{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.stats as sps\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"from statsmodels.distributions.empirical_distribution import ECDF\n",
"from statsmodels.sandbox.stats.multicomp import multipletests\n",
"from collections import Counter\n",
"from tqdm import tqdm_notebook\n",
"\n",
"red = '#FF3300'\n",
"blue = '#0099CC'\n",
"green = '#00CC66'\n",
"\n",
"%matplotlib inline\n",
"sns.set(style='ticks', font_scale=1.7)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Критерии согласия\n",
"\n",
"### Критерий согласия Пирсона (хи-квадрат)\n",
"\n",
"$\\mathsf{H}_0\\colon$ Выборка из некоторого класса распределений\n",
"\n",
"$\\mathsf{H}_1\\colon\\ \\mathsf{H}_0$ не верна.\n",
"\n",
"`chisquare``(f_obs, f_exp=None, ddof=0)`\n",
"\n",
"* `f_obs` --- число элементов выборки, попавших в каждый из интервалов\n",
"* `f_exp` --- ожидаемое число (по умолчанию равномерное)\n",
"* `ddof` --- поправка на число степеней свободы. Статистика асимптотически будет иметь распределение $k - 1 - ddof$, где $k$ --- число интервалов."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Power_divergenceResult(statistic=2.0, pvalue=0.8491450360846096)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sps.chisquare([16, 18, 16, 14, 12, 12])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Power_divergenceResult(statistic=19.7, pvalue=0.0014224993317060594)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sps.chisquare([16, 18, 16, 14, 12, 12], f_exp=[16, 16, 16, 16, 20, 4])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.7/dist-packages/scipy/stats/stats.py:5048: RuntimeWarning: divide by zero encountered in true_divide\n",
" terms = (f_obs - f_exp)**2 / f_exp\n"
]
},
{
"data": {
"text/plain": [
"Power_divergenceResult(statistic=inf, pvalue=0.0)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sps.chisquare([16, 18, 16, 14, 12, 12], f_exp=[16, 16, 16, 16, 24, 0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Эксперимент с группами крови"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Power_divergenceResult(statistic=0.001011144526478114, pvalue=0.9746327438096731)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sps.chisquare([121, 120, 79, 33], f_exp=np.array([0.343, 0.340, 0.224, 0.093]) * 353, ddof=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Посмотрим, насколько хорошо выполняется асимптотика при справедливости нулевой гипотезы для разных распределений.\n",
"\n",
"**1.** Равномерное на 5 элементах"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "bf14df4a516f4f09ac00957490ba585c",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"HBox(children=(IntProgress(value=0, max=100000), HTML(value='')))"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
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\n",
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