO+64QxeNGNaIKQ2XE/hOI/IJ/IDvv//+YFZN5w2Bfu6552o+\n5sLg9gEXnVBYn1EuRLJr+5jr4/oSAnH/2GOPmXfhMgmQQIwSwHTSmdcPlMMfzpED3y+Xo+Pv\nl9yWLSRhx9+aSIEy6DCRQKwT4EyEAfoFeDsToTfFIdIDutThn4oEIYswZ8G27npTN2Mf+NMi\nbBxmQ0SC5RyDIxFBIhQJE5cgHCB8qs866yynGQ2tyg/ETIRW+VqtgxsOfNox66QxJTksz/AP\nd9fDYJVPadaBD3osrFxdSsoXLih4WQtV4kyEoSLtezl4AYv6mQh9x2KLIxDGrpwKYwd3Ol+v\n8dKcQPy2PyVZRfPI6nHFiZB7pcktOo+FsQTuhO7cMaPzrCPjrAI9EyEFdIDaPZACGlWCRRDT\nOCNfWF3tmg6rIP7wzzbcOwJVTwhjTN8Nv2X4X1uFf/OlrFAKaKNecKOAq0QtNe0uXixwYw1l\nQti88ePHO3yfUTZEET6GP7S5PnggY5BmKBMFdChp+1YWBbRvvEK5d7gEdCjPMVLLooC2b8sF\nWkAXd2S177nbvmawBsCNAGHeYBVo37699i11NyCupBOCzy5cDwKdIHYRLg8+zbBwI+IG6uyv\nQHWdATAQ9f300091nVBXuIXAlxdxlYPtHhKIupvzgGUcn3CloUOHap/r5557TmBZxmQ0V199\ntf5NutYJN/1LL73UdTW/RxiBhQsX6igw8GuHKxFiq+MlnIkESIAESCCwBGiBDhBPWIwRAWL/\n/v2OHGHBQXf4F198IQgPF86EekE4wzcYXUuGDyyEOgbeYRIPTNAS7gTXEMSOdrWQop6IG+3v\nTIKBtkDDMg6WH3/8sX5Zuuiii/QEOMF4oQh0m3z00Udy++23a0u0MdDQ8LuHtX+GGjiKN/VQ\nJFqgA0MZ1zMGyeLlHS+eSBh43ED1XmEdLJa+JlqgfSUWuv1pgQ4da19LogXaV2Kh2z/QFmgO\nIgxQ2w0aNMhJPCNbPNQgUB5++OEAleJfNghXBmvUs88+q+toiGfkBuGPmfPgc22VEFd5586d\nbiNLwNIOVwVMLmKe+MUqL2/WQbzhwe2aUE/MdmiHhDbt3bu3PProo4JpxX/66Sftow4RbX6B\nskNdrerQs2dPWbFihX5xMljjhQUf+G1DiDFFFgGIZLN4Ru3xO922bRsHh0ZWU7K2JBDzBKAl\nXnjhBW1MQyADRImy47M1IgQ0LCo//PCDzJo1Sws1u/26YNH9+uuv3VYLvrzhTLA2wqcYItQq\ngS9C1ZkTRDVcO2A5h1USbigQ4GbxDcs6BjZCkEFQYlY+uIaUJkHsGxY013wwSYkdEn6HmFnQ\nPHgHy5hmfMqUyAjz9PPPP+sXJ3N7gi3OY+nSpSGLOW6H9oyGOqAnxOq6QXuix4GJBEiABCKB\ngGGgeuKJJ/RzFuNyMJ4HBio8Y+2UbC+g8VDApB4PPfSQfqjDmospm+2U1q9fb2k1NepodI8b\n30P5/+DBg9qqaPVwNdfDVUgNHjxY5s+f73gowxL9zDPPOKbfxhTR8LE1BhEif0zeAdHtKsbN\n5XhadnXdMO8PH147pM8++8xJPBt1gliBK0wkJMyA6W5QI36voZq0JxJYBbOOmHgIPSsjR46U\nCRMm6N4Mf8ozIvZYHQt3IyYSKC0B9ETCQHDTTTfpWPswdjCRQKAJIFoVenXxPDUSlmGoRK+v\nnZLtBxFicgc8HObMmSPwl8RgKLhLXHHFFW5nqws1YNQLXeGuItSoR7BnvzPKsfoP4etNwoBH\nI61atUpP5e0quvEjxsMecaAx5biV2MU6WKrhMuJr+vXXXwVlWyXwhTi3Q7I6b6NeJW0z9rHD\nf/jGuhNWOAf4zzIFlwAESI8ePXRPAKwu8PPHbJ8QKYhl7kvC9YaeLuRjTngZwsRHTCRQGgJw\n0cMkVrg34DeGsT1Tp06V119/Xbp161aarHksCTgR+Pzzz53Es7ERPeiLFy82vtriv+0t0Ij1\n27VrVy2eQQwD3eAqYCeQGDxYuXJlywaF8Atnt37t2rWlWrVqlnUzrzQPMoJ7grtYwHhJwKQk\nJblT+GuZQPQNxE22Sij3sssus9oU8nX4PVoJTAigLl26hLw+/hSIqeTdvfBBdK1evdqfbHmM\nDwTga4543YboxQMCbYLJlHbs2OFDTqLjjmOgLH6DRkI74jpGKEMmEvCXAAwpmOUVfqnGbxXG\nFKyHMQW/YSYSCBQBd88l5F/StkCV70s+RXdbX44K4b4QahCB5oTve/bsMa/Sy//5z3+cHjxN\nmjQJ2YCod955R7p3765vKngQQjjjg+6I0047rVhdQ7ni+eefl+uuu87SYmzUAz7cxktASdNd\nwwIBa0RJ6eSTT3bkVdJ+rttwc3bnp419IVqNOroe6+k7xIS/x7rmjQlk4OsNi7nRzQShgggc\n6GIKVDmu5QbyO1xv3CW4duC8QnEehhsJenEwq2SspN27dwvcoKwSfudwg/JlMCfaavny5XLf\nfffpyDDoXejYsaOe3AgGB39TIK8bf+vA44oTMF6UYPgItqjA/d7dAC48DzCQGuNgmAoJ4LmP\n9gnF/TMamffq1UsbcIyXNeMc8YyFEa00XA3DIJ7VJV03rr3vRh1c/9taQENMIbYypmM2J3y3\nmvABVrMtW7Y4dsXAuVDFQIVV8pdfftHWWYRig3gfPny4xxnyHJUN4gK63vCjw3/4XFolPHDx\n4MYDEz/gUaNGFdsNNwUMGizph4eD7r77br+444GPGRetfryYjKS0PtCB+i0gH7iaTJ48WebO\nnautMoihPGHCBL/jaReDHeQV+H0ipI+73wPaIlC8vDkVK4u+N8dF6j7Gi5dV/XF94Xr0lT9e\nfN966y2rLEu1ztd6lKowHuwTAXc9dj5l4mFn/FbxXLC6L+MFGEKHv5HiEA3jQPEtXFMSAWgP\nww/aENEQvtAwGFgYiN+ap+vGKLekemKbrQU0foC4cF2tkvgOi5VrQnQE876ADktPKBIaFe4l\n6H7FYDojhap8ozx3/yF8UTd051r9OGClMlv1MeoVAwnxMMeNE+1QpUoVLXAx1TisElb5QJid\nf/75fnHv3LmznHLKKXoGRrPAwO8A4rQ0LOHGEugRvIhugo85laaO5nxCsYzfwj333OP0YMQ1\ngynAMQFMKM4FMcjxQgwhH4gwiKHgFogyjPO26v7Gbx9Rb0LBv6RzgSUN1zyMGEz2IoBZQ/GB\nZdh8rwxGLevUqePWaIIxNrhnh/u3Gozz9jdPPK9wT8MAfib/CMAw9corr+gIQtAZF154oaDn\nF/ek0vzWYHlGTye0gNULoVFbtKE3rq+2FtCAhSmiYUk2Jzx0rGbOc7VU45iSRqeb8yztsmGV\nxX9jubR5Bvr4vn376oEf8K8033TxY0F0E3O9zznnHN2NghBY+MFCGMNFBT++G2+8Ub8h4kdo\nvLCgrWBFhPA25+PLOaAeH3zwgYwbN84xQQncdSCer7zySr/zNergb72M46PtP2apg2B+5JFH\n5N9//9Xth3CEkyZN0qcaSl4oK5Tlhbst8UKKa+6uu+5yupGjPWD9xwyhduFhl3qEu83sWH4o\nrhs8V/E7feqppxz3e7DAbxW9mg0bNrTNb9UObWRcL8Z/O9Qp0uoAnQHBjI85BYqpp+vG23Js\nPxMh3AEwOOb//u//HBwhBPv06SP47ymVNNjN07G+bIcFGl0M8C01W6B9ySMU++KtGJbHBQsW\n6G5iDCaDYPI1UgjEM4QtYkFDROOhj2DnENqBSHg7RDc2LHWBSIGeiTAQdbJTHoj7jZsWhF0o\nE3qSDGtNLFmgDcYYOIuxG4guBH9WRN/AlPWeuhiN44P5Hy/FVatWDXjPTTDrHCt5h2MmQnSr\