R/entropy.MillerMadow.R

In entropy: Estimation of Entropy, Mutual Information and Related Quantities

### entropy.MillerMadow.R  (2008-08-20)
###
###    Miller-Madow entropy estimator (1955)
###
### Copyright 2008 Korbinian Strimmer
###
###
### This file is part of the `entropy' library for R and related languages.
### It is made available under the terms of the GNU General Public
### License, version 3, or at your option, any later version,
### incorporated herein by reference.
### 
### This program is distributed in the hope that it will be
### useful, but WITHOUT ANY WARRANTY; without even the implied
### warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
### PURPOSE.  See the GNU General Public License for more
### details.
### 
### You should have received a copy of the GNU General Public
### License along with this program; if not, write to the Free
### Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
### MA 02111-1307, USA


# compute Miller-Madow (1955) entropy estimator

# y is a vector of counts (may include zeros)
entropy.MillerMadow = function(y, unit=c("log", "log2", "log10"))
{
  unit = match.arg(unit)
  
  n = sum(y)      # total number of counts
  m = sum(y>0)    # number of bins with non-zero counts 

  # bias-corrected empirical estimate
  H = entropy.empirical(y, unit="log") + (m-1)/(2*n)

  if (unit == "log2")  H = H/log(2)  # change from log to log2 scale
  if (unit == "log10") H = H/log(10) # change from log to log10 scale

  return(H)
}