One of my students wrote the following code for his R exam, trying to do accept-reject simulation (of a Rayleigh distribution) and constant approximation at the same time:

fAR1=function(n){
 u=runif(n)
 x=rexp(n)
 f=(C*(x)*exp(-2*x^2/3))
 g=dexp(n,1)
 test=(u<f/(3*g))
 y=x[test]
 p=length(y)/n #acceptance probability
 M=1/p
 C=M/3
 hist(y,20,freq=FALSE)
 return(x)
 }

which I find remarkable if alas doomed to fail! I wonder if there exists a (real as opposed to fantasy) computer language where you could introduce constants C and only define them later… (What’s rather sad is that I keep insisting on the fact that accept-reject does not need the constant C to operate. And that I found the same mistake in several of the students’ code. There is a further mistake in the above code when defining g. I also wonder where the 3 came from…)