{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "##内容索引\n", "1. 随机数 --- 二项分布binomial\n", "2. 超几何分布 --- hypergeometric\n", "3. 连续分布 --- normal、lognormal函数" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from matplotlib.pyplot import show, plot\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##1. 随机数\n", "随机数在蒙特卡罗方法(Monto Carlo method)、随机积分等很多方面都有应用。真随机数的产生很困难,因此在实际应用中我们通常使用伪随机数。\n", "\n", "有关随机数的函数可以在NumPy的random模块中找到。随机数发生器的核心算法是基于马特赛特旋转演算法(Mersenne Twister algorithm)。随机数可以从离散分布或连续分布中产生。\n", "\n", "**分布函数有一个可选的参数size,用于指定需要产生的随机数的数量。该参数允许设置为一个整数或元组,生成的随机数将填满指定形状的数组。**支持的离散分布包括几何分布、超几何分布和二项分布等。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###硬币赌博游戏\n", "二项分布是n个独立重复的是非试验中成功次数的离散概率分布,这些概率是固定不变的,与试验结果无关。\n", "\n", "- 现在对一个硬币赌博游戏下8份赌注\n", "- 在硬币赌博游戏中,每一轮抛9枚硬币,如果少于5枚硬币正面朝上,你将损失8份赌注中的1份;否则,你将赢得1份赌注\n", "- 初始资本为1000份赌注" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# 初始化一个全0的数组来存放剩余资本\n", "# 以参数10000调用binomial函数,进行10000轮硬币赌博游戏\n", "cash = np.zeros(10000)\n", "cash[0] = 1000\n", "outcome = np.random.binomial(9, 0.5, size=len(cash))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 9\n" ] } ], "source": [ "# 模拟每一轮抛硬币的结果,更新cash数组\n", "# 打印出outcome的最大最小值,检查输出中是否有异常\n", "for i in xrange(1, len(cash)):\n", " if outcome[i] < 5:\n", " cash[i] = cash[i-1] - 1\n", " elif outcome[i] < 10:\n", " cash[i] = cash[i-1] + 1\n", " else:\n", " raise AssertionError(\"Unexpected outcome\" + outcome)\n", "\n", "print outcome.min(), outcome.max()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ulTgwOd6G8J3cLF+uV/gX1hkXRLuHv1Fr7Vxv5tDUD43E7SWGkgmH+3P5nyjR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\ndZxeUGXbJk2WFU4uHBzH6Zj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(np.arange(len(cash)), cash)\n", "show" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##2. 超几何分布\n", "超几何分布(hypergeometric distribution)是一种离散概率分布,它描述的是一个罐子有两种物件,无放回地从中抽取指定数量的物件后,抽出指定种类物件的数量。\n", "\n", "NumPy的random模块中的hypergeometric函数可以模拟这种分布。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###模拟游戏秀节目\n", "游戏规则:\n", "- 每当参赛者回答对一个问题,他们可以从一个罐子里摸出3个球并放回\n", "- 罐子里有一个“倒霉球”,一旦摸到这个球,参赛者会被扣去6分\n", "- 如果摸出3个球全部来自其余的25个普通球,可以得1分\n", "- 100道问题被正确回答,其得分情况如何?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "points = np.zeros(100)\n", "# 第一个参数是罐中普通球的个数\n", "# 第二个参数是倒霉球的个数\n", "# 第三个参数是每次摸球的个数(采样数)\n", "outcomes = np.random.hypergeometric(25, 1, 3, size=len(points))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "for i in xrange(len(points)):\n", " if outcomes[i] == 3:\n", " points[i] = points[i-1] + 1\n", " elif outcomes[i] == 2:\n", " points[i] = points[i-1] - 6\n", " else:\n", " print outcomes[i]" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(points)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##3. 连续分布\n", "连续分布可以用概率密度函数(Probability Density Function, PDF)来描述。**随机变量落在某一区间内的概率等于概率密度函数在该区间的曲线下方的面积。**\n", "\n", "NumPy的random模块中有一系列连续分布的函数——beta、chisquare、exponential、f、gamma、gumbel、laplace、lognormal、logistic、multivariate_normal、nonchetral_chisquare、noncentral_f、normal等。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###3.1 绘制正态分布" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bwPclXamuix1QR5LeL2kNoVfFXZLuiR1Tlpk1E0Znzyb0VJiVxkF6\nkn5DmCDpCElrJF0cO6YunAScD5ySvB8XJJWQtNkf+HPy+Z5LaINP+/2rvPnSBzo551yNSmMN3jnn\nXAl4gnfOuRrlCd4552qUJ3jnnKtRnuCdc65GeYJ3zrka5QneOedqlCd455yrUf8fHScTBAP7ZskA\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 产生指定数量的随机数\n", "N = 10000\n", "normal_values = np.random.normal(size=N)\n", "\n", "# 绘制分布直方图\n", "dummy, bins, dummy = plt.hist(normal_values, np.sqrt(N), normed=True, lw=1)\n", "sigma = 1\n", "mu = 0\n", "plot(bins, 1/(sigma*np.sqrt(2*np.pi)) * np.exp(-(bins-mu)**2 / (2*sigma**2)), lw=2)\n", "show()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5M1Gyp5T2Tuu+SD91c/fy/sCALfDcibAxRqYa1npT2E7s+TQRkYjC/MfLTily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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.gridspec as gridspec\n", "gs = gridspec.GridSpec(2,2)\n", "fig = plt.figure(figsize=(10,8))\n", "ax = []\n", "\n", "N = 10000\n", "sigma = 1\n", "mu = 0\n", "\n", "for a in xrange(2):\n", " for b in xrange(2):\n", " ax.append(fig.add_subplot(gs[a,b]))\n", " normal_values = np.random.normal(size=N)\n", " dummy, bins, dummy = plt.hist(normal_values, np.sqrt(N), normed=True, lw=1)\n", " ax[-1].plot(bins, 1/(sigma*np.sqrt(2*np.pi)) * np.exp(-(bins-mu)**2 / (2*sigma**2)), lw=2)\n", "\n", "# 使得子图适应figure的间距\n", "fig.tight_layout()\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###3.2 对数正态分布\n", "对数正态分布(lognormal distribution)是自然对数服从正态分布的任意随机变量的概率分布。" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10000\n", "lognormal_values = np.random.lognormal(size=N)\n", "\n", "dummy, bins, dummy = plt.hist(lognormal_values, np.sqrt(N), normed=True, lw=1)\n", "sigma = 1\n", "mu = 0\n", "\n", "x = np.linspace(min(bins), max(bins), len(bins))\n", "pdf = np.exp(-(np.log(x)-mu)**2 / (2*sigma**2)) / (x*sigma*np.sqrt(2*np.pi))\n", "plot(x, pdf, lw=3)\n", "show()" ] } ], "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": "2.7.5" } }, "nbformat": 4, "nbformat_minor": 0 }