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"))

*Related*

To

**leave a comment** for the author, please follow the link and comment on their blog:

** CloudStat**.

R-bloggers.com offers

**daily e-mail updates** about

R news and

tutorials on topics such as:

Data science,

Big Data, R jobs, visualization (

ggplot2,

Boxplots,

maps,

animation), programming (

RStudio,

Sweave,

LaTeX,

SQL,

Eclipse,

git,

hadoop,

Web Scraping) statistics (

regression,

PCA,

time series,

trading) and more...

If you got this far, why not

__subscribe for updates__ from the site? Choose your flavor:

e-mail,

twitter,

RSS, or

facebook...

**Tags:** mean, median, R, Simulation