{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Вероятность и Мат. Статистика ч.2\n",
"Шестаков А.В. Майнор по анализу данных - 16/02/2016"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.stats as stats\n",
"import matplotlib.pyplot as plt \n",
"\n",
"plt.style.use('ggplot')\n",
"\n",
"font = {'family': 'Verdana',\n",
" 'weight': 'normal'}\n",
"plt.rc('font', **font)\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Распределения случайных величин"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"На лекциях были рассмотрены распределения дискретных и непрерывных случайных величин.
Были изучены соотношения, которые устанавливают связь значений случайных величин и соответствующие им вероятноти - **функции распределения** (cumulative density function/probability mass function) и **плотности распределения** (probability density function).\n",
"\n",
"Посмотрим, как можно обращатся к законам распределения в Python"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Распределение Бернулли"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Случайная величина принимает 2 возможных значения (успех или провал, мужской или женский пол и тп)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ F(X=x)=p^x(1-p)^{1-x}, \\quad x = \\{0, 1\\}$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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FfNbd9+zM56khx9pkDegO7v5ga+ObWcd9wH3uvtjlyy3VO5GO1uolbSGEfmSnjXcl6/IH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\nowAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 1\n",
"p = 0.8\n",
"\n",
"fig, ax = plt.subplots(1,2)\n",
"fig.set_size_inches(14,6)\n",
"x = np.arange(0,n+1)\n",
"\n",
"prob_mass = stats.bernoulli.pmf(x, p)\n",
"prob = stats.bernoulli.cdf(x, p)\n",
"ax[0].bar(x,prob_mass)\n",
"ax[1].plot(x, prob)\n",
"\n",
"ax[0].set_title(u'Закон распределения')\n",
"ax[1].set_title(u'Функция распределения')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Биномиальный закон распределения"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Вероятность наступления числа $X=m$ события в $n$ независимых испытаниях, в каждом из которых оно может наступить с вероятностью $p$:\n",
"$$ F(X=m|p,n)=C_n^m p^m (1-p)^{n-m} $$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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c/OGHwP+KMR4FROAtnTuOMa4H1k8tp5QYHR3tIezBMDIy0pj6NqGurVZrr+VA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\npEmSJEmSZmHSJEmSJEmz+P8BmGbBOKEcMJ8AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 5000\n",
"p = 0.6\n",
"\n",
"fig, ax = plt.subplots(1,2)\n",
"fig.set_size_inches(14,6)\n",
"x = np.arange(0, n+1)\n",
"prob_mass = stats.binom.pmf(x, n, p)\n",
