{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "\n", "#
R для тервера и матстата.

3.1 Какими бывают сходимости случайных величин.
\n", "\n", "Данный ноутбук является конспектом по курсу «R для теории вероятностей и математической статистики» (РАНХиГС, 2017-2018). 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", "\n", "В теории вероятностей выделяют четыре основных вида сходимости: по распределению, по вероятноти, в среднем порядка $p$ и почти наверное. Нам с вами довольно часто придется иметь дело в матстате и эконометрике дело с разными асимптотическими штуками. В связи с этим, хорошо было бы представлять себе как они выглядят. В этой тетрадке мы попробуем понять в чём разница между сходимостями и постараемся разглядеть её на картинках. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "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=6, repr.plot.height=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Какими бывают сходимости \n", "\n", "Когда мы с вами изучали математический анализ, мы довольно много говорили про сходимости. Мы говорили о поточечной сходимости, о равномерной сходимости и делали мы это довольно долго. Первым же делом в голове возникает вопрос. Почему мы не можем ещё немного поговорить про те же самые сходимости и на этом успокоится. Всё дело в случайностях. Из-за того, что мы вводим их, старые сходимости в каком-то смысле начинают портиться, и для случайных величин приходится выдумывать что-то своё.\n", "\n", "Навыдумывали четыре основных вида сходимости. Все они имеют разную силу. Из одних видов следуют другие. И вся взаимосвязь может быть нарисована на вот такой вот замечательной картинке: \n", "\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Проведём краткое знакомство. Пойдём с правой части кратинки в левую. \n", "\n", "* Самая слабая сходимость, __сходисость по распределению!__ Чтобы сказать, что последовательность случайных величин $X_n$ сходится по распределению к случайной величине $X$, обычно над стрелочкой пишут букву $L$ или букву $d$ или просто рисуют такую стрелочку $\\Rightarrow$. Из-за того, что эта сходимость самая слабая её так иногда и называют, __слабой.__\n", "* Сходимость чуть посильнее, из которой сходимость по распределению является следствием, это __сходимость по вероятности.__ Обычно её обозначают, подписывая над стрелкой букву $p$.\n", "* Сходимость по вероятности, в свою очередь следует из __сходимости почти наверное__ (almost surely). Чтобы обозначить эту сходимость, над стрелкой пишут $a.s.$\n", "* Также сходимость по вероятности следует из __сходимости в среднем порядка $r$.__ Над стрелкой в случае такой сходимости либо подписывают порядок сходимости, либо пишут $L^r$. \n", "\n", "Последние два вида сходимостей самые сильные. Между ними нет чёткой взаимосвязи. Давайте познакомимся со всеми этими сходимостями чуть ближе. Начнём мы при этом со сходимости по вероятности. Она находится на схемке в середине. На её примере легче всего увидеть какие проблемы возникают со случайными величинами, когда мы начинаем рассуждать о них как об обычных последовательностях. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Cходимость по вероятности" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Перед тем как говорить о вероятностных сходимостях, давайте вспомним определение обычной сходимости. Говорят, что последовательность неслучайных чисел $a_n$ сходится к числу $A$, если для любого сколь угодно малого числа $\\varepsilon >0$ существует число $N(\\varepsilon)$ токое, что $\\forall n > N(\\varepsilon)$ выполняется $\\mid a_n - A \\mid < \\varepsilon$.\n", "\n", "Перефразируем. Последовательность сходится к $A$, если мы можем выбрать какое-то маленькое положительное число после которого разница между пределом и каждым членом последовательности будет меньше этого числа. Давайте посмотрим на это чудо из матана на конкретном примере. Представим себе последовательность \n", "\n", "$$\n", "a_n = 10 \\cdot n^{0.99} \\cdot \\sin(n) + \\pi\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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CABCXQRAQV0joWFH7QW6ByBm5QEJCAB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\nf46zyk9XzwxiAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "x = 1:n\n", "g = function(x){\n", " return(10*x^(-99/100) * sin(x) + pi)\n", " } \n", "\n", "ggplot(data.frame('x'=x, 'y'=g(x))) + \n", " geom_line(aes(x, y)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Мы видим замечательную штуку. Последовательность сходится! Причём к числу $\\pi$. Если мы зафиусируем произвольное число $\\varepsilon$, например $1$, мы увидим, что начиная с $N$ примерно равного $10$ все члены последовательности оказываются зажаты в карсной окрестности. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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hKQgAQkIAEJdBEBBXSOhYUftBboHIGb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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eps1 = 1\n", "\n", "ggplot(data.frame('x'=x, 'y'=g(x))) + \n", " geom_line(aes(x, y)) +\n", "\n", " geom_line(aes(x, pi+eps1), col='red')+\n", " geom_line(aes(x, pi-eps1), col='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Если взять $\\varepsilon$ немного поменьше, то, ясное дело, $N$ сдвинется вправо. Если мы для каждго $\\varepsilon$ можем осуществить такой сдвиг вправо, и, начиная с этого сдвига, все члены последовательности будут лежать в намеченом коридоре, то с последовательностью всё в полном порядке. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AEJSEACXURAAZ1jZuEHrQU6R+BeSgIS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\nIchLieebj6E6AaypfJYsWRJofBuqE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p\nSR7etAQkIIFGCWiBbpSYx0tAAhLocgKHHXZYeOihh8JZZ50Vu3KsWLEi7LfffoFp7gwSkIAE\nJFCfgAK6PiOPkIAEJDBsCFx22WXhzDPPDJ/97GfDbrvtFjbbbLNw3HHHxTNwHH/88cPmPr0R\nCUhAAu0koAtHO+katwQkIIECEZgxY0Y8+wZzPTPzxhprrBGnDsvzrrvuGm6//fZw6623hu23\n375AqTYpEpCABIpHQAFdvDwxRRKQgAQkIAEJSEACBSagC0eBM8ekSUACEpCABCQgAQkUj4AC\nunh5YookIAEJSEACEpCABApMQAFd4MwxaRKQgAQkIAEJSEACxSOggC5enpgiCUhAAhKQgAQk\nIIECE1BAFzhzTJoEJCABCUhAAhKQQPEIKKCLlyemSAISkIAEJCABCUigwAQU0AXOHJMmAQlI\nQAISkIAEJFA8Agro4uWJKZKABCQgAQlIQAISKDCB/w+xktXObJfgdAAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "eps1 = 1\n", "eps2 = 0.5\n", "\n", "ggplot(data.frame('x'=x, 'y'=g(x))) + \n", " geom_line(aes(x, y)) +\n", "\n", " geom_line(aes(x, pi+eps1), col='red')+\n", " geom_line(aes(x, pi-eps1), col='red')+\n", "\n", " geom_line(aes(x, pi+eps2), col='blue')+\n", " geom_line(aes(x, pi-eps2), col='blue')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Если мы хотим взять более мелкое значение $\\varepsilon$, нам просто надо будет сдвинуться вправо. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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KPxJolqXwJg6S+itVtGKSXH0htrFxocg2jmf0TYkLXRLCWWegJad+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Wql+rce1Dtmx3YV2rR6y7YlMPfvf5gy/I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\nu/HneNgm754QA4eg6fGA63EpNGtc7gdjh7O06KfHI67EQV9P+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a1G9o/ERG7isx9F4whPazZrJjfzd0yMyRu9vqItr7d4wJKzmDw2b1Pv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\n6HbSz7Ds3hDQWVQvKwF90UUXZVEd8oAABCAAAQhAAAJNE8A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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = 100:300\n", "eps3 = 0.05\n", "\n", "ggplot(data.frame('x'=x, 'y'=g(x))) + \n", " geom_line(aes(x, y)) +\n", "\n", " geom_line(aes(x, pi+eps3), col='magenta')+\n", " geom_line(aes(x, pi-eps3), col='magenta')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Вот так обстоят дела с детерминированными последовательностями. В случае, когда речь идёт о последовательностях из случайных величин, всё оказывается немного сложнее.