Goal: Show the efficiency of the mean when compared with the median using a large simulation where both estimators are applied on a sample of U(0,1) uniformly distributed random numbers.

Input:

# Goal: Show the efficiency of the mean when compared with the median
# using a large simulation where both estimators are applied on
# a sample of U(0,1) uniformly distributed random numbers.

one.simulation = function(N=100) { # N defaults to 100 if not supplied
x = runif(N)
return(c(mean(x), median(x)))
}

# Simulation --
results = replicate(100000, one.simulation(20)) # Gives back a 2x100000 matrix

# Two kernel densities --
k1 = density(results[1,]) # results[1,] is the 1st row
k2 = density(results[2,])

# A pretty picture --
xrange = range(k1$x, k2$x)
plot(k1$x, k1$y, xlim=xrange, type="l", xlab="Estimated value", ylab="")
grid()
lines(k2$x, k2$y, col="red")
abline(v=.5)
legend(x="topleft", bty="n",
lty=c(1,1),
col=c("black", "red"),
legend=c("Mean", "Median"))