(This article was first published on

**CloudStat**, and kindly contributed to R-bloggers)Simulation: Efficiency of mean with median

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"))

To

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