nI5Qpnqnombj55pt1+MVQ3zPs3sYwBMHSibBrTPYiEOiZCG0voBGaCYIPodGaN2+uLZRw1YCv\nH7qwPCUKaPeEMAAkVm5+FNDufwfh3BLrAtpgb8drkQLaaB37/Q+HgLYfBXvWiALanu2CWgVa\nQNvahQMn3KFDB0FXM0ako8sI/ljo4vdGPON4JvcEYkU8uyfALSRgDwK8Fu3RDqwFCZAACXhL\nwPYCGieCGe8GDhyo402iS5GJBEiABEiABEiABEiABMJFILQOj6U4SwxQo3guBUAeSgIkQAIk\nQAIkQAIkEBACESOgA3K2zIQESIAESIAESIAESIAESkmAArqUAHk4CZAACZAACZAACZBAbBGg\ngI6t9ubZkgAJkAAJkAAJkAAJlJIABXQpAfJwEiABEiABEiABEiCB2CJAAR1b7c2zJQESIAES\nIAESIAESKCUB20+kUsrzC9l89JiZb/PmzdK4cWMdq7q09ebxgSWAKC7Z2dmBzZS5lZrA33//\nLb///rucdtppUq1atVLnxwwCS4DXTWB5Biq3P/74Q3bs2CGtWrXSs94FKl/mU3oCmIAoMTFR\ncnJySp8ZcwgogS1btsi///6rZ17G7NHuEuLyYzZJTyki4kB7OomStmN67VCk5cuX6yl4H3jg\nAWnRokUoimQZPhLArHdM9iIwf/58eeyxx/RMo02bNrVX5VgbTYDXjf1+CEuWLJFp06YJptdu\n0KCB/SrIGpGADQnMmzdPPvnkE1m8eLHUqlWr1DWkC0epETIDEiABEiABEiABEiCBWCJAAR1L\nrc1zJQESIAESIAESIAESKDUBCuhSI2QGJEACJEACJEACJEACsUQg6gcRhqoxDx48KH/++afU\nrVuXg6FCBZ3lRDyBPXv2yD///KP9OEM1XiHiofEEYp7Azp079WCoJk2aSLly5WKeBwGQgDcE\ntm/fLgcOHJDTTz9dMEC6tIkCurQEeTwJkAAJkAAJkAAJkEBMEaALR0w1N0+WBEiABEiABEiA\nBEigtAQooEtLkMeTAAmQAAmQAAmQAAnEFIGECSrF1BkH4WTz8vJk7dq1gticmKyjTp06QSiF\nWZJAZBM4fvy4fP311/Ltt98KrhnXOJy8jiK7fVn74BLYt2+fvPvuu3LGGWcIJnowEq8bgwT/\nk0ARgUOHDsmXX34pP/zwg2B8TYUKFYo2qqX09HRZunSp1m7ly5f3auIUpwzUFwpoVyI+fsfN\na8SIETo4Nxrprbfekt27d0vHjh19zIm7k0D0Evj8889l1KhRcvjwYf15/fXXBYKgU6dO+qR5\nHUVv2/PMSk+goKBAxo8fLwsWLJBBgwZJQkICr5vSY2UOUUoAs9veeuutsmvXLsnMzJRnnnlG\n8vPzpXXr1vqMt23bJtdee61j+wsvvCCYyAtBIHxJUT8ToS8w/Nn3vffek6NHj8qcOXMEM3Zh\nlCducFdccYWceuqp/mTJY0ggqgjgxjVz5kz9onnNNdfoc1u2bJlg1s5evXpJ48aNhddRVDU5\nTybABObOnSubN28uliuvm2JIuIIE5OWXX5bmzZvL5MmTNY2VK1fKQw89JH369BFYmx999FHp\n0aOH3HHHHYKp1/F8gshGDw++e5uK+oG8PYL7ORFAd3TXrl21eMaG+vXr66m8MVUkEwmQgOiw\nQe3atdPXicHDsAQgHBcSryODDP+TgDMBWMvwgB85cqTzBvWN100xJFwR4wTwTFm1apU22Bgo\nzj77bJk+fbqkpqbK/v375eeff5aePXs6xPKVV14pOM7qJdXIw+o/LdBWVHxYhy6C2rVrOx2B\n74hvy0QCJCBStWpVGTNmjBMKjBdAN7TRS8PryAkPv5CAJpCTkyMTJ06U4cOHW46t4XXDHwoJ\nOBPYsWOHfrbAkvzEE09or4DTTjtNhgwZIklJSdrFFkeYdVuVKlV0XGjoNsSI