inst/scripts/Appendix/cheby.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

# cheby.R
# Script: shows the Chebyshev relation by means of simulation



rm(list=ls())
P.hat<-NULL
Bound<-NULL
mu<-0
N<-100
for (sig in seq(.1,1,by=.1)){
  for ( d in seq (.1,1,by=.1)){
    z<-rnorm(N,mean=mu,sd=sig); # random sampling of the r.v. z
    P.hat<- cbind(P.hat,sum(abs(z-mu)>=d)/N) # frequency of the event: z-mu>=d
    Bound<-cbind(Bound,min(1,(sig^2)/(d^2))) # upper bound of the Chebyshev relation
  }
}

if (any(P.hat>Bound)){  #check if the relation is satisfied
  print("Chebyshev relation NOT satisfied")
} else  {
  print("Chebyshev relation IS satisfied")
}