{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 生成正态分布随机数\n", "NumPy包和random包中都有生成正态分布随机数的函数。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P(|X|<1.65)= 0.8974\n", "P(|X|<1.96)= 0.9472\n", "P(|X|<2)= 0.9506\n", "P(|X|<2.58)= 0.9906\n", "P(|X|<3)= 0.9968\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.random as nprd\n", "\n", "## 设定参数\n", "N=5000 #样本容量\n", "\n", "## 生成标准正态分布\n", "X=nprd.randn(N)\n", "\n", "## 计算频率\n", "print(\"P(|X|<1.65)=\",np.sum(abs(X)<1.65)/N)\n", "print(\"P(|X|<1.96)=\",np.sum(abs(X)<1.96)/N)\n", "print(\"P(|X|<2)=\",np.sum(abs(X)<2)/N)\n", "print(\"P(|X|<2.58)=\",np.sum(abs(X)<2.58)/N)\n", "print(\"P(|X|<3)=\",np.sum(abs(X)<3)/N)\n", "\n", "## 画图\n", "import matplotlib.pyplot as plt\n", "## 使图形直接插入到jupyter中\n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (10.0, 8.0)\n", "plt.hist(X,bins=11) ##柱状图\n", "plt.xlabel('X')\n", "plt.ylabel(\"Density\")\n", "plt.title('Normal Distribution')\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 生成二元联合正态分布\n", "如果$(X_1,X_2)\\sim N\\left(\\mu,\\Sigma\\right)$,那么我们可以使用条件分布生成联合分布。由于:$$X_{1}|X_{2}\\sim N\\left(\\mu_{1}+\\rho\\frac{\\sigma_{1}}{\\sigma_{2}}\\left(X_{2}-\\mu_{2}\\right),\\sigma_{1}^{2}\\left(1-\\rho^{2}\\right)\\right)$$可以将其进行分解:$$X_{1}=\\mu_{1}-\\rho\\frac{\\sigma_{1}}{\\sigma_{2}}\\mu_{2}+\\rho\\frac{\\sigma_{1}}{\\sigma_{2}}X_{2}+\\epsilon$$其中:$\\epsilon\\sim N\\left(0,\\left(1-\\rho^{2}\\right)\\sigma_{1}^{2}\\right)$。因而我们可以先生成$X_2$,再使用以上公式生成$X_1$。" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X1,X2的协方差矩阵:\n", " [[ 0.98665378 0.70444526]\n", " [ 0.70444526 2.03890462]]\n", "X1方差: 0.985667125823\n", "X2方差: 2.03686571636\n", "X1,X2相关系数: 0.496668259849\n" ] }, { "data": { "image/png": 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TMAiL0LZWYGC3vcHMS4hUU/BUuwRIrZBmnlwdexMptgghxSauwV2/Kd+QRJQXLamXzeXt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\nzgjptI9to2PAHAY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4xTSDBjh8DFMius25u4QpW5q9BCOV6NONPe79kCTnrmBs2ABcdRVw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\nACgRYQsAAKBEhC0AAIAS/X8x22bcv9VizwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.random as nprd\n", "\n", "## 设定参数\n", "mu1=2\n", "mu2=1\n", "sigma1=np.sqrt(1)\n", "sigma2=np.sqrt(2)\n", "rho=0.5\n", "N=1000 #样本容量\n", "\n", "## 生成正态分布X2\n", "X2=(nprd.randn(N)+mu2)*sigma2\n", "## 生成epsilon\n", "epsilon=nprd.randn(N)*(sigma1*np.sqrt(1-rho**2))\n", "## 生成X1\n", "X1=mu1-rho*sigma1/sigma2*mu2+rho*sigma1/sigma2*X2+epsilon\n", "\n", "## 计算协方差\n", "print(\"X1,X2的协方差矩阵:\\n\",np.cov(X1,X2))\n", "print(\"X1方差:\",np.var(X1))\n", "print(\"X2方差:\",np.var(X2))\n", "print(\"X1,X2相关系数:\",np.corrcoef(X1,X2)[0,1])\n", "\n", "## 画图\n", "import matplotlib.pyplot as plt\n", "## 使图形直接插入到jupyter中\n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (10.0, 8.0)\n", "plt.scatter(X2,X1,color='pink') ##散点图\n", "## 回归曲线\n", "lp=np.linspace(-4,6,20)\n", "y=mu1-rho*sigma1/sigma2*mu2+rho*sigma1/sigma2*lp\n", "plt.plot(lp,y,color='blue') \n", "plt.xlabel('X2')\n", "plt.ylabel(\"X1\")\n", "plt.title('Relationship of x and y')\n", "plt.show() ## 画图" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "此外,还可以使用协方差矩阵直接生成。如果$U\\sim N\\left(0,I\\right)$为联合标准正态分布,那么:$$X=\\Sigma^{1/2}U+\\mu$$即服从$N\\left(\\mu,\\Sigma\\right)$。" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X1,X2的协方差矩阵:\n", " [[ 0.95536898 0.68892306]\n", " [ 0.68892306 1.96590072]]\n", "X1方差: 0.95441360962\n", "X2方差: 1.96393481578\n", "X1,X2相关系数: 0.502694769881\n" ] }, { "data": { "image/png": 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0SVXFv+wyYMUKYNYsVSvszDOBcePqPpzaybJESAtAMUZIK2LblFknbrJ2Eybh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\nOpyTbr7ZD0XecIMvwj/lFOmcc6TDDmv85fNt2JT+/aTjU/QGPszyDVJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.random as nprd\n", "\n", "## 设定参数\n", "mu1=2\n", "mu2=1\n", "sigma1=np.sqrt(1)\n", "sigma2=np.sqrt(2)\n", "rho=0.5\n", "N=1000 #样本容量\n", "Sigma=np.array([[sigma1**2,rho*sigma1*sigma2],[rho*sigma1*sigma2,sigma2**2]])\n", "\n", "## 计算Sigma^0.5\n", "l,L=np.linalg.eig(Sigma)\n", "Lamb=np.array([ll**0.5 for ll in l])\n", "Sigma1p2=np.dot(np.dot(L,np.diag(Lamb)),L.transpose())\n", "\n", "## 生成正态分布u\n", "U1=nprd.randn(N)\n", "U2=nprd.randn(N)\n", "U=np.array([U1,U2])\n", "\n", "## 生成X\n", "X=np.dot(Sigma1p2,U)\n", "X1=X[0,]+mu1\n", "X2=X[1,]+mu2\n", "\n", "## 计算协方差\n", "print(\"X1,X2的协方差矩阵:\\n\",np.cov(X1,X2))\n", "print(\"X1方差:\",np.var(X1))\n", "print(\"X2方差:\",np.var(X2))\n", "print(\"X1,X2相关系数:\",np.corrcoef(X1,X2)[0,1])\n", "\n", "## 画图\n", "import matplotlib.pyplot as plt\n", "## 使图形直接插入到jupyter中\n", "%matplotlib inline\n", "# 设定图像大小\n", "plt.rcParams['figure.figsize'] = (10.0, 8.0)\n", "plt.scatter(X2,X1,color='pink') ##散点图\n", "## 回归曲线\n", "lp=np.linspace(-4,6,20)\n", "y=mu1-rho*sigma1/sigma2*mu2+rho*sigma1/sigma2*lp\n", "plt.plot(lp,y,color='blue') \n", "plt.xlabel('X2')\n", "plt.ylabel(\"X1\")\n", "plt.title('Relationship of x and y')\n", "plt.show() ## 画图" ] } ], "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": "3.5.1" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false } }, "nbformat": 4, "nbformat_minor": 2 }