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总体比例的区间估计

attach(faithful)                                 #获取火山灰数据population <- sample(eruptions,1000,replace = T)     #获取总体N <- length(population)                          #计算总体个数p<-length(population[population>2.5])/N     #计算population>2.5占总体的比例  Pi <- p                                          #总体比例为PiPi##[1] 0.658layout(matrix(1:1, 1, 1))n <- 30z<-qnorm(0.975)                         #计算置信水平为95%的z值plot(Pi,experimentes,type="n",xlim=c(Pi-6*sigma,Pi+6*sigma),ylim=c(0,experimentes))abline(v=Pi)#做100次实验experimentes=100 for(i in 1:experiments){  Pi_of_sample <- sample(population, n)          #从总体随机取30个样本  Pi_of_x <- length(Pi_of_sample[Pi_of_sample>2.5])/n #计算大于2.5的比例  sigma = sqrt(Pi_of_x*(1-Pi_of_x)/n)                     co.inter <- c(Pi_of_x - z*sigma, Pi_of_x + z*sigma)  #计算总体比例的置信区间  if(co.inter[1] < Pi & Pi <= co.inter[2]) lines(co.inter, c(i, i), type="l")   else lines(co.inter, c(i, i), type="l", col=2)      #如果总体比例不在该区间内，用红线表示，否则，用黑线}#做1000次实验experiments=1000                                success <- 0 for(i in 1:experiments){   Pi_of_sample <- sample(population, n)  Pi_of_x <- length(Pi_of_sample[Pi_of_sample>2.5])/n  sigma = sqrt(Pi_of_x*(1-Pi_of_x)/n)  co.inter <- c(Pi_of_x - z*sigma, Pi_of_x + z*sigma)  if(co.inter[1] < Pi & Pi <= co.inter[2]) success <- success +1  }success/experiments   ![效果截图](http://img.blog.csdn.net/20161106223843396)

总体方差的区间估计

attach(faithful) population <- sample(eruptions,1000,replace = T)sigma <- var(population)*((N-1)/N)                  #总体方差1.306628layout(matrix(1:1, 1, 1))experimentes=100n <- 30kafang_left = qchisq(0.975,29)kafang_right = qchisq(0.025,29)plot(sigma,experimentes,type="n",xlim=c(sigma-3*sigma,sigma+3*sigma),ylim=c(0,experimentes))abline(v=sigma)for(i in 1:experiments){   sigma_of_x = var(sample(population, n))   sigma_of_x   co.inter <- c((n-1)*sigma_of_x/kafang_left, (n-1)*sigma_of_x/kafang_right)   co.inter   if(co.inter[1] < sigma & sigma <= co.inter[2]) lines(co.inter, c(i, i), type="l")    else lines(co.inter, c(i, i), type="l", col=2)}experiments=100success <- 0 for(i in 1:experiments){   sigma_of_x = var(sample(population, n))  co.inter <- c((n-1)*sigma_of_x/kafang_left, (n-1)*sigma_of_x/kafang_right)  if(co.inter[1] < sigma & sigma <= co.inter[2]) success <- success +1   }success/experiments

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