wilcoxon_rank_sum_interval = function( x_data, y_data, c, Delta_0=0, debugging=FALSE ){
  #
  # Returns:
  # 
  # See Page 617 from the book Probability and Statistics: For Engineering and the Sciences by Jay L. Devore
  #
  # 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.
  #
  #-----

  if( length(x_data) > length(y_data) ){
      print('Exchanging x_data and y_data since initially x_data is longer than y_data')
      tmp = x_data;
      x_data = y_data;
      y_data = tmp;
  }
  m = length(x_data)
  n = length(y_data)
  x_data = x_data - Delta_0 
  if( debugging ){ 
      print("x_data="); print( x_data )
      print("y_data="); print( y_data ) 
  }

  data_outer = outer( x_data, y_data, FUN="-" )
  data_outer_sorted = sort( as.vector( data_outer ) )

  ll_index = as.integer( n*m - c + 1 )
  ul_index = as.integer( c ) 

  list( ll=data_outer_sorted[ll_index], ul=data_outer_sorted[ul_index] )

}