文章标题

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Pi
Pi
##[1] 0.658
layout(matrix(1:1, 1, 1))
n <- 30
z<-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1.306628
layout(matrix(1:1, 1, 1))
experimentes=100
n <- 30
kafang_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=100
success <- 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