9jbRAu0tKYv9\ncnNztR+nq3M6viNYNxMJkEBxAvBPe/XVV2XAgAFSo0YN4XVUnBHXkAAIvPbaa1K9enXd3exK\nhNeNKxF+JwHRmgyW5nvuuUdbmNu0aSNffPGFjB49WvtB46UzJSVFf8y84NqBCfF8SbRA+0LL\nZV9Y0DAaGjcyc8J3+EMzkQAJOBPYsGGD3HvvvdKlSxe58cYb9UZeR86M+I0EQODHH3+Uzz77\nTLtvWBHhdWNFhetinQD017Fjx2To0KHSt29fjaNt27Zyyy23aNcOWKFdNRt2wkD2MmXK+ISP\nAtonXM47o4vgpJNO0uFQzFuOHDkiNWvWNK/iMgnEPAH4a2IgB25qN998s4MHryMHCi6QgIMA\nemnwQH/88cf1OkSwQRo3bpx0795dzj33XD5/NBH+IYEiAtWqVdNfzj//fMfKFi1a6DB2f//9\nt8CdA2IZYVXNghm6zTW0qiMDNwt04XADxtvVjRo1kp9++slpdziiMxa0ExJ+iXECiLeJMFy3\n3367k3g2sPA6MkjwPwkUEkAkp8svv1w/8PHQxwB1pGbNmmnhjGVeN6DARAJFBBo0aKC/IJyw\nkfbu3SsQyNiGUHWJiYlOug2DChEtyuwXbRxb0n8K6JLoeLENYVH+97//6dGbiNU5b948PZkK\nbnxMJEACokc9P/bYY3LBBRfoG9j69evF+BhjBXgd8ZdCAs4EEGbr+uuvd3wuueQSvcPAgQMd\nA5143Tgz4zcSgAjGs+a///2vfvag52batGl6LAEGCFasWFFwLSEqB0IQI0405iW49NJLxbBe\ne0sxTom+Am935n7WBN544w2ZNWuWHuEJyzMCeMPnhokESED05ELojrZK8IeGpQ2J15EVIa4j\ngUICmFENA6EQwSY5OdmBhdeNAwUXSEATwCyDiPW8fPlyHZEDuuzhhx/WBhzsgMGCiG4DQw4G\nFJ555pl6XgLXgBCecFJAeyLk5XZM4Y0uAoTsYiIBEvCPAK8j/7jxqNgmwOsmttufZ29NAH7O\nsDBjrJpVgmbDYFx/gz5QQFtR5ToSIAESIAESIAESIAEScEOAPtBuwHA1CZAACZAACZAACZAA\nCVgRoIC2osJ1JEACJEACJEACJEACJOCGAAW0GzBcTQIkQAIkQAIkQAIkQAJWBCigrahwHQmQ\nAAmQAAmQAAmQAAm4IUAB7QYMV5MACZAACZAACZAACZCAFQEKaCsqXEcCJEACJEACJEACJEAC\nbghQQLsBw9UkQAIkEGkEMH3tzp07I63arC8JkAAJRBwBCuiIazJWmARIgARENm7cqKegNbPo\n1auXnqbWvI7LJEACJEACgSdAAR14psyRBEiABIJOoE2bNrJq1Sqnctq3by+dOnVyWscvJEAC\nJEACgSeQGPgsmSMJkAAJkECwCeTm5hYr4rnnniu2jitIgARIgAT+v717CcUtigI4vlyXPJJ3\noTwHFCFlQAyMGUlJGEhIEcmEUgaGhmTAQCkDKWamSFJeRQwoJAbkkeSVknvXLl/Ojcntc49z\n9/8UzmN/e+/12/W12vY5x/8CJND+N6VGBBBA4MsEzs/PZWRkRF5fX2VjY0P6+/ulqalJkpOT\nZWxsTJ6fn6Wtrc20Pzo6KjExMVJaWioTExOyubkp+fn5Ul9fb8qvrKzI9PS0PD09SW1trZSU\nlEhAQICv75qkj4+Py+rqqjw8PEhBQYE0NzdLZGSkrww7CCCAgI0CAb+/hF9tDJyYEUAAAS8K\nHB0dSWNjoywsLEhiYqJkZWXJ8PCw5OTkSFFRkdzd3cnOzo4JTZd0BAcHmxsLNTEODw83a6e1\nbHd3t7S0tEhubq7c3NyI1tve3i5DQ0PmsxcXF1JeXi7r6+uSmZkp2dnZpk1Nnufm5syxF/3o\nMwIIIOAPAdZA+0OROhBAAIF/JJCeni7z8/NmpriiosLsa0L82