#  2004 年 12 月 14 日作成
# simulation of CLT from triangular sample
num.rep<-10000
#
# number of sample size
#
num.sam<-5
qusai.ran<-rep(0,num.rep)
#
#
# generate sample mean
#
for (i in 1:num.sam){
tra<-sqrt(2)-sqrt(2-2*runif(num.rep,0,1))
qusai.ran<-qusai.ran+tra/num.sam
}
qusai.ran<-3*sqrt(num.sam)*(qusai.ran-sqrt(2)/3)
# 
#
# drat graph of centered sample mean 
#
plot(density(qusai.ran),xlim=c(-4,4),ylim=c(0,0.5),type="l")
#
# drat graph of standard normal
#
xx<-seq(-4,4,by=0.001)
par(new=T)
plot(xx,dnorm(xx,0,1),xlim=c(-4,4),ylim=c(0,0.5),type="l")
num.rep<-10000
num.sam<-12
qusai.ran<-rep(0,num.rep)
for (i in 1:num.sam){
tra<-sqrt(2)-sqrt(2-2*runif(num.rep,0,1))
qusai.ran<-qusai.ran+tra/num.sam
}
qusai.ran<-3*sqrt(num.sam)*(qusai.ran-sqrt(2)/3)
par(new=T)
# 
#
# drat graph of centered sample mean 
#
plot(density(qusai.ran),xlim=c(-4,4),ylim=c(0,0.5),type="l")