From d44f5e65af9a2e92e8062609eef617c048c93934 Mon Sep 17 00:00:00 2001 From: kidaufo Date: Sat, 6 Jul 2019 11:09:33 +0900 Subject: [PATCH] Add files via upload --- Central Limit Theorem.ipynb | 153 ++++++++++++++++++++++++ ProbabilityDistribution.ipynb | 216 ++++++++++++++++++++++++++++++++++ 2 files changed, 369 insertions(+) create mode 100644 Central Limit Theorem.ipynb create mode 100644 ProbabilityDistribution.ipynb diff --git a/Central Limit Theorem.ipynb b/Central Limit Theorem.ipynb new file mode 100644 index 0000000..8b7180d --- /dev/null +++ b/Central Limit Theorem.ipynb @@ -0,0 +1,153 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 中心極限定理\n", + "平均$\\mu$、分散$\\sigma^2$の任意の確率分布に従う母集団から抽出した標本において、サンプルサイズが大きくなるにつれて標本平均の分布は平均$\\mu$、分散$\\sigma^2/n$の正規分布に近づく。　　\n", + "\n", + "sample from aribitrary probability distribution, sample mean" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "import scipy as sp\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import cm\n", + "import seaborn as sns\n", + "from tqdm import tqdm_notebook\n", + "from scipy.stats import norm, poisson, gamma, uniform\n", + "\n", + "sns.set_style('white')\n", + "sns.set_context('talk')\n", + "\n", + "np.random.seed(123)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import stats" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "mu = 3.0\n", + "n_sample = 100\n", + "\n", + "def poisson_means(n_sample):\n", + " means = []\n", + " for _ in range(1000):\n", + " data = poisson.rvs(mu=mu, size=n_sample)\n", + " means.append(data.mean())\n", + "\n", + " means = np.array(means)\n", + " plt.figure()\n", + " plt.hist(means)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "for i in [2, 10, 100, 1000]:\n", + " poisson_means(i)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/ProbabilityDistribution.ipynb b/ProbabilityDistribution.ipynb new file mode 100644 index 0000000..826a900 --- /dev/null +++ b/ProbabilityDistribution.ipynb @@ -0,0 +1,216 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.random as rnd\n", + "from scipy import stats\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### t distribution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### geometric distribution\n", + "確率pで成功する試行が初めて成功するまでの試行回数nが従う確率分布。" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "s = rnd.geometric(p=0.2, size=10000)\n", + "sns.distplot(s, kde=False, bins=np.arange(max(s)+1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### exponential distribution\n", + "ある期間に平均してラムダ回起こる現象が次に起きるまでの期間Xが従う確率分布。幾何分布の連続変数バージョン。\n", + " \n", + "例） 機械が故障してから次に故障するまでの期間　　\n", + " \n", + "$$f\\left( x\\right) =\\dfrac {1}{\\mu }\\exp \\left( -\\dfrac {x}{\\mu }\\right)　$$\n", + "$\\mu$: scale parameter" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "s = rnd.exponential(scale=5.0, size=10000)\n", + "sns.distplot(s, kde=False, bins=30)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### poisson distribution\n", + "一定期間においてある事象が発生する回数が従う確率分布\n", + "\n", + "* probability of a given number of events occurring in a fixed interval of time \n", + "\n", + "if these events occur\n", + "* with a known constant rate\n", + "* independently of the time since the last event \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### negative binomial distribution\n", + "\n", + "成功確率pの試行がk回成功するまでに必要な試行回数xが従う確率分布。 \n", + " \n", + "numpyの場合、成功回数 n、成功確率pとした場合の失敗回数が従う確率分布となる。 \n", + "この場合平均は$n(1-p)/p$、分散$n(1-p)/p^2$\n", + "\n", + "$$p\\left( x\\right) =\\begin{pmatrix} x-1 \\\\ k-1 \\end{pmatrix} {p^{k}\\left( 1-p\\right) ^{x-k}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "s = rnd.negative_binomial(n=1.0, p=0.2, size=1000)\n", + "sns.distplot(s, kde=False, bins=np.arange(max(s)+1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### gamma distribution" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}