ba8vCxVVVVycHAg29vb0tfX\nJ7u7u9LZ2Sk6A62z0nt7e6JrqnW2+W3r6ekxyfPMzIy5Pjs7K1tbW2aGu7W19a0YfxFAAAEr\nBUigrRx2gkYAAVsEdOZ5YGDAF67OKutWU1MjhYWFZj8oKMgs37i/v5erqyszI63JdHFxsVRW\nVpoy+islJcUs9VhaWjLJuO8COwgggIBlAqyBtmzACRcBBOwSSEpKkpCQEF/Q8fHxZj81NdV3\nTnfe1jW/vLzI4eGhWWN9e3sr1dXVjnKnp6fmeH9/X/Ly8hzXOEAAAQRsESCBtmWkiRMBBKwU\niI2N/TDunz+dX//vb4e5vLw0nwkNDZUfP5z/qNRZaP2JiIj4sF5OIoAAAjYIOL9BbYiYGBFA\nAAEEPhXQRDojI8Nc15sHJycnHWV1hjowMNBxjgMEEEDANgHn1IJt0RMvAggg4FEBTWL1kXVf\nsWkCnZCQIHrjoC7jeL/V1dVJVFSUHB8fvz/NPgIIIGCVAAm0VcNNsAgg8L8IREdHmydw6DOh\nT05O/BqW3lQ4ODgoj4+Poq8HX1xclLW1NfPou6mpKeno6JA/11D7tQNUhgACCHxzAZZwfPMB\nonsIIIDARwL6OLre3l7z0pSwsDBpaGj4qNhfn9OXregzpLu6uqSsrMzUo+um9RnU2jYbAggg\nYLMAL1KxefSJHQEEPC2g65Gvr68lLi7O8QZBfwd1dnZmHm+XlpZmXsbi7/qpDwEEEPCaAAm0\n10aM/iKAAAIIIIAAAgi4KsAaaFf5aRwBBBBAAAEEEEDAawIk0F4bMfqLAAIIIIAAAggg4KoA\nCbSr/DSOAAIIIIAAAggg4DUBEmivjRj9RQABBBBAAAEEEHBVgATaVX4aRwABBBBAAAEEEPCa\nAAm010aM/iKAAAIIIIAAAgi4KkAC7So/jSOAAAIIIIAAAgh4TYAE2msjRn8RQAABBBBAAAEE\nXBUggXaVn8YRQAABBBBAAAEEvCZAAu21EaO/CCCAAAIIIIAAAq4KkEC7yk/jCCCAAAIIIIAA\nAl4T+AWXNbFrVUQ9zAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b = result$estimate\n",
    "\n",
    "ggplot(X, aes(x=time))+\n",
    "      geom_point(aes(y=betwen_kill)) + \n",
    "      geom_line(aes(y=b[1] + b[2]*exp(b[3]*betwen_kill)), col='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Давайте посмотрим внимательно на протокол оценивания. Вполне возможно, что трэнд незначим, и на самом деле параметр $\\alpha$ никак не зависит от времени, которое длится игра. В протоколе для каждого из коэффициентов трэнда проверяется гипотеза о том, что они равны нулю. Это делается на основе асимптотически нормального распределения, так как метод максимального правдоподобия хорошо дружит с ЦПТ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "--------------------------------------------\n",
       "Maximum Likelihood estimation\n",
       "Newton-Raphson maximisation, 10 iterations\n",
