#
# EPage 140
#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

library(DAAG)

set.seed(0)

stdErrorOfMedian = function(n_samples=100,exp_rate=1){

  # Generate data from our exponential distribution: 
  X = rexp(n_samples,rate=exp_rate)

  # The function we will want to compute bootstrap samples of: 
  median.fn = function(data, indices){
    median(data[indices])
  }

  # Run the bootstrap: 
  median.boot = boot( X, median.fn, R=99999 )

  print( sprintf("rate= %5.2f; standard error of median (bootstrapped) %10.6f", exp_rate, sd( median.boot$t ) ) )
  print( sprintf("rate= %5.2f; standard error of median (normal approximation) %10.6f", exp_rate, sqrt( pi / (2*n_samples) ) ) )
}

# Run function once: 
stdErrorOfMedian()