\n", "\n", "__Определение:__ Говорят, что последовательность случайных величин $X_n$ _сходится по вероятности_ к $X$ при $n \\to \\infty$, если\n", "\n", "$$ \n", "P(\\mid X_n - X \\mid \\ge \\varepsilon) \\to 0\n", "$$\n", "\n", "или если \n", "\n", "$$ \n", "P(\\mid X_n - X \\mid < \\varepsilon) \\to 1\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "В случае сходимости по вероятности, когда мы оказываемся справа за некоторым номером $N(\\varepsilon)$, последовательность может пробивать коридор. Но по мере нашего продвижения вправо, вероятность того, что она пробьёт коридор падает. \n", "\n", "Давайте попробуем посмотреть на это на конкретном примере. Предположим, что в наших руках оказалась генеральная совокупность из нормального распределения. Мы сделали из неё выборку некоторого объёма и посчитали по ней выборочное среднее. \n", "\n", "$$\n", "\\bar x = \\sum_{i=1}^n x_i\n", "$$\n", "\n", "Из ЗБЧ мы знаем, что выборочное среднее сходится по вероятности к математическому ожиданию при росте $n$. Давайте посмотрим как это выглядит на практике. \n", "\n", "Зафиксируем какой-нибудь коридор, $\\varepsilon$, за которым мы будем в дальнейшем наблюдать. Как можно увидеть, поначалу, при мальньком числе наблюдений, последовательность довольно часто пробивает коридор. Нет такого, чтобы она один раз погрузилась в него и никогда больше из него не выходила. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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/rT0Xe+852YmM+8yLn56Ec/Gh199NFRUT6OP/746Kijjoq+8IUvRE996lNzYuz+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\n8haSAHWOWfGrPlW/Wf6Sz5MSpDIEGgk0BBpyzAbQtM5eksMkgSZ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NviwrnPzWue63337xRjPaHiSOTWdNOhFDVJLC/KN+gOSfMRQ75lnS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\ni6TDGQE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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 1:100 # выборка\n", "s <- rep(0, times=100) # пустой вектор для средних \n", "\n", "for(i in n){\n", " x <- rnorm(i, mean=2,sd=4)\n", " s[i] <- mean(x)\n", "}\n", "\n", "eps3 = 0.5\n", "\n", "ggplot(data.frame('x'=n, 'y'=s)) + \n", " geom_line(aes(x, y)) +\n", " geom_line(aes(x, 2+eps3), col='magenta')+\n", " geom_line(aes(x, 2-eps3), col='magenta')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Со временем, количество пробоин в зафиксированном коридоре падает, дисперсия становится все меньше и меньше, так как наша последовательность сходится к константе $2$. Последовательность всё ещё иногда пробивает коридор, но вероятность этого падает. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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BKBRCARmDUCqzYVAn+YdRKzjH/ppZdO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ReSOv5h15LXUckPPc/G/91m9d3HzzzUt19Vir3QHavW9pcKjiF8fYE7s1g5pzpNqu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\nUo82B2di4VczeQGyqthn9PShTcW2D1L10k7Zb//2by8+9alP7diHU8+6VDs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ru1Rd/1tO48WOUDHPe3qstnj7/85S8fdh2q\nepv2JgN7ycDmAL2XrB1lmyc96UnToYtNrSt103cDSl15biRcOOSlvXU2HTcwqfqJ29XVT5m2\n4qcs617IEsN6pdjlnQPliTeq83GLj3/849MTOXgBYl6Ms9oZd+cD3gUXXFBNdrTFBSfrO5QO\nNb73e793ccLWhWvucXzVzvgqv4u36tA27xVHe2PubOVpq418qT5sQyuuOh5sUndUH/kVS3m1\n9x0Y+OioT5snjozskFOMfdTfba0j+08MfAFqN/k4Mo/7Z23+V+XdCHerrx3UMTOvjuW6vhPr\nq7F+z3vec/GpT31qx5o4Xv10LKRH6pcx7T7/DC77vnv/kfrZ2G8yUDOwOUDXjOxDm1f0c6/q\n66Zf24TsxcbNgs3JDSr1vbBIsVUuBrzdls4XGGKL5wUNvrJKM7a9HqDxx5f/jMsvjYw+hqFP\nqfGuS7MPWe/s73GPe0wHcvU6ncqzH5W/brzOi+rT9gg//ak78tlhaCOOc0wqf46KW/06lypf\nrLve9a5WpwOVODBHNkuD0Em7lB+NOvnhAO34HA3Mg4phHuucGMXr+K6rnzjaOM/0vc64J85X\nc93cHO8+OhbSI/XPWOd14kjxNvabDKybgc0Bet1M7aNe3fS7jUeeFx2ovLT3wgJPvrx1NlR1\nazrkS5XXtj7g639EwciDRcXSxxwVm49hvPe97135TWj15zA7mXbkfC9xdpjJEz951Nf15byo\nONpXfvWTvka6jm3aii9PHan8OSpG9bsKIw/QYKS9mOv4XUd3DmdOZkyr+jKHcWeR2Uf7vCpu\n9feSf30478HaC86qGDfy3WfgSMa188YTLvghqE3ZZOB4Z2BzgD7eGd+Dv7rxezBOKDclD5x5\nkEt9Lyxgiisv9RI769okj7q2YimvbS9o8JWJWSkYeWdBfbHXoYnJl5FGRb2RfBVfe2jWV9mt\nKxez6q+bk8x7Yojr+KWs1tWVVnmHUXWdp9KK0bXFrX21T9WHGHe5y12sTmMiDsyRzdIgdNIu\n5UejThyu2aOBd5AxzOM6uacfjm8d93X6qI0Y5PhrJc/r5Gc/dRx/6ZHGctNNN621no/Uz8Z+\nk4Gagc0BumbkALbrRlPbhOzFyYsEBxR5qe+FBWpd+TqHGnVrmjpf6FR9feBbWaXGhb39oZ58\n2uuUij2yEVs60hvx9YN91kf6u+Wb32qnr8qvbQ8SVd/2CD9xzI00ZdQ7DPHVVcd45M9RMarf\nnEudPV/Axc9XvvKVae7oG92sd7bwRn5H+nvh40M/e7G/M9msGq/aF/X3kh9tnGfXXHPN4gtf\n+EJ1sWnvQwaOZFy7cEeff+50N7xNBo5mBjYH6KOZzWOElQeHrKc7LxQ8eYLP/nL37Utf+tKk\n4sWEhvbS5O3mUDEBxz9tEzexVXXzTD3rUnWh/ogJ9U4Of65okzno9NWTdjpzPPGhWZ+z2Y1M\nzGqzbrzOj5H+CD/9qSNNGXXHNvlV1zicL6k7qoshVU+sUZ/QYx38+7//+44x4TPHFUvMpOrs\nJta0X7eeLxLXtbkz6jk/zOuqPji+6+onnnPi/7d3JsByFeUe/25uLknIzXazYBYBE9YYILwo\nayAVEJVUCigQCSjlhjyWyBOXEhEtQAWMPnCNWBWJKYJAcKkA8ixRqzQLEEoCPJAtEZAtZLvZ\nbm7uNvPma95/6Ok5Z+Zss57/qUq+091ff939677T3/T06YMyS/36ZOfjfeUJ4FdFyMqXyBJI\noDIE6EBXhmuiVu0J3L63C9GTHfRNR/p0tR7Grw/LLVy40KjYExAmFpWIRxwmG9uuew9dNx62\nIJHu6qMM1YMudFypNvQtiy+88IKsWLEikgONMiBRL1d6le3qlArDvkrcw2apfEHT/PodZZWz\n4+eMID9kKTvQgXR1vero6kIH9XFteIWRx+UJG0j3yqvnwOo56qiHjr/e3l4v1aI4lFfKflGm\nkBFar7Q40OAIruVQ2Z8V5XTddPQ3xoibznDtCHz6058WfZB61qxZtasESyaBBAjQgU4AYqVN\n6AkSOvnoGc2YhNwy9fWk+k8vPDwFXUwmmobJSyXukY4JS/X8Lui66SgLNpHuhjGheZUP23Ye\nPdpvwYIFde9Ao87KAe2ABIs4Evaj2gB3t04Io/9K2Yeun47X+HHzQAfSz5YdDxsuA33l8Sc/\n+Uk555xzbPWC++uuu07eeOON/Fi3+6dA0SOAciE9VGJHaZvQN7GN1bkB9HlQnuASVN9uPvLA\nhp3G+9oS0Pnpoosuqm0lWDoJJECADnQCECttQlfRHn/8cZk/f750dnYGLg5OESYTzYh7nbjh\nkEBCX/V04tG9o+6F/G488rrpbthrEoUOJOqDMhCGRHwQiTyw7ZcHepB+en7xsK/SvvfTDxsP\nm24+v3hXD46E2z7kh3Tz2WHoQNppeo8xoPe6qnr00UeL+/pz9D+k6pa7UJ5bd/2VZdGiReZN\nkX4vAHJfZ611tOtZqmzoofxSulHTtF/SsoczLE8dO9rnGLthGGOsRMkbphzqkgAJpJcAHegG\n6XtdiVWnA5NQkGpDF1LzYGJRiXs4CLZTo5PXzp07i4pBHjcBZcAW0l19TGhe5UMXEjZg041H\neimJvJB+urAN6afnFw/7mh/3frpR4sHXzRu0vtgm4OqjrpCufTuMvJB2mt7b40ff8rdy5UpX\nJa+DcVCk4BGBtvuV65HFN0rr6PXF0CsDmEB66cSN+9a3vpV/VXxcW/WeH+MjaD/eeOON5teD\nMGMFDFAGykQ8JQmQAAkkRYAOdFIkq2BHJwU4E0GKw8SPyUTz4B5S46Bn2/ZyoDs6OmT48OGa\npeiCDduuKiEeGTChqR7SkMcNI4+bjvggMmhe6EEGsW3roO4qwRFxtl7Uez9bfvFuOXBCXH20\nF3V289lh5IW00/Qefav3sKv39gUdSDvN796vPD/9UvHazqD2oBeETakyS6VdcMEFpZKbKg19\n7jc23MYecsghov+iXOg7jPsoNpiHBEiABEoRoANdik6dpekqdJifezHxYzLR5mDy0jjcQ2KC\nUz379AsN67V8+fL8/up3Yt79H2XBFlLcMPS8ykc93TwIQ8J2EAmbkOXyRClDbcK+tg/3UW15\n1RE23bSgZcCRcPVhF9K1b4eh49qADvpWw346GGOQyFtKolzIUrrl0rRcv7q5eaGXRLmu7TSG\nMT6qwRN9h3GfRt5sMwmQQGUJ0IGuLN9Erd99993mtb9BjWLCgtR8mLx0grHvNc2ebLxWmvXh\nD33rk9eFMmATOnZYy4TjpPeY5GwdzYd42EAYEvFBJGxD+uWJYtu2pfb1gbbp06fL6tWrTVK5\nMu385e79bPnFu/awhcPVRxj95+azw9CFtNP0PogN9D+ka8MrDLtx+wh1hD2vsuw4tBPSTuN9\neALo8yT6sVzp6DP7M61cHqaTAAmQQBgCdKDD0KqxbpjVZ60qJhFIjcPkpRL3SLcdC/fhL9ue\n3rsX8sIW0lGGhvXe1kMa8kAiHjb84pFeSiIvpJ8u0t2y/fS94vWBNr3Wrl1rZBxbxoD1H+pn\nRYUqA86Lawd1dOPdcjQMHeRxdVCGxvvp6Jcw1Zs8ebKb3TdcrlzfjB4JOv5gzyO5IAp6GLMF\niQyEJgCO4BraQIgMGH/2mAyRnaokQAIkUJYAHeiyiBpXwWvCwsQCqa3DPfTHjRsnRx11lDz2\n2GMFjS818SENEhlhG+VgQtN4pEEiL8KuDTce6UEk2uanG8e2axNloT1uepSwn62g9cZKnKsP\nu6hzqbohL6Sra9vw09HzX5955hnRF/4EvWDXz2ZQO6qnX0J7enoCZQEbyECZqORLAH/71eCJ\nMjDufSvFBBIgARKISGBQxHzM1gAE4HhgMtEqwwnROMRDYoJ7+OGH5fjjjy9qIfSKEnIRyAv7\n0LHz6D309B5pkMgLCRsIQyI+iNQJFBxK6cM2ZCndcmlue8rpB0mHTdchCFpf5HP1YReyVF2g\nA+nq6jnk8+bNM9FuObZuGOdZ88EWpG0r7P1PfvITWbJkSaBsaGeQ8RPIYMqV8LefRD+WQ4ky\nMO7L6TOdBEiABMIS4Ap0WGINpI+JH46AVt2+xyQDiQlOdWw9NBl6CNsS+pBIQx6ti96jTohX\nPeSBRF5X2nncNL/wV77yFfMmOr90xMM2JOKjSNiAjGLDzQM27e3t5ixw3dOsb9RDvKvvhuFI\nuPqoI/rFzWeHkRd57DS91/3xP/rRj+Shhx7KO72uTpQw6obyo9hAHj2bOuiF8vzaG9QO9d4h\ngH6sBk+Ugc809gEJkAAJJE2ADnTSROvIHhwASK0aJhaVuEf6zJkz5eWXXxZ98yHi7OZA347D\nvd/kCDtDhgwpeJOibQv30EUYtv3ikV5Kzpkzp1RyPg1lQuYTItygvpARTBRlAV/dm64v01Ge\n6kAHrW+5hwiD1BU6kEWVzEWoo65Oi9ceei/9IHFoe9C2BrEZRAftRPlB8lDHnwCcWXD114yf\ngjLwxTG+RVogARIggUICdKALeTRVCBM/JhNtHO7VGYFDAnn11VeL/tMLeU3g//9DXjsO99B3\ndRDWvad79+4t2MKRzWZNdpTvSthGPGwhPkkJ2ygrjm2wSMIW6jF79mx59NFHZfTo0eblEn4O\nMfRdCefFrRPCaL+bzw5DB3nsNNxrvR588EHf4w6hF0ai3DB5ktBFuZBJ2EyzDb8xWAkm6DOU\nWYkyaJMESCDdBLgHuon7H44cJhNtKpwfjcM9pI0Cee04244dr/dIc20hrCumeg+7eo80Ny/C\nKAN6kIhPUsI2ZBzbqD9kHFvIq3vS77vvvvwxgjiRJWh9sSIMxxt20R+QiPeSaA+kl47G6TYJ\nPbM8qQvlBW1r0uUGYZNUmc1sBxzRn5VsK8aKO94rWSZtkwAJpIsAV6CbuL8xUUHaTdUJBpOM\nV7pXHPRtO7j3mxyRBxMZVoTUPlagURYk8sA2wpCIr4RMogy/diRRX9iGQxz0J+pp06bJT3/6\nUznuuOMKqoH2ov8KEp0AdCGd5IoFUbdqlwvW1S63YiBrbNj+2690VdB3KLPS5dE+CZBA+gjQ\ngW7iPsckAqlNhTMAqXF2uob1Chr3jvY7p3Do2wv1ITf7mjFjhnGUu7q6TNmw61W+V5ra8ou3\ny4l7j/pAxrEHG6h3HFtuXti84oorpK+vT4488khXxTd87rnnFqXBHupcpGBF4OU6kFZSRW9R\nR8iKFmYZ12cBdEzjy5+VxNsIBPBFqBr9iPEc9AtmhOYwCwmQQMoJ0IFu4gGACQtSm4rJSycY\nTDKQNgo7D+K99JCmdv/4xz+aPbqIU/n973/fBHVv9Ztvvpl/26HqZzIZkwa7rjSJuf/84pGe\nhEyyDC92SdRRbZx88smybt06Of3000XP6457od1B6jx16lR54IEH5LDDDotbbKj8qBvqGipz\nDOUf/vCHsnPnzvy2oximmDVHYMyYMYbDiBEjKs4DY4Ur0BVHzQJIILUE6EA3cdfD8YDTrE3F\nxKJxiIe0UQSNs/MceuihdrDg/rbbbjPhO++8Mx+PukCiTIShiDAk4pOUsA0ZxzbaARnHlpv3\ntNNOE/2X1IU6YqyUsztr1qxyKomno08gEy/Ax6A+sKn/eCVD4DOf+Yz5Avj+978/GYMlrGBc\n89eDEpCYRAIkEItAXT9EODAwIMuWLZNdu3aVbeSGDRvk3nvvNaugul2AV+FqM3jom+AOOOAA\nmT59et6ZRpotMQHZcUk4MHDU1D7soSyEIe2y9d4v3tWLEk7SNtoDGaU+1cqDOkJWq9ww5WDM\nJNlHYcqnbjIEdDtFNZxnrS3GClegk+k7WiEBEigmUNcO9OLFi81bw/bs2VNccyvmd7/7neie\n0Oeff15WrlwpZ511lrz00kuWRjpvMXnAAVEKejrC+vXr5YILLshPMl7OE/La5Lz07PQg97CL\nCU7zwK4dZ9uaPHmyeTPiqaeeakcneo+yIeMYL9eeOLaTzou6QiZtPwl7GL9J9E0S9aGN+ieA\n8cw90PXfV6whCTQqgbrcwvH222/LD37wA3niiSfKctWXSvzsZz+Ta665Rs444wyjf/PNN8vS\npUvlpptuKpu/mRXw8yWk21Y4JJhs7PSgcXaeIPdwhtQ+TuFw64Ew7OmJE7///e8RrIhEe92y\noxQGW5BRbFQrD+qIfqlWuWHKQR2T6Jsw5VK3cQlgzOALe+O2hDUnARKoVwJ16UDfcsst5sGd\n733ve/kXe/gB1NcG67YEOM+qd9VVV0l3d7dfltTEn3/++eaNcH57ZuGQQNpgMAGVi7PTg9zD\nUVP7eIgQZUF61SeI7Tg6KBMyjq1atiNsvdFe1Dls/mroo26oazXKZBmNTUAfWNQTVKp9Ykxj\nU2PtSYAEwhCoSwdaV5N1n+6rr75ati2vvfaaHHTQQbJmzRpRZ3rfvn3mhIJ58+YV5dUVbXdV\n+stf/rLU4sGoospVIGLs2LGycOFCX8t4GYdONqprX25Y0+xTH3Rlp6OjI7+KbOctdY+HsrTs\n/v5+o4ry8XMrwqXsJJ2GkwF0tdur7WHKw6StspQtfJlQJliND1NOErp6VJteevxgqbomUVZU\nGxgz+jIerzoqR+WHs7GjlpPmfPhyogzxudDIPPQXyB07duRfPFSttihHHY9e47RadWiWcnQ+\nIMd4vamLD2QYnqE+fxfkqksHWp3noNeWLVvkrbfekhdffFHmz58vr7zyijk6Tbd2fOITnygw\ns3v3bnn22WcL4vT10nDcChJSEIADp1s8XAbqrLiXqxPl51FMzpoXTiPKL1Ufty5Jh9EWlW47\nw5YV1hb0w5aThD7aqhL3SdhN0ga2IOlkUKqOGD9Jlp02W8qwGTjqF0N8OaxFH5Yap7WoTyOW\nqV9GyDF+z5FhfIZ+FurSgfarrFe8flN4/fXXzWuO4XjraqKe3nHhhRfmH1DTvHPmzJHnnnuu\nwMy2bdtk06ZNBXFpCehqvV7bt28vYqBx9qXOi81Jv9XqlxRsw7B1S93rlxi9dIsNVqDRBwhv\n3bq16IUspWwmkabn/eqlD6za7YxiG9uH9DSYUrZ0gtcVP20v2h6lvDh50G6tc6m6xikjbl6c\nwtPb2+tZR109188BcI9bXhrz6xdm/UVJ/z55ilH0EaDOiv7ypKvfvKITmDhxoujfuzsPRbeY\nzpwTJkyQzZs3p7PxMVqtiwjKrtxV16dwlKu8po8fP968jQ3Os8bNnj3bTKb841Ma/hd+toW0\nNbHvFHFuGPFhJVZb1R5sQqIekGFtx9FHmZBxbKE9kHFsVTqvbn/SL5zVfjlKmHahTyDD5KUu\nCZAACZAACVSCQMOvQOvb0R5//HGzHQAT7MaNG41TwL0/pYcMeEHa2u7PuF46tn7Qe9hVe/hp\nyf6JXu0kVVbQOtllJlE2HOckbIVpQxRdffnNCy+8ECVr1fJgzIBr1QpmQSRAAiRAAiTgQ6Ah\nV6Dvuuuu/F5m3fesP93efvvt5icf3Qt9//33y9y5c2viiPlwrstoOHhejokdp+cw678kLtsZ\n+sIXvmD67ZBDDjGmUSbqlUR5QW2gTMig+bz00A5ILx3GBSeAMZNE3wQvlZokQAIkQAIk4E+g\nIR1odZaffPJJ0yr9+fnWW2+Vv/3tb3LmmWfKZZddJtOmTZMvfvGL/q1miiEAh8TL0YPToop3\n3HGH/PWvf02EGuxqmZMmTTIvvYFh1AcS8dWQWAXHqnicMsGzFu2IU+96zUue9dozrBcJkAAJ\npJdAXW/h0P2Zq1atKuodN05fD3vPPfeYh7HUofY6QaLICCPk8MMPN0fTeW2Wh9OimNS5xOkZ\ncbFhD7SXc4kyvdLillsuv56VrV/EvI4/LJfXTa9lO9y6NEMYPJuhLWwDCZAACZBAcxBoyBVo\nP/R6TjGdZz86xfGXXnqpPP300+bpezcVK8Uan6RDqw+rqbPq9XIXlAPp1qmSYR03CxYskJEj\nR8YuBg5fLdoRu/J1aABjkTzrsHNYJRIgARJIKYG6XoFOaZ/URbPhtGhlknRc1EFdvny5Zxub\nxfFEOyA9G8vIwATAETJwRiqSAAmQAAmQQIUINNUKdIUYpdKs7TTb95WEgXIgK1lWJW3jy0ej\nt6OSjMLYJs8wtKhLAiRAAiRQDQJ0oKtBuQHLgNOiVa+WI4gVxmqVV6luQf3RnkqVkxa74AmZ\nlnaznSRAAiRAAvVLgA50/fZNTWtGBzo6fjjOkNEtMacSwFikA83xQAIkQAIkUC8E6EDXS0/U\nWT3gtGi1quUIjh492rxcRV9v3cgXeNHhS6YXMRbJMxmetEICJEACJBCfAB3o+Ayb0oLtrNj3\nlWzsd7/7XVmzZo20t7dXspiK26YDnSxi8kyWJ62RAAmQAAnEJ8BTOOIzbEoLWPXTxlXLgdaV\n50ZffVZeYFctblpmM190oJu5d9k2EiABEmhMAlyBbsx+q3it4QRqQXQEw+HW154rsylTpoTL\nSG1PAnr0oTrRY8aM8UxnJAmQAAmQAAlUmwBXoKtNvEHKw6qfVpcOdLhOmzt3rmzYsEGGDRsW\nLiO1PQmMHz9e1q5dK15vzPTMwEgSIAESIAESqDABOtAVBtyo5m2n2b5v1PZUu950npMlfuCB\nByZrkNZIgARIgARIIAYBbuGIAa/Zs2IbBx3oZu9pto8ESIAESIAESCAMATrQYWilTBcOtL2d\nI2UI2FwSIAESIAESIAESKCLALRxFSCof0frMYBl2T/2fdfzfA7dJvwzIpEVTik7HaBnaKvv3\njBDJZiMBGxiTkdbOdH9/GzRxsAzsEhnW3S7ZTCYSx0bPlG3NSstAS6xmtLW1SWtuHLb2t8Wy\nU8vMmVEZGbSzdn8P+mV5YKhIW+9Qae9rrQmKgbG5z4RttWOQRKN1sWFQbjy294yMZC4zJDcO\nehqbQaSGO5kGJuaevekcLO37onF0zDVkMDNuQAZtjfe3mB3WIu3djcswMzwjfSf1St+c3rrs\nw5Zs7qrLmlWpUtu2bZPe3up2zpAHhsrI/0z3iQJ9/9ErbU/sV6Vers9iMifkPiAfjfcBWZ8t\nC16r7LCMtHTTYeib0SdtzzTuF4DgPe6v2Xt8j+z32BB/hRSkDEwYkNbN6f5MMN18RO7/51PQ\n4SWa2Hti7u/hkXT/PfQf3Cc9F3TL3v/qKkEq+SRdUAjy0DpXoJNnX9Zi7yk90vk/W8vq1Vrh\nvPPOk71798rdd98t+pZA+xo1apTs2rUrtwAd7ftXdlBu5TETb+XRrk8j3g8fOVyG7TdMOjs7\nZWBgoBGbkECddfzEGwf6wGYmt4Lf09OTQH1qY6LWfw+6iq9/01179kj3vn01gZAdlPsylWns\nL1ODB+d+XRw6VHbnOEa5si25z8VsvL+HKOXWW56xE8ZJ375eM8fUW92qVZ8kPhP06E+dXxr1\nUgaZA+r311k60DUYWdnRWekf3VeDksMV+b/7PS079u6Qnhn7pH+sU9+xWRno7DeOSzir1M4T\nGJWbLHM7eQa29Et/f38+mjfhCGTbh0gm9wWkv9sZo+HMpFq7dcggaekQyezKSH9XLTk29hfJ\nltyPCNnhuc/3HbVk2PhDeVBuC4f05DhuJ8c4vdkyQaR/MxnGYVgqb2N/3S/VMqbFJsCHB2Mj\npAESIAESIAESIIEmJEAHugk7NakmwYGGTMou7ZAACZAACZAACZBAIxOgA93IvVfhuuMYO54D\nXWHQNE8CJEACJEACJNBQBOhAN1R3VbeydKCry5ulkQAJkAA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QgW6CTmQTSIAESIAESIAESIAEqkeADnT1WLMkEiABEiABEiABEiCBJiBA\nB7oJOpFNIAESIAESIAESIAESqB4BOtDVY82SSIAESIAESIAESIAEmoAAHegm6EQ2gQRIgARI\ngARIgARIoHoE6EBXjzVLIgESIAESIAESIAESaAIC/wdGMv7s9yCgnwAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 300:1200 # выборка\n", "s <- rep(0, times=100) # пустой вектор для средних \n", "\n", "for(i in n){\n", " x <- rnorm(i, mean=2,sd=4)\n", " s[i-299] <- mean(x)\n", "}\n", "\n", "eps3 = 0.5\n", "\n", "ggplot(data.frame('x'=n, 'y'=s)) + \n", " geom_line(aes(x, y)) +\n", " geom_line(aes(x, 2+eps3), col='magenta')+\n", " geom_line(aes(x, 2-eps3), col='magenta')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Если мы промотаем нашу последовательность при текущем коридоре глубоко вперёд, мы неожиданно для себя обнаружим, что она полностью оказалась внутри коридора. Обратите внимание, что это ни коем образом не означает, что последовательность этот коридор никогда больше не пробьёт. Она пробьёт его, правда вероятность этого стала значительно ниже. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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BOJQCKQCCQCiUAikAgkAonAUAS2rHzJ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\nkpevFpcyZR4Z9ZOulUM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3YseA3qxP/Y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4JgyKjhnk83F8e5AGIboTojsGBPwu8rPoTUuSR0cDLE0GKJAnO1rvqplC+R7LJEMb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\n08HJxxa2icv0KUdfcbRBvuR0wChgS2k9yKE13FrXpF/xCpRHO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f7yL/9yjAmOn/xdgjFCHdjwALoDEHMm6J/EueIptykO9OdBb/y22247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\nCZiACZiACZiACZiACYwS8AB6lIVTJmACJmACJmACJmACJlBJwAPoSkQWMAE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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 3000:5000 # выборка\n", "s <- rep(0, times=100) # пустой вектор для средних \n", "\n", "for(i in n){\n", " x <- rnorm(i, mean=2,sd=4)\n", " s[i-2999] <- mean(x)\n", "}\n", "\n", "eps3 = 0.5\n", "\n", "ggplot(data.frame('x'=n, 'y'=s)) + \n", " geom_line(aes(x, y)) +\n", " geom_line(aes(x, 2+eps3), col='magenta')+\n", " geom_line(aes(x, 2-eps3), col='magenta')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Построим картинку на всём диапазоне." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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M3PWRvbHeh8hWM+dpEIAkEgCASBIBAE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gCBy/COQrHJtQ95Lkaaohu9MIr4SUXwXU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\nBUigHTa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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 1:1000 # выборка\n", "s <- rep(0, times=100) # пустой вектор для средних \n", "\n", "for(i in n){\n", " x <- rnorm(i, mean=2,sd=4)\n", " s[i] <- mean(x)\n", "}\n", "\n", "eps3 = 0.5\n", "\n", "ggplot(data.frame('x'=n, 'y'=s)) + \n", " geom_line(aes(x, y)) +\n", " geom_line(aes(x, 2+eps3), col='magenta')+\n", " geom_line(aes(x, 2-eps3), col='magenta')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Можно попробовать оценить вероятность того, что последовательность из средних пробьёт на конкретном шаге установленный нами коридор. Для этого нам понадобится написать двойной цикл. Почему двойной? Потому что мы хотим получить мног-много траекторий, таких как на картинке выше, а после посмотреть как часто на конкретном шаге, эти траектории пробивают коридор. Частота таких пробоин и будет оценкой вероятности пробить коридор. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AQgAAEIQCA9CSCgk3xcPAHNRMIkg6c7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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "s <- rep(0,times=n) # вектор из нулей \n", "\n", "for(i in 1:n){\n", " x <- rep(0,times=n)\n", " for(j in 1:1000){\n", " x[j] <- mean(rnorm(i, mean=2, sd=4))\n", " }\n", " s[i] <- sum(abs(x) > 2+eps3)/1000\n", " }\n", "\n", "qplot(1:n, s, geom='line')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Как мы видим, вероятность пробить коридор поначалу является высокой, но постепенно убывает. Давайте попробуем зафиксировать несколько коридоров и посмотрим как будут вести себя вероятности. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AIkQAKZIZD1SYQY1ujRo+Xll1820gxo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CwZfvsBCRFRNbFZKzmjmoq6Kudzyms6Ns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\nH7gvH1O7zZH1Qj8YIWf7zLG9Eg49S7jLRKCiEZADXdFmVOMRA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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "s1 <- rep(0,times=n) # вектор из нулей для первого коридора\n", "s2 <- rep(0,times=n) # вектор из нулей для второго коридора\n", "\n", "for(i in 1:n){\n", " x <- rep(0,times=n)\n", " for(j in 1:1000){\n", " x[j] <- mean(rnorm(i, mean=2, sd=4))\n", " }\n", " s1[i] <- sum(abs(x) > 2+0.5)/1000\n", " s2[i] <- sum(abs(x) > 2+0.1)/1000\n", " }\n", "\n", "ggplot(data.frame('x'=1:n, 's1'=s1, 's2'=s2)) + \n", " geom_line(aes(x, s1, color='eps=0.5')) +\n", " geom_line(aes(x, s2, color='eps=0.1'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Аналогичные графики можно было бы построить для дисперсии среднего. Мы же помним, что \n", "\n", "$$\n", "Var(\\bar X) = \\frac{Var(X_1 + \\ldots + X_n)}{n^2} = \\frac{Var(X_1)}{n}.\n", "$$\n", "\n", "В знаменателе у нас $n$. По мере роста выборки разброс убывает и среднее сходится к математическому ожиданию. Разобраться в таком графике вам придётся дома. Если не получится, не отчаивайтесь. Мы в следующий раз вспомним про него, когда будем говорить про состоятельность оценок.\n", "\n", "Теперь мы знаем как выглядит сходимость по вероятности. Интересно было бы посмотреть как выглядит её отсутствие. Давайте вспомним такую замечательную штуку, как распределение Коши. Помните? Ещё бы не помнили, оно было в домашке! У него не существует математического ожидания и для него выборочному среднему некуда сходиться. Давайте построим для него пару таких же рисунков. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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3CDVO+Pen7wKeyj40uDLl5qUwxdBUaPHk376cri5vj2wzWsG6Bots4/LS0tHF/d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\nuAY5Ll+x3EaNHGXjJ4y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MpRYYEvfelL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\nRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 1:1000 # выборка\n", "s <- rep(0, times=100) # пустой вектор для средних \n", "\n", "for(i in n){\n", " x <- rcauchy(i)\n", " s[i] <- mean(x)\n", "}\n", "\n", "eps3 = 0.5\n", "\n", "ggplot(data.frame('x'=n, 'y'=s)) + \n", " geom_line(aes(x, y)) +\n", " geom_line(aes(x, 2+eps3), col='magenta')+\n", " geom_line(aes(x, 2-eps3), col='magenta')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Постоянные пробои в нашем коридоре. При этом во времени их количество никак не уменьшается. Вот так вот и выглядит отсутствие сходимости по вероятности. Обратите внимание, что величина пробоя не очень важна. В случае, когда сходимость есть, пробои также могут быть очень большими, но они происходят всё реже. Тут они не происходят реже. Давайте убедимся в этом, построив оценку вероятности пробоя для каждого шага. Прямо как мы сделали выше. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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49uChc8SuRHVDBCKMipbwMXyC+arAc6AujcT5UvykQP8RRAAwTYpEwBvqk3DjAO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\nfimAOkONSKQvKBbEx7x4zZqwbExf4ppx4p2Hxz/+8aPJ44H2CU9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e3/nOdzYXX3xxTLrStQDaOC8NpYbzShVWSuAx45vf/OZFWtO7PgTU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QMF7x8L40ASxL/PMv//IvN0984hOb008/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\nk5OAjkWUT4C3337bbLvttma33XY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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "s <- rep(0,times=n) # вектор из нулей \n", "\n", "for(i in 1:n){\n", " x <- rep(0,times=n)\n", " for(j in 1:1000){\n", " x[j] <- mean(rcauchy(i))\n", " }\n", " s[i] <- sum(abs(x) > 2+eps3)/1000\n", " }\n", "\n", "qplot(1:n, s, geom='line')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Вероятность пробоя на всём промежутке ведёт себя абсолютно непредсказуемо. Одним словом говоря, ужас. Вот мы и познакомились со сходимостью по вероятности. На этом наш спид дэйтинг не останавливается. Мы переходим за следующий стол. Там нас заждалась слабая и ранимая сходимость по распределению." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Сходимость по распределению\n", "\n", "Осознать сходимость по распределению довольно просто. Поэтому сразу определение.\n", "\n", "__Определение:__ говорят, что последовательность случайных величин $X_1, X_2, \\ldots$ сходится к случайной величине $X$ _по распределению,_ если $F_{X_n}(x) \\to F_X(x)$ для всех $x$, в которых $F_X(x)$ непрерывна.\n", "\n", "Если функции сходятся, она есть. Если не сходятся, её нет. Всё просто. Давайте посмотрим на конкретный пример. \n", "\n", "#### Пример: \n", "\n", "Пусть последовательность $X_1, X_2, \\ldots $ это последовательность случайных величин с функциями распределения \n", "\n", "$$\n", "F_{X_n}(x) = \\begin{cases} 1 - \\left(1 - \\frac{1}{n} \\right)^{nx} \\quad& x > 0 \\\\ 0 \\quad & \\text{иначе} \\end{cases}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "К чему же сходится такое добро? Ответ очевиден! Надо просто найти предел для $F_{X_n}(x)$. Если вы ещё не забыли математический анализ за первый курс, вы легко сможете выяснить, что \n", "\n", "$$\n", "F_X(x) = \\lim_{n \\to \\infty} F_{X_n}(x) = 1 - e^{-x}.\n", "$$\n", "\n", "Получаем в пределе экспоненциальное распределение, $Exp(1)$. Теперь давайте посмотрим на всё это добро в картинках. И сразу же мы сталкиваемся с проблемой: нужно сгенерировать специфичное распределение. Но мы то с вами знаем, как эту проблему решить. Помните квантильное преобразование? Давайте подготовим для него обратную функцию, $F_{X_n}^{-1}(x)$:\n", "\n", "$$\n", "y = 1 - \\left(1 - \\frac{1}{n} \\right)^{nx} \\Rightarrow x = \\frac{\\ln(1-y)}{n\\cdot \\ln(1 - ^1/_n)}\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1] 25\n", "[1] 5929\n", "[1] 9\n" ] } ], "source": [ "# В R можно писать вот такие пафосные циклы:\n", "# item будет по очереди принимать все значения из списка c(5,77,3)\n", "# это питоновский стиль написания циклов, привыкайте :)\n", "\n", "for(item in c(5,77,3)){\n", " print(item^2)\n", "}" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