"prob = stats.binom.cdf(x, n, p)\n",
"ax[0].bar(x,prob_mass)\n",
"ax[1].plot(x, prob)\n",
"\n",
"ax[0].set_title(u'Закон распределения')\n",
"ax[1].set_title(u'Функция распределения')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Распределение Пуассона"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ F(X=m|\\lambda)=\\lambda^m \\frac{\\exp(-\\lambda)}{m!} $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Является предельным приближением к биномиальному распределению!"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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myzLrqYHnTXu1Wo2U0rqy45DUQ5xyXCWacXheSmkncAl54nIvcFtK6U7gAmD9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\npAGHJkmSJEka+AG2xVO0lVp3hgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 5000\n",
"p = 0.6\n",
"\n",
"lamb = n*p\n",
"\n",
"fig, ax = plt.subplots(1,2)\n",
"fig.set_size_inches(14,6)\n",
"x = np.arange(0, n)\n",
"prob_dens = stats.poisson.pmf(x, lamb)\n",
"prob = stats.poisson.cdf(x, lamb)\n",
"ax[0].bar(x, prob_dens)\n",
"ax[1].plot(x, prob)\n",
"\n",
"ax[0].set_title(u'Закон распределения')\n",
"ax[1].set_title(u'Функция распределения')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Нормальное распределение"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Самое известное распределение - нормальное распрежедение. Параметры: $\\mu$ - среднее значение, $\\sigma$ - дисперсия"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ f_X(x | \\mu, \\sigma) = \\frac{1}{\\sigma \\sqrt{2 \\pi}} \\exp{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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wnVI6ABBj/BBwca+dxRgngcn2dkqJiYl6zGsYGxuzrhXUruue6SYTJzycML5x\n2CEtmzodV6hffWOMOzo2p1JKU/OVN9GRJI26W4H3xBi3AHuAC4FLYoybgWNSSncCnwbeEWP8yZTS\nd4Bnl687TNlwTnU8dGmj0VjG8FePiYkJrGv1TExMsPfee2H/PhoHZggVrnedjivUq74TExOklHYs\n5jUOXZMkjbSUUgu4iCI5uR24IaV0C3ABsLMs0wBeBnw4xng7Ra/PlUMJWBqG6SaMbyKEMOxIpBVj\nj44kaeSllHYBu7oe20mZ6JTbNwFnrXBo0urQajg/R7Vjj44kSVLVeQ8d1VBfPTp93nH6RRQTO48C\nvgC8OKU0PcBYJUmStBStYuiaVCcL9uh03HH6POB0YHuM8ayuMscDr6O4GdtpFPcweMXgw5UkSdJi\n5VaDYI+OaqafoWsL3nGa4n4F40D7LlR3A/sHFqUkSZKWrtWETSY6qpd+Ep1ed5w+sbNASum7wB8D\nX4kxvhs4m6IXSJIkScPmYgSqoX5XXZv3jtPlvQp+ETgHOIPibtPnAR/r3pE3YrOuVRP27u2r3Nq1\na0f+M6nTca1TXdsWeyM2SSOk1YStjxx2FNKK6ifR6eeO088AvpxS+jrw9RhjE/hNeiQ63ojNulZN\nnp3tq9zMzMzIfyZ1Oq51qiss7UZskkZIq+FiBKqdfoau3QqcHWPcEmNcR3HH6RtjjJtjjO1LA3cA\nT4sxHltunw18dfDhSpIkabFyq+liBKqdBROdPu84/U/A24F/iDF+CXgccNkyxSxJkqTF8D46qqG+\n5uj0ecfpt1MkO5IkSVpNXIxANdTP0DVJkiSNslbTHh3VjomOJElSheWZGdh3H2wYH3Yo0ooy0ZEk\nSaqw3GrC+EbCGr/2qV78jZckSaqw3NwL4w5bU/2Y6EiSJFVYdiEC1ZSJjiRJUoXl5l4XIlAtmehI\nkiRVWG7sJdijoxoy0ZEkSaowe3RUVyY6kiRJFTbrHB3VlImOJElSheVmwx4d1ZKJjiRJUoU5dE11\nZaIjSZJUYbnZIJjoqIZMdCRJkiqs6NFxjo7qx0RHkiSpwoobhtqjo/ox0ZEkSaqwYjECe3RUPyY6\nkiRJFZVnZ8jTTRjfOOxQpBVnoiNJklRV900TNowT1qwddiTSijPRkSRJqqpWg7Bx87CjkIbCREeS\nJKmqWk3ChImO6slER5IkqapaDYILEaimTHQkSZIqKreahE326KieTHQkSZKqqtUw0VFtmehIkiRV\nVatJ2OQpVzIGAAAU/ElEQVTNQlVPJjqSJElVZY+OasxER5IkqapaDdbYo6OaMtGRJEmqqNxqeh8d\n1ZaJjiRJUlW1Gs7RUW2Z6EiSJFWVNwxVjZnoSJIkVZWLEajGTHQkSZIqKM/OwnSTsNGha6onEx1J\nkqQquv8+WH80Ye3aYUciDYWJjiRJUhW1GjC+adhRSENjoiNJklRFrQY4bE01ZqIjSZJURa0mbLRH\nR/VloiNJklRBudVwIQLVmomOJElSFdmjo5oz0ZEkSaqiVgM2eg8d1ZeJjiRJUhXZo6OaM9GRJEmq\nIlddU82t66dQjHE7cEVZfmdK6fIeZTYAVwLPAsaAM1JKPx5grJIkSepTnm6yxh4d1diCiU6McRy4\nCvhp4IfAVIzx+pTSP3cV/RPgzpTSYwYfpiRJkhaludceHdVaP0PXtgG3pZR2p5RmgWuB7Z0FYown\nAOeklC5bhhglSZK0WM7RUc31M3RtK3BPx/Zu4NSuMk8AiDHeDDwc+Bzw8pTSfYMIUpIkSYvkHB3V\nXF9zdICZru2xru3jga8BzyvLvhm4FHhN945ijJPAZHs7pcTERD3+CMfGxqxrBYW9e/sqt3bt2pH/\nTOp0XOtU17YY446OzamU0tSQQpF0hHLOMG2Pjuqtn0TnbopEpu248rFO9wLTKaUDADHGDwEX99pZ\n2XBOdTx0aaPR6DPc0TYxMYF1rZ48O9tXuZmZmZH/TOp0XOtUVyjqm1LaMew4JA3Ivvtg3Rhh3VHD\njkQamn7m6NwKnB1j3BJjXAdcCNwYY9wcY3xkWebTwNNijD9Zbj+7fJ0kSZJWmvNzpIUTnZRSC7iI\nohfmduCGlNItwAXAzrJMA3gZ8OEY4+0UvT5XLlPMkiRJmk+rYaKj2utrjk5KaRewq+uxnZSJTrl9\nE3DWQKOTJEnS4rWaLkSg2ut3MQJJklatfm5s3VH21cALU0pPXKn4pBVnj47U1xwdSZJWrY4bW58H\nnA5sjzH2HGEQY3wq8Hwgr1yE0srLzQbBHh3VnImOJGnULXhja4AY4xbgLcDLVzg+aeXZoyOZ6EiS\nRl6vG1uf2KPce4FXl89L1TbtHB3JREeSVAXz3tg6xvgq4NPlqqFhxaKShqXVgHF7dFRvLkYgSRp1\n/dzY+mTgGTHGX6VIgh4RY/xUSunp3TuLMU4Ck+3tlBITE/W4Mj42NmZdK6K5737GjjuBsYmJyte1\nU53qCvWrb4xxR8fmVEppar7yIeehz8fMd91117BjWBF1utN6ner6jT0zXHzdNxYsd8X5p3Daw8YW\nLLea1em41qmuAFu3boUR7emIMW4EvkgxV2cPcBNwCfB54JiU0p1d5U8CPpJSOqPPt7CdqqCq13Xm\nTa9hzXN+hfDYJ1S+rp3qVFeoV32X0k45dE2SNNL6ubG1VDveR0dy6JokafT1c2Prjsf/Fei3N0ca\nTa2mq66p9uzRkSRJqpCcM7T2uhiBas9ER5IkqUr274M1awhj64cdiTRUJjqSJElV0mrAuPNzJBMd\nSZKkKnF+jgSY6EiSJFVLqwGbNg87CmnoTHQkSZKqxB4dCTDRkSRJqpTcahC8h45koiNJklQpraZL\nS0uY6EiSJFVLqwH26EgmOpIkSZXSajhHR8JER5IkqVKcoyMVTHQkSZKqxFXXJMBER5IkqVqcoyMB\nJjqSJEnV0mqa6EiY6EiSJFXLtD06EpjoSJIkVUbevw9mM4yNDTsUaehMdCRJkqpiuhi2FkIYdiTS\n0JnoSJIkVUXTe+hIbSY6kiRJVeHS0tJBJjqSJElV4dLS0kEmOpIkSRWRWw2CPToSYKIjSZJUHdPe\nQ0dqM9GRJEmqCoeuSQeZ6EiSJFVFyx4dqc1ER5IkqSKcoyM9yERHkiSpKuzRkQ4y0ZEkSaoKbxgq\nHWSiI0mSVBXTLkYgtZnoSJIkVUWraY+OVFrXT6EY43bgirL8zpTS5fOUfTXwwpTSEwcToiRJkhaS\nH3gADhyA9RuGHYq0KizYoxNjHAeuAs4DTge2xxjPmqPsU4HnA3mQQUqSJGkB00VvTghh2JFIq0I/\nQ9e2AbellHanlGaBa4Ht3YVijFuAtwAvH2yIkiRJWpA3C5UO0U+isxW4p2N7N3Bij3LvBV5dPi9J\nkqSV5Pwc6RD9LkYw07U91rkRY3wV8OmU0i2A/aWSJEkrzR4d6RD9LEZwN3B8x/Zx5WOdTgaeEWP8\nVYok6BExxk+llJ7evbMY4yQw2d5OKTExUY8/yrGxMetaQWHv3r7KrV27duQ/kzod1zrVtS3GuKNj\ncyqlNDWkUCQtQW41COP26EhtIef51w2IMW4EvkgxV2cPcBNwCfB54JiU0p1d5U8CPpJSOqPPGPJd\nd9