inst/scripts/Appendix/central.R

In gbonte/gbcode: Code from the handbook "Statistical foundations of machine learning"

## "Statistical foundations of machine learning" software
## R package gbcode 
## Author: G. Bontempi

# central.R
# Script: visualizes the distribution of the estimator
# of the variance of a non gaussian random variableshows the central limit theorem

rm(list=ls())
graphics.off()
par(ask=TRUE)
N<-1
R<-1000

I<-seq(-50,50,by=.5)

Mn<--10
Mx<-10
var.th<-(1/(Mx-Mn))*((Mx^3)/3-(Mn^3)/3)
p<-dunif(I,min=Mn,max=Mx)
plot(I,p,type="l",
     main=paste("Distribution of  r.v. z: var=",round(var.th,digits=1)))

aver<-rep(0,R)

for (N in 2:1000){
  for (i in 1:N){
    aver<-aver+runif(R,min=Mn,max=Mx)
  }
  aver<-aver/N
  hist(aver,freq=FALSE, main= paste("Average of N=",N, " r.v.s"),xlim=c(Mn,Mx)) #,xlim=range(I2))
  I2<-seq(-5*sd(aver),5*sd(aver),by=.5)
  
  p.var.hat<-dnorm(I2,mean=0,sd=sqrt(var.th/N))
  lines(I2,p.var.hat,type="l")
}