numberX2X5X10X100exp
1 0.2224893 0.0071638171.9585980 0.3207099 0.1519846
2 0.1970676 2.2448514462.5238174 0.9661386 0.7064626
3 0.2073205 0.6484365180.8112927 0.8919213 3.0894521
4 1.6080170 0.5680362230.6948494 0.6180957 0.1525272
5 1.0398946 1.4626431610.1254729 0.1573997 0.4034915
6 0.1382477 0.5768810180.2857508 0.4577309 0.3287159
\n" ], "text/latex": [ "\\begin{tabular}{r|llllll}\n", " number & X2 & X5 & X10 & X100 & exp\\\\\n", "\\hline\n", "\t 1 & 0.2224893 & 0.007163817 & 1.9585980 & 0.3207099 & 0.1519846 \\\\\n", "\t 2 & 0.1970676 & 2.244851446 & 2.5238174 & 0.9661386 & 0.7064626 \\\\\n", "\t 3 & 0.2073205 & 0.648436518 & 0.8112927 & 0.8919213 & 3.0894521 \\\\\n", "\t 4 & 1.6080170 & 0.568036223 & 0.6948494 & 0.6180957 & 0.1525272 \\\\\n", "\t 5 & 1.0398946 & 1.462643161 & 0.1254729 & 0.1573997 & 0.4034915 \\\\\n", "\t 6 & 0.1382477 & 0.576881018 & 0.2857508 & 0.4577309 & 0.3287159 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "number | X2 | X5 | X10 | X100 | exp | \n", "|---|---|---|---|---|---|\n", "| 1 | 0.2224893 | 0.007163817 | 1.9585980 | 0.3207099 | 0.1519846 | \n", "| 2 | 0.1970676 | 2.244851446 | 2.5238174 | 0.9661386 | 0.7064626 | \n", "| 3 | 0.2073205 | 0.648436518 | 0.8112927 | 0.8919213 | 3.0894521 | \n", "| 4 | 1.6080170 | 0.568036223 | 0.6948494 | 0.6180957 | 0.1525272 | \n", "| 5 | 1.0398946 | 1.462643161 | 0.1254729 | 0.1573997 | 0.4034915 | \n", "| 6 | 0.1382477 | 0.576881018 | 0.2857508 | 0.4577309 | 0.3287159 | \n", "\n", "\n" ], "text/plain": [ " number X2 X5 X10 X100 exp \n", "1 1 0.2224893 0.007163817 1.9585980 0.3207099 0.1519846\n", "2 2 0.1970676 2.244851446 2.5238174 0.9661386 0.7064626\n", "3 3 0.2073205 0.648436518 0.8112927 0.8919213 3.0894521\n", "4 4 1.6080170 0.568036223 0.6948494 0.6180957 0.1525272\n", "5 5 1.0398946 1.462643161 0.1254729 0.1573997 0.4034915\n", "6 6 0.1382477 0.576881018 0.2857508 0.4577309 0.3287159" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_obs = 10000\n", "\n", "# Создадим табличку, куда мы будем заносить выборки из нашей последовательности.\n", "df = data.frame(number = 1:n_obs)\n", "\n", "# Возьмём в табличку 2,5,10 и 100-ую случайные величины из последовательности\n", "for(n in c(2,5,10,100)){\n", " Y = runif(n_obs, min = 0, max = 1) # равномерное \n", " X = log(1-Y)/(n*log(1-1/n)) # сделали квантильное преобразование\n", " df[paste0('X',n)] = X # запомнили в табличку выборку\n", "}\n", "df$exp = rexp(n_obs, rate = 1) # записали в табличку выборку из Exp(1), к ней же всё сходится\n", "head(df)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Removed 143 rows containing non-finite values (stat_ecdf).”Warning message:\n", "“Removed 345 rows containing non-finite values (stat_ecdf).”Warning message:\n", "“Removed 409 rows containing non-finite values (stat_ecdf).”Warning message:\n", "“Removed 498 rows containing non-finite values (stat_ecdf).”Warning message:\n", "“Removed 481 rows containing non-finite values (stat_ecdf).”" ] }, { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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zWOMivrSCx/bSZrBoW6AyLhINHsHVCJ2vlrUZu6HbtzXyPBvIcyadB4KyldnDcC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gU4pY39UBUz87Fv1ymwqOvx0x0Rdjb6PH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\nauaMTYforXtQ03Fca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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Строим все функции распределения на одном графике\n", "ggplot(df) + \n", " stat_ecdf(aes(x = X2, colour = 'X2')) +\n", " stat_ecdf(aes(x = X5, colour = 'X5')) +\n", " stat_ecdf(aes(x = X10, colour = 'X10')) +\n", " stat_ecdf(aes(x = X100, colour = 'X100')) +\n", " stat_ecdf(aes(x = exp, colour = 'Exp(1)'), size = 1) +\n", " xlab('x') + ylab('F(x)') + xlim(0,3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Что мы видим? Последовательность из заданных выше функций распределения сходится к функции распределения экспоненциальной случайной величины, как мы и ожидали. Как выглядит отсутствие такой сходимости, я думаю, понятно. Поэтому примера для демонстрации её отсутствия, я искать не буду. \n", "\n", "Напомню, что сходимость по распределению самая слабая. Если есть сходимость по вероятности, то будет и сходимость по распределению. Переходим за следующий стол. Впереди третье свидание." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Сходимость в среднем\n", "\n", "И снова сразу же определение. \n", "\n", "__Определение:__ последовательность случайных величин $X_1, X_2, \\ldots$ сходится _в среднем порядка $r$_ к случайной величине $X$, если \n", "\n", "$$\n", "\\lim_{n \\to \\infty} E(|X_n - X|^r) = 0.\n", "$$\n", "\n", "Снова идеологически ничего сложного. Если модуль математического ожидания между $X_n$ и $X$ с ростом $n$ уменьшается, то всё отлично. А если не уменьшается, то не очень отлично. Давайте посомтрим на конкретном примере. \n", "\n", "#### Пример:\n", "\n", "Пусть $X_n \\sim U[0, \\frac{1}{n}]$. Покажем, что $X_n$ сходится в среднем порядка $r$ к нулю для любого положительного $r$. Сначала сделаем это в теории. Для равномерного распределения \n", "\n", "$$\n", "f_{X_n}(x) = \\begin{cases} n, \\quad 0 \\le x \\le \\frac{1}{n} \\\\ 0, \\quad \\text{ иначе} \\end{cases}\n", "$$\n", "\n", "Найдём \n", "\n", "$$\n", "E(|X_n - 0|^r) = \\int_0^{^1/_n} x^r \\cdot n dx = \\frac{1}{(r + 1) \\cdot n^r} \\to 0 \\quad \\forall r \\ge 1.\n", "$$\n", "\n", "В подобранном примере все $x$ положительные, поэтому проблем с модулем не возникло. \n", "\n", "Как это изобразить на картинке? Ну, наверное просто нарисовать последовательность из математических ожиданий. Другого способа я не вижу. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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jnaf559vZfqs/9uStL3kuqyoqIi1P/c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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_obs = 10^6 # число симуляций\n", "n = 50 # длина последовательности для рисунка\n", "ev = rep(0,n) # сюда будем записывать мат ожидания, ev ~ expected value\n", "\n", "for(i in 1:n){\n", " ev[i] = mean(runif(n_obs, min = 0, max = 1/i))\n", "}\n", "\n", "qplot(1:n, ev, geom='line')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Обратите внимание, что из сходимости в среднем автоматически следует сходимость по вероятности и сходимость по распределению. Так всегда.\n", "\n", "Сходимость по вероятности можно углядеть, если понять, что дисперсия случайной величины $X_n$ с каждым новым $n$ всё меньше. Сходимость по распределению к вырожденному распределению можно углядеть, если заметить, что в плтоности распределения фигурирует $1/n$. Точно такое же $1/n$ будет фигурировать в функции распределения и последовательность из них будет сходиться к вырожденному распределению.