212LhH0sTEBI1GY9hhrIg61fUbe2a4+LpvLFjuivNP4bSHjS1YbjWr03GtU10Btm7dCvbIz8V2\nqoKqWNfZj38Q7v0Ra577skMer2Jd51KnukK96ruUdmrBoWsppRZwETAF3A7cUA5RuwDYuegoJUmS\nNHjO0ZEO0dd9dFJKu4BdXY/tpEeik1L6V6Df3hxJkiQNQqsBP/GoYUchrRr9LkYgSZKk1cweHekQ\nJjqSJEkVkFsNwqZ6LaIizcdER5IkqQpaTZeXljqY6EiSJFVBqwEuLy0dZKIjSZJUBdP26EidTHQk\nSZJGXD5wAPbdDxvGhx2KtGqY6EiSJI266SaMbyIE7/srtZnoSJIkjToXIpAOY6IjSZI06loN76Ej\ndTHRkSRJGnX26EiHMdGRJEkacbnVIJjoSIcw0ZEkSRp10w5dk7qZ6EiSJI06h65JhzHRkSRJGnVN\ne3SkbiY6kiRJo67VsEdH6mKiI0mSNOJyq0mwR0c6hImOJEnSqLNHRzqMiY4kSdKom246R0fqYqIj\nSZI06loN2Lh52FFIq4qJjiRJ0gjLszNw/32wYXzYoUiryrphByBJ0pGKMW4HrqBo13amlC7ven49\n8FHgZOBAWeaNKx6otBymW7BhI2GN16+lTv5FSJJGWoxxHLgKOA84HdgeYzyrR9HLU0qnAmcCz40x\nnrGCYUrLp+X8HKkXEx1J0qjbBtyWUtqdUpoFrgW2dxZIKe1LKd3Y/hn4JnDCikcqLYfmXldck3ow\n0ZEkjbqtwD0d27uBE+cqHGM8ATgHuHWZ45JWhiuuST2Z6EiSqmCma3usV6EY49FAAl6bUtq77FFJ\nKyC3GoRxe3Skbi5GIEkadXcDx3dsH1c+dogY4xjwfuC6lNI1c+0sxjgJTLa3U0pMTNTjS+TY2Jh1\nHUH7DjzAzLEPZXyO+lSprgupU12hfvWNMe7o2JxKKU3NV95ER5I06m4F3hNj3ALsAS4ELokxbgaO\nSSndGWPcAHwI+GRK6cr5dlY2nFMdD13aaDSWJfDVZmJiAus6emZ/9AM4av2c9alSXRdSp7pCveo7\nMTFBSmnHYl7j0DVJ0khLKbWAiyiSk9uBG1JKtwAXADvLYtuAc4GXxBi/EmP8cozx9cOIVxq4VhM2\n1eeqvtQve3QkSSMvpbQL2NX12E7KRCel9ClgwxBCk5ZfqwEbHzPsKKRVxx4dSZKkEZZbTYLLS0uH\nMdGRJEkaZa0GjLu8tNTNREeSJGmUtRreMFTqwURHkiRplLWaJjpSDyY6kiRJIyrPzsJ9LRjfOOxQ\npFXHREeSJGlU3TcN6zcQ1q4ddiTSqmOiI0mSNKpaDdjoQgRSLyY6kiRJo8r5OdKcTHQkSZJGlSuu\nSXMy0ZEkSRpRudUgOHRN6mldP4VijNuBK8ryO1NKl3c9vx74KHAycKAs88YBxypJkqRO9uhIc1qw\nRyfGOA5cBZwHnA5sjzGe1aPo5SmlU4EzgefGGM8YaKSSJEk6VKvpYgTSHPoZurYNuC2ltDulNAtc\nC2zvLJBS2pdSurH9M/BN4IRBBytJkqQO9uhIc+on0dkK3NOxvRs4ca7CMcYTgHOAW48sNEmSJM3L\nHh1pTv0uRjDTtT3Wq1CM8WggAa9NKe09ksAkSZI0v2IxAnt0pF76WYzgbuD4ju3jyscOEWMcA94P\nXJdSumauncUYJ4HJ9nZKiYmJevyBjo2NWdcKCnv7y+nXrl078p9JnY5rneraFmPc0bE5lVKaGlIo\nkvo17X10pLn0k+jcCrwnxrgF2ANcCFwSY9wMHJNSujPGuAH4EPDJlNKV8+2sbDinOh66tNFoLCX2\nkTMxMYF1rZ48O9tXuZmZmZH/TOp0XOtUVyjqm1LaMew4JC2Sc3SkOS04dC2l1AIuokhObgduSCnd\nAlwA7CyLbQPOBV4SY/xKjPHLMcbXL0/IkiRJApyjI82jr/vopJR2Abu6HttJmeiklD4FbBh4dJIk\nSeop51wMXRs30ZF66XcxAkmSJK0m903DUWOEdX1dt5Zqx0RHkiRpFDk/R5qXiY4kSdIomnZ+jjQf\nEx1JkqRRZI+ONC8THUmSpBGUW02CCxFIczLRkSRJGkWtBmyyR0eai4mOJEnSKGo1HbomzcNER5Ik\naRS1Gi5GIM3DREeSJGkUNV2MQJqPiY4kSdIIytNNgj060pxMdCRJkkZRqwHj9uhIczHRkSRJGkUu\nRiDNy0RHkiRpFLkYgTQvEx1JkqQRk3O2R0dagImOJEnSqNl3P6xbRzjqqGFHIq1aJjqSJEmjptV0\n2Jq0ABMdSZKkUdPa64pr0gJMdCRJkkaNPTrSgkx0JEmSRk2r4UIE0gJMdCRJkkZMbjUJ9uhI8zLR\nkSRJGjX26EgLMtGRJEkaNc7RkRZkoiNJkjRq7NGRFmSiI0mSNGKKOTomOtJ8THQkSZJGzbQ9OtJC\nTHQkSZJGTbPhHB1pASY6kiRJo6bVtEdHWoCJjiRJ0gjJOZeLEdijI83HREeSJGmU7N8PIRDG1g87\nEmlVM9GRJEkaJfbmSH0x0ZEkSRolrrgm9cVER5IkaZS4EIHUFxMdSZKkUeLQNakvJjqSJEkjJDcb\nBHt0pAWZ6EiSJI2SVtMeHakPJjqSJEmjpOViBFI/THQkSZJGybQ9OlI/THQkSZJGSG45R0fqh4mO\nJEnSKGk1YdweHWkh6/opFGPcDlxRlt+ZUrp8KWUkSVoOtlOqlVYDNm0edhTSqrdgj06McRy4CjgP\nOB3YHmM8a7FlJElaDrZTqh1XXZP60s/QtW3AbSml3SmlWeBaYPsSykiStBxsp1Qvrrom9aWfRGcr\ncE/H9m7gxCWUkSRpOdhOqTbyA/thdgbG1g87FGnV62uODjDTtT22xDLSqveD+2f5QevAguW2bFzH\nlqMXv55HP/tf6r6lGlvWdmrmT/77ogMaRc1165g5sPD5rwpWVV1zhjwLs53/Zrq2Z4syBw7AxEMI\nIQw7amnV6yfRuRs4vmP7uPKxxZYBIMY4CUy2t1NKbN26tY8wqmFioj5dzaNa18X+Nm7dCp97/COX\nbf+rzage16WoU10BYow7OjanUkpTQwplsZa9nXrkG98xiDiloanT+axOdYV61Xex7VTIOS+0w43A\nFynGN+8BbgIuAT4PHJNSunOuMimlW/oJOKW0Y6FyVWBdq8m6VlOd6gqjXV/bqcGxrtVkXaurTvVd\nSl0XHBuTUmoBFwFTwO3ADWXDcAGwc4EykiQtK9spSVIvfc3RSSntAnZ1PbaTsgGZq4wkSSvBdkqS\n1G01zHaeGnYAK2hq2AGsoKlhB7CCpoYdwAqaGnYAK2hq2AGssKlhB7CKTQ07gBU0NewAVtDUsANY\nQVPDDmAFTQ07gBU2NewAVtDUYl+w4BwdSZIkSRo1q6FHR5IkSZIGykRHkiRJUuX0e8PQgYsxbgeu\nKGPYmVK6fFixrIQY483Ao4D7gQz8ZUrpDUMNaoBijE8Grk4pnVluPxT4K+Bk4A7gl1NKe4YY4sD0\nqOuLgD+muCdHAJoppZ8eYogDEWNcD3yU4hgeoPg7fWMVj22Pur43pXR5hY/tNcA5FOeiLwAvBDZQ\nseN6pGynbKdGle1U9Y6t7dTS2qmh9OjEGMeBq4DzgNOB7THGs4YRywr7Tymlx6WUHl+xxuPNwMcp\n/sDargT+NqV0GvAh4LJhxDZoc9QVii8Ejy+P78ifYDpcnlI6FTgTiDHGMymO7Qeqdmw5tK7PizGe\nUT5exWN7dUrpsSmlnwL2A5HqHtclsZ2ynRpVtlO2U0OMb5AG0k4Na+jaNuC2lNLulNIscC2wfUix\nrKRKDhVMKV0MPKXr4Z8H/qb8+a+pyPGdo65weIMy8lJK+1JKN7Z/Br4FnEBxbP+6LFaJY9ujrt+k\nqCtU89jeBAdvtLkF+DIVPK5HyHaqQmyngGqey2ynClU8tgNpp4Z1QtsK3NOxvRs4cUixrJQMvD/G\n+JUY41tijJX7pezy0JRSAyCltBc4dsjxLLfnxxi/FmO8PsZ42rCDGbQY4wkUXcj/ADysyse2o663\nlg9V8tjGGF8CfB/4fErpc1T8uC6B7ZTtVNVU8lzWZjtVvWM7iHZqmFduZrq2x4YSxco5P6V0CvAk\n4JHAbw85nuVWp+P7vpTSlrJ79c948AphJcQYjwYS8NryxHKgq0hljm2Pulb22KaUrgYeAhxfjvGu\n7HE9AnU6j4HtVJWPb2XPZWA7VdVjO4h2aliJzt3A8R3bx5WPVVZKaX/5//3AR4BHDzeiZffjcow7\nMcbNwI+GHM+ySSk90LF5LXDSsGIZtBjjGPB+4LqU0jXlw5U8tr3qWuVjC1AOyboROJuKHtcjYDtl\nO1UZVT6X2U5V99jCkbdTw0p0bgXOjjFuiTGuAy6kqEQlxRjXxxifXv58FHAB8PfDjWrgAoeOEb0J\neF758/Op1vE9pK4xxnPLKywA/5kHu5JHWoxxA8WXnf+dUnpTx1OVO7Zz1bWKxzbG+JAY4y+UPx8F\nPAf4HBU8rkfIdsp2apTZTlXs2NpOLa2dCjnn5YpzXuWynW+iWLbzmpTS64cSyAoofwFvoBgKcD/w\n0ZTS7w03qsGJMV5G8Ut4KvAl4HeBr1AsAXgS8C/AC1JKPxxWjIMyR12fCvwGcB/wPeDXU0r/MqwY\nB6X80nM98G2KBjMDHwT+B/A+KnRs56lrg4od2xjjscDfUiwj/ADwkZTSxTHGLVTwb/ZI2E7ZTo0i\n2ynbqVE/toNsp4aW6EiSJEnScqnkMpKSJEmS6s1ER5IkSVLlmOhIkiRJqhwTHUmSJEmVY6IjSZIk\nqXJMdCRJkiRVjomOJEmSpMox0ZEkSZJUOf8/fy+TlZehVNIAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu = 15\n",
"sig = 0.3\n",
"\n",
"fig, ax = plt.subplots(1,2)\n",
"fig.set_size_inches(14,6)\n",
"x = np.arange(0, 2*mu)\n",
"prob_dens = stats.norm.pdf(x, mu, sig)\n",
"prob = stats.norm.cdf(x, mu, sig)\n",
"ax[0].bar(x,prob_dens)\n",
"ax[1].plot(x, prob)\n",
"\n",
"ax[0].set_title(u'Плотность распределения')\n",
