**O**ne 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…)

Filed under: Books, R, Statistics, University life Tagged: accept-reject algorithm, computer language, exam, Monte Carlo methods, normalising constant, R, recursion

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**Tags:** accept-reject algorithm, Books, computer language, exam, Monte Carlo methods, normalising constant, R, recursion, statistics, University life