\n", "\n", "Но это нас сейчас не особо интересует. Сходимость в среднем сильнее сходимости по вероятности. В связи с этим нам хотелось бы увидеть живое подтверждение этому. Давайте убедимся, что последовательность случайных величин из следующего примера будет сходиться к нулю по вероятности, но никакой сходимостью в среднем, там и в помине не пахнет. \n", "\n", "#### Пример: \n", "\n", "Пусть последовательность дискретных случайных величин задаётся следующим незатейливым образом: \n", "\n", "$$\n", "X_n = \\begin{cases} n^2, \\qquad p = \\frac{1}{n} \\\\ 0, \\qquad p = 1 - \\frac{1}{n} \\end{cases} \n", "$$\n", "\n", "Эта последовательность будет сходиться к нулю по вероятности. В теории это можно довольно легко показать:\n", "$$\n", "\\lim_{n \\to \\infty} P(|X_n - 0| \\ge \\varepsilon) = \\lim_{n \\to \\infty} P(X_n = n^2) = \\lim_{n \\to \\infty} \\frac{1}{n} = 0\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Почему $P(|X_n - 0| \\ge \\varepsilon) = P(X_n = n^2)$, я думаю, понятно. Число $n$ растёт во времени, а $\\varepsilon$ произвольное маленькое число. Чтобы разница $X_n - 0$ оказалась больше этого произвольного маленького числа, нужно, чтобы случайная величина приняла значение $n^2$. \n", "\n", "Эта последовательность не будет сходиться к нулю в среднем. Покажем это! \n", "\n", "$$\n", "\\lim_{n \\to \\infty} E(|X_n|^r) = \\lim_{n \\to \\infty} (n^{2r} \\cdot \\frac{1}{n} + 0 \\cdot (1- \\frac{1}{n})) = \\lim_{n \\to \\infty} n^{2r - 1} = \\infty \\qquad \\forall r \\ge 1\n", "$$\n", "\n", "Вот такая вот досада. А теперь, картинки! " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "n_obs = 10^4\n", "\n", "ev = rep(0,500) # вектор для средних\n", "s = rep(0,500) # вектор для значений случайной величины\n", "\n", "for(i in 2:501){\n", " x = sample(c(i^2,0), size=n_obs, p = c(1/i, 1-1/i), replace = TRUE)\n", " ev[i] = mean(x) \n", " s[i] = x[1] # чтобы посмотреть на одну траекторию, подойдёт любое значение\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Видим, что в случае сходимости по вероятности переодически случаются пробои нашего вооброжаемого коридоа, но их вероятность всё меньше и меньше. Это означет, что последовательность сходится по вероятности к нулю. Мы это уже должны осознавать также как то, что небо голубое." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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Sj55+OiOZR7jc8xyvkpOieLRTnKdZHF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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "qplot(1:501,s,geom='line')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "А вот со средними возникают проблемы. Их довольно жёстко колбасит. причём колбасит со всё возрастающей дисперсией. Никакой сходимостью в среднем тут и не пахнет." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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1Ceg5bxEHfizUkce9AhmH8553a+HE/NsON69ZoVZNv1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\ntz0sS+vJEGBwIP2CJurSpYs77bTT/PXJdcskR3HXYj736GRa8r9aVg49T7L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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "qplot(1:501,ev,geom='line')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Вот такая вот история. Одни сходимости непривередливы, другие довольно капризны. Осталась встреча с ещё одной, на мой взгляд, самой капризной сходимостью. Сходимостью почти наверное." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Сходимость почти наверное\n", "\n", "Ух. Остался самый хард. Приготовьте свой мозг. Его сейчас начнёт потихонечку сводить. Дело в том, что сходимость почти наверное довольно глубокая штука и определяется на фундаментальных понятиях из тервера. Поэтому нам придётся копнуть в теорию, прежде чем сформулировать определение. \n", "\n", "На одной из первых лекции, вам сказали, что есть пространство элементарных исходов $\\Omega$. В этом пространстве живут исходы $\\{\\omega_1, \\ldots, \\omega_n\\}$. Множества из таких исходов - это события. Из событий составляется список с определёнными свойствами. Этот список называется сигма-алгеброй. Именно на нём определена вероятность, то есть функция отображающая каждое событие из сигма-алгебры на отрезок $[0; 1]$ и обладающая набором няшных свойств.\n", "\n", "Случайная величина - это функция, которая отображает пространство элементарных исходов на множество действительных чисел, $X(\\omega) : \\Omega \\to \\mathbb{R}$. Ясное дело, у неё тоже должны быть всякие няшные свойства, которые мы опустим для простоты. \n", "\n", "Если уже начало сводить мозг, откиньтесь назад на стуле и помассируйте себе виски. Это только начало, нам нужно сохранять себя в тонусе. Судороги прекратились? Продолжаем чтение! \n", "\n", "До текущего момента мы не особо вдавались в подробности, связанные с тем как устроена случайная величина $X(\\omega)$ при разных значениях $\\omega$. Всем сходимостям выше было на это наплевать. Со сходимостью почти наверное другая история. \n", "\n", "Чтобы стало немного полегче понять определение, давайте решим упражнение. Пусть у нас есть монетка и мы подкидываем её один раз. Проcтранство элементарных исходов в таком случае выглядит как-то так: $\\Omega = \\{О, Р\\}$. В пространстве живут два исхода. Определим последовательность случайных величин следующим образом.\n", "\n", "$$\n", "X_n(\\omega) = \\begin{cases} \\frac{n}{n+1}, \\qquad \\omega = O \\\\ (-1)^n, \\qquad \\omega = P \\end{cases}\n", "$$\n", "\n", "Пусть мы один раз подбрасываем монетку, а затем выписываем последовательность. Давайте ответим на пару вопросов. \n", "\n", "a) Для каких $\\omega$ последовательность случайных велчин сходится? \n", "\n", "Ответ прост. Ежели выпал орёл, то последовательность вошла в траекторию $\\frac{n}{n+1}$ и сошлась к единице. Если выпала решка, то всё пропало. \n", "\n", "b) Найдём вероятность $$ P(\\lim_{n \\to \\infty} X_n(\\omega) = 1).$$\n", "\n", "Перевожу. Нам нужно найти вероятность события, которое заключается в том, что наша последовательность сойдётся. Очевидно, что такая вероятность равна $0.5$, так как последовательность будет сходиться только при выпадении орла. Обычно эту вероятность записывают вот так: \n", "\n", "$$ P(\\{\\omega \\in \\Omega : \\lim_{n \\to \\infty} X_n(\\omega) = 1\\}).$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Читаем по символам: вероятность множества омег, на которых последовательность сходится. То есть вероятность события, состоящего в том, что последовательность сходится. Ежели эта вероятность равна единице, то сходимость наступает почти наверное. Если среди омег можно найти какую-то подпоследовательность из случайных величин, где сходимости нет, то всё пропало, сходимости нет. В нашем случае таким набором омег является решка. Ей соответствует расходящаяся последовательность. Ух! Копнули так копнули. Внимание, определение! \n", "\n", "__Определение:__ говорят, что последовательность случайных величин $X_1, X_2, \\ldots$ сходится к случайной величине $X$ почти наверное, если \n", "\n", "$$ P(\\{\\omega \\in \\Omega : \\lim_{n \\to \\infty} X_n(\\omega) = X(\\omega)\\}) = 1.$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Давайте попробуем проилюстрировать всё вот это вот на примере, который мы уже видели выше. Возьмём дискретную случайную величину\n", "\n", "$$\n", "X_n = \\begin{cases} n^2, \\qquad p = \\frac{1}{n} \\\\ 0, \\qquad p = 1 - \\frac{1}{n} \\end{cases} \n", "$$\n", "\n", "Как мы уже знаем, она сходится по вероятности. Почему? Потому что, она с ростом $n$ принимает всё большие значения с всё меньшей вероятностью.\n", "\n", "Сходимость почти наверное для этой случайной величины зависит от того как именно она устроена на пространстве элементарных исходов. Например, она может быть устроена вот так: \n", "\n", "\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Простите. Я брал этот пример из [учебника Черновой (нет, не Марии Игоревны, другой Черновы)](http://old.nsu.ru/mmf/tvims/chernova/tv/lec/node53.html). Мне было лень исправлять буквы кси на иксы, а седьмые степени на вторые. Вы мысленно должны это сделать сами. Обещаю исправится. Кстати говоря, если я пишу не очень понятно, загляните в Чернову. \n", "\n", "Что происходит на картинке? Значения, которые принимает случайная величина уточняются в соотвествии с возможными омегами. Мы влезаем в структуру этой величины и говорим, что \n", "\n", "$$\n", "X_n = \\begin{cases} n^2, \\qquad \\omega \\in (1-\\frac{1}{n}, 1] \\\\ 0, \\qquad \\omega \\in [0, 1 - \\frac{1}{n}] \\end{cases} \n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Получается, что у нас отрезочек из элементарных исходов, на котором случайная величина принимает большие значения, становится всё меньше и меньше и вероятность того, что среди элементарных исходов нельзя подобрать расходящейся подпоследовательности,\n", "\n", "$$P(\\{\\omega \\in \\Omega : \\lim_{n \\to \\infty} X_n(\\omega) = X(\\omega)\\}),$$ действительно, равна единице. Последовательность сходится почти наверное. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Мы могли бы задать последовательность как-нибудь иначе. Например, заставить отрезок длины $^1/_n$, на котором выпадает $n^2$, бегать по отрезку $[0; 1]$ так, чтобы любое $\\omega$ попадала в него бесконечное число раз и тем самым существовала бы подпоследовательность $X_{n_k} \\to \\infty$. Тогда бы никакой сходимости почти наверное не было бы. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Сложно ли это? Похоже на то. Кстати говоря, ещё раз обратите внимание на то, что сходимость почти наверное не имеет прямых связей со сходимостью в среднем. Для рассмотренного выше примера сходимость в среднем не выполняется. Сходимость почти наверное может как выполняться, так и не выполняться в зависимости от устройства пространства элементарных исходов.\n", "\n", "Какого-то примера с генерациями я, к сожалению, для этого раздела не подобрал. Если кто-то что-то знает и может подсказать, буду рад! \n", "\n", "Остался последний нюанс. А почему сходимость называется сходимостью почти наверное? Что за игра слов такая? Ответ на этот вопрос довольно мозгодробительный. Ваше естество будет сопротивляться ему." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6. Почему почти наверное? \n", "\n", "Если вероятность некоторого события равна единице, то такое событие называют достоверным. Если вероятность некоторого события равна нулю, то такое событие называют невозможным. \n", "\n", "__Очень важно__ понимать тонкую разницу между событием, которое не произойдёт никогда и тем, вероятность которого равна нулю. Нулевая вероятность события вовсе не означает того, что это событие никогда не наступит. Чисто теоретически наступление такого события возможно, но вероятность этого события равна нулю. Например, вероятность того, что непрерывная случайная величина попадёт в какую-то конкретную точку равна нулю. Тем не менее, сгенерировав такую случайную величину на компьютере, мы увидим, что она приняла конкретное значение, то есть попала в некоторую точку. Удивительно, но при каждой реализации случайной величины мы наблюдаем невозможное событие. Шокирует, не правда ли? Точно также важно понимать разницу между утверждением верным всегда и почти наверное верным. \n", "\n", "Ещё один пример. Представим себе как игрок в дартс бросает в мишень дротик. Пусть, как бы игрок не метнул дротик, он всегда попадает в мишень. Вероятность того, что дротик попадёт в какой-то конкретный регион мишени равна отношению площади этого региона к общей площади мишени. Например, вероятность того, что дротик попадет в правую половину мишени равна $0.5$. \n", "\n", "Рассмотрим событие \"дротик попадает в конкретную хорду мишени\". Площадь хорды равна нулю. То есть дротик не попадет в хорду почти наверное.\n", "\n", "Тем не менее множество точек на хорде не пусто и попадание в неё является чисто теоретически возможным. То же самое можно сказать и о любой другой точке на мишени. Так как любая точка будет иметь нулевую площадь, дротик не попадет в неё почти наверное. Однако дротик точно должен попасть в какую-то точку мишени! Таким образом при каждом бросании дротика происходит событие, имеющее нулевую вероятность. Вот такой вот странный объект - вероятность. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7. Знаменитые сходимости, про которые вы уже знаете\n", "\n", "Мы осознали, что сходимости бывают разными и постарались на интуитивном уровне прочувствовать их. Давайте теперь освежим в голове те сходимости, которые мы уже знаем. \n", "\n", "### 7.1 Закон больших чисел\n", "\n", "Этому парню мы посвятили итак много времени. Скажем лишь две вещи. Есть __слабый закон больших чисел__, который говорит, что выборочное среднее __сходится по вероятности__ к математическому ожиданию. Есть __усиленный закон больших чисел__, который говорит, что выборочное среднее __почти наверное сходится__ к математическому ожиданию. Ясное дело, в законах разные предпосылки, накладываемые на случайные величины. За подробностями в учебники! \n", "\n", "### 7.2 Центральная предельная теорема\n", "\n", "Этой даме мы тоже посвятили много времени. Скажем лишь то, что в ЦПТ имеет место __сходимость по распредлению,__ и двинемся дальше. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7.3 Схема испытаний Бернулли и теорема Муавра-Лапласа\n", "\n", "Помните схему исптаний Бернулли? Она состояа в том, что у нас есть монетка, которая выпадает орлом с вероятностью $p$. Если он выпал, то это успех. Мы делали $n$ подбрасываний и хотели узнать какова вероятность того, что успехов будет ровно $m$. Иными словами, нас интересовало распределение случайной величины $X$, числа успехов, то есть орлов. Вероятность того, что у нас окажется ровно $m$ успехов выглядела так: \n", "\n", "$$\n", "P(X = m) = C_n^m \\cdot p^m \\cdot (1-p)^{n-m}.\n", "$$\n", "\n", "Мы говорили, что если значения $m$ и $n$ очень высоки, то считать $C_n^m$ будет затруднительно из-за того, что там возникают факториалы. Из-за этого мы искали формулы для приближённого вычисления. Таких формул было целых три, каждая из них была сформулированна как отдельная теорема со своими предпосылками. Исторически эти формулы родились ещё до ЦПТ и изначально были доказаны при участии формулы стирлинга, рядов тэйлора и прочих брутальных приколов из матана. Тем не менее, две из них являются прямым следствием из ЦПТ.\n", "\n", "__Предельная теорема Муавра-Лапласа:__\n", "\n", "Пусть успех может произойти в любом из испытаний с вероятностью $p$ и пусть $m$ - число успехов, а $n$ - число испытаний, тогда\n", "\n", "$$\n", "P_n(m) = \\frac{1}{\\sqrt{npq}} \\cdot \\frac{1}{\\sqrt{2\\pi}} \\cdot e^{-\\frac{x^2}{2}},\\text{ где } x = \\frac{m - np}{\\sqrt{npq}}.\n", "$$\n", "\n", "Так было написано в лекциях. Мы сформулируем это немного иначе. \n", "\n", "Пусть успех может произойти в любом из испытаний с вероятностью $p$ и пусть $m$ - число успехов, а $n$ - число испытаний, тогда $\\frac{m - np}{\\sqrt{npq}} \\Rightarrow N(0,1)$.\n", "\n", "Стало как-то полаконичнее. Докажем это. Мы знаем, что $m = X_1 + \\ldots + X_n,$ где каждая случайная величина $X_i$ принимает значение $1$ с вероятностью $p$. Мы можем вычислить, что $E(X_i) = p$, а $Var(X_i) = pq$. Осталось дело за малым, просто использовать ЦПТ. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "n_obs = 10000 # число наблюдений \n", "p = 0.5\n", "\n", "df = data.frame(number = 1:n_obs) # табличка для наблюдений \n", "\n", "for(n in c(10,20,100,2000)){\n", " # X <- rbinom(n_obs, size = n, prob = p) # генерим выборку неправильно \n", " # генерим выборку правильно\n", " X <- (rbinom(n_obs, size = n, prob = p) - n*p)/(sqrt(n*p*(1-p))) \n", " df[paste0('X',n)] = X # заносим её в табличку \n", "}\n", "\n", "df$norm = rnorm(n_obs) # разбавляем всё это добро Нормальным распределением" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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JGJ4/dVZOYnARJwCQF+jbvkQVAMEiABEiABEiABEshXAqHySmkeO0krwGjjCdu2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\nUGqrk0Uo5Z8dnKwqLwvZZXoxu3TyOhg2jJHAQIB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0m/dKT8e5+Dt5Jxu/TWVVtKWkkk5v2qVG1KTzLMKAwGQJ6OWwtgaCFO/pJCfr8dof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\nk27MmDHGcvQLL7wgOivXvqPnyzxKDtSSqM7YqgD1d3qu6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II=", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "options(repr.plot.width=8, repr.plot.height=5) # размеры картинки\n", "\n", "p1 = ggplot(df)+\n", " # гистограмма для текущей случайной величины\n", " geom_histogram(aes(y=..density.., x=X10, colour = 'X10'), alpha=0.5, bins=10) +\n", " # гистограмма для предельного распределения \n", " geom_histogram(aes(y=..density.., x=norm, colour = 'Norm'),fill = \"cornflowerblue\", alpha=0.2, bins = 100)\n", "\n", "p2 = ggplot(df)+\n", " geom_histogram(aes(y=..density.., x=X20, colour = 'X20'), alpha=0.5, bins = 20) +\n", " geom_histogram(aes(y=..density.., x=norm, colour = 'Norm'),fill = \"cornflowerblue\", alpha=0.2, bins = 100)\n", "\n", "p3 = ggplot(df)+\n", " geom_histogram(aes(y=..density.., x=X100, colour = 'X100'), alpha=0.5, bins = 50) +\n", " geom_histogram(aes(y=..density.., x=norm, colour = 'Norm'),fill = \"cornflowerblue\", alpha=0.2, bins = 100)\n", "\n", "p4 = ggplot(df)+\n", " geom_histogram(aes(y=..density.., x=X2000, colour = 'X2000'), alpha=0.5, bins = 100) +\n", " geom_histogram(aes(y=..density.., x=norm, colour = 'Norm'),fill = \"cornflowerblue\", alpha=0.2, bins = 100)\n", "\n", "# Располагаем графики рядом.\n", "pushViewport(viewport(layout = grid.layout(2, 2)))\n", "print(p1, vp = viewport(layout.pos.row = 1, layout.pos.col = 1))\n", "print(p2, vp = viewport(layout.pos.row = 1, layout.pos.col = 2))\n", "print(p3, vp = viewport(layout.pos.row = 2, layout.pos.col = 1))\n", "print(p4, vp = viewport(layout.pos.row = 2, layout.pos.col = 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Интегральную предельную теоремы с доказательством я тут расписывать не хочу. За ней в учебник Черновой.\n", "\n", "### 7.4 Формула Пуассона\n", "\n", "Когда значение $n$ было довольно большим, а вероятность успеха $p$ была довольно маленькой, мы пользовались другой приближённой формулой. Теорему с ней можно найти либо в своих записях лекций, либо в учебнике Черновой на странице 47. Можно ещё посмотреть её в [онлайн версии учебника.](http://old.nsu.ru/mmf/tvims/chernova/tv/lec/node21.html#SECTION000650)\n", "\n", "Если перевести всё, что там написано на язык последовательностей, можно сказать, что дана последовательность случайных величин $X_n \\sim Binomial(n, \\frac{\\lambda}{n})$. В данном случае $\\frac{\\lambda}{n}$ как раз и обеспечивает убывание вероятности успеха от серии к серии. Давайте посмотрим к чему сходится такая последовательность случайных величин. Сначала в теории, потом в симуляциях.\n", "\n", "В теории последовательность сходится по распределению к распределению Пуассона, $X_n \\Rightarrow Poiss(\\lambda)$. В первом семестре вы доказали это вот таким вот незатейливым образом:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\begin{multline}\n", "\\lim_{n \\to \\infty} P_{X_n}(k) = \\lim_{n \\to \\infty} C_n^k \\cdot \\left( \\frac{\\lambda}{n} \\right)^k \\cdot \\left(1 - \\frac{\\lambda}{n} \\right)^{n-k} = \\lambda^k \\cdot \\lim_{n \\to \\infty} \\frac{n!}{k! \\cdot (n-k)!} \\cdot \\frac{1}{n^k} \\cdot \\left(1 - \\frac{\\lambda}{n} \\right)^{n-k} = \\\\ =\n", "\\frac{\\lambda^k}{k!} \\lim_{n \\to \\infty} \\underbrace{\\left[ \\frac{n (n-1) \\ldots (n-k+1)}{n^k}\\right]}_{1} \\cdot \\underbrace{\\left[ 1 - \\frac{\\lambda}{n} \\right]^n}_{e^{-\\lambda}} \\cdot \\underbrace{\\left[ 1 - \\frac{\\lambda}{n} \\right]^{-k}}_{1} = \\frac{e^{-\\lambda} \\cdot \\lambda^k}{k!}\n", "\\end{multline}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Если говорить подробнее, то вы просто-напросто посмотрели к чему сойдётся последовательность из законов распределений Бернулли и нашли распределение Пуассона. Это была ваша первая встреча с ним. Если задуматься и глянуть на это всё, то становится понятно, что такое приближение уместно применять тогда, когда $n$ велико, а $p$ мало. Отсюда выскакиевает непосредственное применение случайной величины, имеющей распределения Пуассона для моделирвоания счётчиков: число лайков, число людей в очереди и т.п.\n", "\n", "Посмотрим как это выглядит на картинке. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "n_obs = 10000 # число наблюдений \n", "lambda = 8 # значение параметра \n", "\n", "df = data.frame(number = 1:n_obs) # табличка для наблюдений \n", "\n", "for(n in c(10,20,50,200)){\n", " X <- rbinom(n_obs, size = n, prob = lambda/n) # генерим выборку\n", " df[paste0('X',n)] = X # заносим её в табличку \n", "}\n", "\n", "df$poiss = rpois(n_obs, lambda = lambda) # разбавляемс всё это добро Пуассоном" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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sb8X0MOP/zwhHPqjLD8JAESIAESIIFcJoAG6L///e+6N8pYmyBRA3Q8Xqi/b775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WL9K9/vrr7uM/VjGO9FPMx7THHaWreqH6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\n77D1tu3zuoUlFg1rnyxU76lUeEzbI/GUpNmIg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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width=8, repr.plot.height=5) # размеры картинки\n", "\n", "p1 = ggplot(df)+\n", " # гистограмма для текущей случайной величины\n", " geom_histogram(aes(y=..density.., x=X10, colour = 'X10'), alpha=0.5, bins = 15) +\n", " # гистограмма для предельного распределения \n", " geom_histogram(aes(y=..density.., x=poiss, colour = 'Poiss'),fill = \"cornflowerblue\", \n", " alpha=0.2, bins = 15)\n", "\n", "p2 = ggplot(df)+\n", " geom_histogram(aes(y=..density.., x=X20, colour = 'X20'), alpha=0.5, bins = 15) +\n", " geom_histogram(aes(y=..density.., x=poiss, colour = 'Poiss'),fill = \"cornflowerblue\",\n", " alpha=0.2, bins = 15) \n", "\n", "p3 = ggplot(df)+\n", " geom_histogram(aes(y=..density.., x=X50, colour = 'X50'), alpha=0.5, bins = 15) +\n", " geom_histogram(aes(y=..density.., x=poiss, colour = 'Poiss'),fill = \"cornflowerblue\",\n", " alpha=0.2, bins = 15)\n", "\n", "p4 = ggplot(df)+\n", " geom_histogram(aes(y=..density.., x=X200, colour = 'X200'), alpha=0.5, bins = 15) +\n", " geom_histogram(aes(y=..density.., x=poiss, colour = 'Poiss'),fill = \"cornflowerblue\",\n", " alpha=0.2, bins = 15)\n", "\n", "# Располагаем графики рядом.\n", "pushViewport(viewport(layout = grid.layout(2, 2)))\n", "print(p1, vp = viewport(layout.pos.row = 1, layout.pos.col = 1))\n", "print(p2, vp = viewport(layout.pos.row = 1, layout.pos.col = 2))\n", "print(p3, vp = viewport(layout.pos.row = 2, layout.pos.col = 1))\n", "print(p4, vp = viewport(layout.pos.row = 2, layout.pos.col = 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Вот такая вот сходимость. Надеюсь, что это небольшой пункт оставил у вас в голове хоть какое-то понимание о том как связаны между собой биномиальное распределение, распределение пуассона и нормальное. В обеих ситуациях __сходимость по распределению.__ На этом про сходимости всё. Они стали для нас обыденным явлением и мы готовы с ними сталкиваться на ежедневной основе. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Почиташки \n", "\n", "* [Иллюстрация теоремы Гливенко-Кантели в R.](https://www.r-bloggers.com/convergence-and-asymptotic-results/) Можно посмотреть как в R построить красивые графики, на которых эмпирическая функция распределения почти наверное сходится к теоретической. На лекциях у вас была такая теорема без красивого названия и без доказательства. \n", "* [Хороший конспект по разновидностям сходимостей](https://www.probabilitycourse.com/chapter7/7_2_8_solved_probs.php) вместе с хорошей коллекцией задачек по ним. Рекомендую немного почитать об этом и попробовать решить задачки. Часть из них есть в домашке. Обратите внимание, что обычно доказывать наличие сходимости почти наверное напрямую это довольно трудная задачка. Поэтому для неё выделяют всякие разные признаки. В этом конспекте есть парочка признаков. Если хочется углубиться в них, добро пожаловать :) \n", "* [Учебник Черновой по терверу.](https://github.com/FUlyankin/r_probability/raw/master/books/Хороший%20учебник%20по%20терверу.pdf)\n" ] } ], "metadata": { "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": "3.4.4" } }, "nbformat": 4, "nbformat_minor": 2 }