"ax[1].set_title(u'Функция распределения')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Степенной закон"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Известно так же как закон Парето. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ f_X(x|\\alpha) = \\alpha x^{-\\alpha - 1}, x\\geq1, \\quad \\alpha>0 $$"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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0QQGAGGM/cCnwhZTSh1vssglY2nD5qPJ7rW5rNbB67HJKqc2onTdv3jwGBgbG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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"alpha = 2.1\n",
"\n",
"\n",
"fig, ax = plt.subplots(1,2)\n",
"fig.set_size_inches(14,6)\n",
"x = np.arange(1, 10, 1)\n",
"prob_dens = stats.pareto.pdf(x, alpha)\n",
"prob = stats.pareto.cdf(x, alpha)\n",
"ax[0].bar(x, prob_dens)\n",
"ax[1].plot(x, prob)\n",
"\n",
"ax[0].set_title(u'Плотность распределения')\n",
"ax[1].set_title(u'Функция распределения')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Генерация случайных величин"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Общий способ генерации случайных величин в соответствии с каким-либо законом: `stats.some_law.rvs(**params)`"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 0.0015071 , 0.0089056 , 0.03571373, 0.09161348, 0.12668783,\n",
" 0.1102924 , 0.06001003, 0.01785686, 0.00351657, 0.00059371]),\n",
" array([ -0.35431821, 1.83531588, 4.02494997, 6.21458406,\n",
" 8.40421814, 10.59385223, 12.78348632, 14.97312041,\n",
" 17.1627545 , 19.35238859, 21.54202267]),\n",
" )"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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geGbOA0TEEWAG+Eadmsx8eKDum8Cto2hckjQadd4jmAKeGVieB65eRw3AbcBDwzQoSWpW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\n/w+Uug6PvU5apwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = stats.norm.rvs(10, 3, size=10000)\n",
"plt.hist(x, normed=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Дополнительные характеристики распределений"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.07344430779542055"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"stats.kurtosis(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Kutorsis (коэффициент эксцесса) - мера остроты распределения. Для нормального распределения $= 0$. Для относительно равномерных распределений $< 0$. Для распределений с резким пиком $> 0$"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.01663325094516027"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"stats.skew(x)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = stats.binom.rvs(40, 0.6, size=100)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 3., 2., 9., 6., 13., 23., 13., 16., 7., 8.]),\n",
