大数の法則.中心極限定理.R

library(WDI)
x <- WDI(country="all", indicator=c("AG.AGR.TRAC.NO"),
    start=1980, end=2011)
y <- na.exclude(x[,3])

mean(y)
  # 881532.3
sd(y)
  # 2925623
var(y)
  # 8.559267e+12
var(y)/10000
  # 855926716

# Central Limit Theorem
sample_mean <- NULL
for (i in 1:10000){
  sample <- sample(y, 2200, replace = FALSE, prob = NULL)
  sample_mean[i] <- mean(sample)
}
hist(sample_mean)
plot(density(sample_mean))
mean(sample_mean)
sd(sample_mean)
sd(y)/sqrt(10000)

# Law of Large Number
#データ数が多いと、サンプル平均は真の平均に近づく
mean(sample(y, 10, replace = FALSE, prob = NULL))
mean(sample(y, 100, replace = FALSE, prob = NULL))
mean(sample(y, 1000, replace = FALSE, prob = NULL))
mean(sample(y, 2000, replace = FALSE, prob = NULL))
mean(sample(y, 3000, replace = FALSE, prob = NULL))

dif_mean <- NULL
for (i in seq(20,3860,20)){
  dif_mean[i] <- mean(y) - mean(sample(y, i, replace = FALSE, prob = NULL))
}
plot(dif_mean)