《抽样技术上机实验中心极限定理验证.docxVIP

均匀分布中心极限定律的实现：clcclearn=200000; %/* ???′′?êy*/k=100;%/* ?ù±???êy*/mu=0;u=0;sigma=1/12;population=0:0.001:1;for i=1:n y = randsample(population,k,1); mu=[mu,mean(y)];endmu=(mu-0.5)/(sqrt(sigma)/sqrt(k));%hist(mu(2:end),1000)[f, x1] = ksdensity(mu(2:end));plot(x1, f) hold onplot(x1,normpdf(x1,0,1),r)hold off%%%%%%%%%%%%%%%%%%%%%%%%两点分布的实现：clcclearn=10000; %/* ???′′?êy*/k=100;%/* ?ù±???êy*/mu=0;u=0;p=0.5;sigma=p*(1-p);population=0:1;for i=1:n y = randsample(population,k,1); mu=[mu,mean(y)];endmu=(mu-p)/(sqrt(sigma)/sqrt(k));%hist(mu(2:end),1000)[f, x1] = ksdensity(mu(2:end));plot(x1, f) hold onplot(x1,normpdf(x1,0,1),r)hold off%%%%%%%%%%%%%%%%%%%%%%%%%%%%%两点分布1以概率0.4发生clcclearn=50000; %/* ????????*/k=100;%/* ?¨′?à?????*/mu=0;u=0;p=0.4;sigma=p*(1-p);a=0:0.1:1;for i=1:n y = randsample(a(2:end)=p,k,1); mu=[mu,mean(y)]; endmu=(mu-p)/(sqrt(sigma)/sqrt(k));hist(mu(2:end),1000)[f, x1] = ksdensity(mu(2:end));plot(x1, f) hold onplot(x1,normpdf(x1,0,1),r)hold off%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%二项分布随机变量的中心极限定理检验：clcclearn=50000; %/* ????????*/k=100;%/* ?¨′?à?????*/bino=0;u=0;p=0.4;sigma=p*(1-p);a=0:0.1:1; for i=1:n y = randsample(a(2:end)=p,k,1); bino=[bino,sum(y)] ; endbino=(bino-k*p)/sqrt((k*sigma));hist(bino(2:end),n/10)[f, x1] = ksdensity(bino(2:end));plot(x1, f) hold onplot(x1,normpdf(x1,0,1),r)hold off%%%%%%%%%%%%%%%%%%%%%%%%%%%%卡方分布：clcclearn=10000; %/* ???′′?êy*/m=500;v=5;%×?óé?èR= chi2rnd(v,n,m);%%%可以换成以下任何一种分布；r=sum(R)/m;%????′?êμ?é??áDè?oímu=(r-v)*sqrt(m)./sqrt(2*v);[f, x1] = ksdensity(mu(2:end));plot(x1, f) hold onplot(x1,normpdf(x1,0,1),r)hold off（一）Matlab内部函数a.?基本随机数Matlab中有两个最基本生成随机数的函数。1．rand()生成（0,1）区间上均匀分布的随机变量。基本语法：rand([M,N,P ...])生成排列成M*N*P... 多维向量的随机数。如果只写M，则生成M*M矩阵；如果参数为[M,N]可以省略掉方括号。一些例子：rand(5,1) %生成5个随机数排列的列向量，一般用这种格式rand(5) %生成5行5列的随机数矩阵rand([5,4]) %生成一个5行4列的随机数矩阵生成的随机数大致的分布。x=rand(100000,1);hist(x,30);由此可以看到生成的随机数很符合均匀分布。(视频教程会略提及hist()函数的作用)2．randn()生成服从标准正态分布（均值为0，方差为1）的随机数。基本语法和rand()类似。randn([M,N,P ...])生成排列成M*N*P... 多维向量的随机数。如果只写M，则生成M*M矩阵；如