" array([ 16. , 17.4, 18.8, 20.2, 21.6, 23. , 24.4, 25.8, 27.2,\n",
" 28.6, 30. ]),\n",
" )"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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4Mx/tLtPYd3nXyb+DzlW70Llyd3FbQw0oMxcz857V28CDwB7gAuC27mK30dAPiOuT/7vA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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(x)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"23.960000000000001"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x.mean()"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"-0.17914234247559177"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"stats.skew(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Skew (коэффициент смещения) - смещение распределения, относительно среднего значения.
Если смещено влево, то $< 0$, если смещено всправо - $> 0$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Оценка параметров"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Общий способ оценки параметров распределений под данные: `stats.some_law.fit(x)`"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"17"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.randint(0,20)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(10.008120596047306, 3.0015599281410399)"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"params = stats.norm.fit(x)\n",
"params"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"В метод fit зашита оценка методом **максимального правдоподобия**\n",
"$$ \\max_\\theta f_X(X=x_1, X=x_2, \\dots, X=x_n | \\theta) = \\max_\\theta \\prod_{i=1}^n f_X(x_i|\\theta)$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Давайте попробуем решить какой-нибудь простой пример у доски.."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Наивный байесовский классификатор и категоризация текстов"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Обучение методом наивного Байеса основывается на достаточно сильном предположении, что все признаки попарно независимы. По формуле Байеса $$P(y|x_1,\\dots,x_n)=\\frac{P(y)P(x_1,\\dots,x_n|y)}{P(x_1,\\dots,x_n)}.$$ В предположении, что признаки независимы получаем, что $$P(y|x_1,\\dots,x_n)=\\frac{P(y)\\prod_{i=1}^n P(x_i|y)}{P(x_1,\\dots,x_n)}$$\n",
"\n",
"Т.к. $$P(x_1,\\dots,x_n)$$ задается условиями задачи, принцип максимального правдоподобия для наивного Байеса запишется следующим образом: $$\\hat y = \\arg\\max_y P(y)\\prod_{i=1}^n P(x_i|y).$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn.datasets import fetch_20newsgroups\n",
"from sklearn.naive_bayes import MultinomialNB\n",
"from sklearn.feature_extraction.text import CountVectorizer"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}