       "Return code 1: gradient close to zero\n",
       "Log-Likelihood: -74.64443 \n",
       "3  free parameters\n",
       "Estimates:\n",
       "     Estimate Std. error t value Pr(> t)   \n",
       "[1,]  0.20592    0.08887   2.317 0.02050 * \n",
       "[2,]  1.69736    0.53791   3.155 0.00160 **\n",
       "[3,] -0.09203    0.03551  -2.591 0.00956 **\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "--------------------------------------------"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В нашем случае все три коэффициента по отдельности значимы. Тем не менее, они могут оказаться нулевыми по отдельности. Давайте проверим гипотезу об этом тестом максимального правдоподобия. В этот раз $q=3$, так как мы зануляем сразу три коэффициента. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eQ5c21twjMBNBcQ2jofXJ3p7LPPlv/973+iY0MPGDDAjBXt6gpTOQQQQAABBBAo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\nGba1DM98lAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "LR_obs = 2*(lnL(b, X) - lnL(c(0,0,0), X))\n",
    "chi_stat_picture(LR_obs, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Отличная новость! Гипотеза отвергается. Это означает, что при симуляции игры в Киллера мы можем попробовать использовать оценённую нами модель. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Что мы сегодня осознали? \n",
    "\n",
    "* Метод максимального правдоподобия - что я вижу, то и есть на самом деле.  \n",
    "* Производные содержут в себе информацию и именно они используются для её передачи в современной статистике и машинном обучении. Например, вторая производная функции правдоподобия говорит о том, насколько ярко выражен пик правдоподобия. \n",
    "* Информация Фишера говорит о острие пика, это усреднённая по выборке вторая производная, взятая со знаком минус (потому что мы максимизируем правдоподобие, в оптимуме вторая производная отрицательна, надо это компенсировать ещё одним минусом).\n"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}