# 2014-02-24 
# simple Illustration for
# the Central Limit Theorem
# 
# I start from a large sample 
# with uniform distribution
# in range 0-1

# sample size
n<-10000
# how many variables 
# should be averaged
nsum<-1000

rhelp<-array(0,dim=c(n))

# LOOP OVER SUMMATION
# runif() produced independent random
# numbers between 0 and 1
for (i in 1:nsum){
  x<-runif(n)
  rhelp<-rhelp+x
}
y<-rhelp/nsum

ymean<-mean(y)
ysd<-sd(y)
print(paste("average of ",nsum," uniformly distributed variables"))
print(paste("mean, sd. of the average:",round(ymean,4),round(ysd,4)))
# plot of the histrogram
# using 51 break points from 0-1
# using density as y-axis
x<-1:51
x<-(x-1)/50

hist(y,breaks=x,prob=TRUE,main=paste("Central Limit Demo: nsum=",nsum))

# load the Gaussian distribution function
source("scripts/myfunctions.R")
yg<-fgauss(x,center=ymean,s=ysd)
lines(x,yg,col=3,lwd=2)