Transformation Rechteckverteilter Zufallszahlen in standardnormalverteilte

RandomNorm.r

# define function
# found in: 
# 				Wilmott, Paul (2007): 
#					Paul Wilmott introduces quantitative finance. 
#					2. Edition. Chichester: Wiley. 
# r: number of random numbers to be calculated
StandNorm<-function(r=30){
	
	# how many iterations should be calculated? 
	# 50 proofed to be a good number to get robust
	# random numbers
	n<-50
	# introduce return value
	z<-NULL
	
	#iterate
	for(i in 1:r){
		#add new number
		z<-c(z,sqrt(12/n)*(sum(runif(n))-n/2))
	}
	z #return
}

# call function and store 100 numbers in z
z<-rep(StandNorm(),100)

#define a sequence
x<-seq(-5,5,by=0.05)

#plot histogram
hist(z,freq=FALSE, main="Histogramm Zufallszahlen")

#draw gaussian density function
lines(x,dnorm(x,0,1),col=2,lty=2)

#draw kernel-density of sample
lines(density(z),lwd=2)

#plot observations
rug(z)