content: /*
   *    This program is free software; you can redistribute it and/or modify
   *    it under the terms of the GNU General Public License as published by
   *    the Free Software Foundation; either version 2 of the License, or
   *    (at your option) any later version.
   *
   *    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., 675 Mass Ave, Cambridge, MA 02139, USA.
   */
  
  /*
   *    Stats.java
   *    Copyright (C) 1999 University of Waikato, Hamilton, New Zealand
   *
   */
  
  package weka.classifiers.trees.j48;
  
  import weka.core.RevisionHandler;
  import weka.core.RevisionUtils;
  import weka.core.Statistics;
  
  /**
   * Class implementing a statistical routine needed by J48 to
   * compute its error estimate.
   *
   * @author Eibe Frank (eibe@cs.waikato.ac.nz)
   * @version $Revision: 1.9 $
   */
  public class Stats
    implements RevisionHandler {
  
    /**
     * Computes estimated extra error for given total number of instances
     * and error using normal approximation to binomial distribution
     * (and continuity correction).
     *
     * @param N number of instances
     * @param e observed error
     * @param CF confidence value
     */
    public static double addErrs(double N, double e, float CF){
  
      // Ignore stupid values for CF
      if (CF > 0.5) {
        System.err.println("WARNING: confidence value for pruning " +
  			 " too high. Error estimate not modified.");
        return 0;
      }
  
      // Check for extreme cases at the low end because the
      // normal approximation won't work
      if (e < 1) {
  
        // Base case (i.e. e == 0) from documenta Geigy Scientific
        // Tables, 6th edition, page 185
        double base = N * (1 - Math.pow(CF, 1 / N)); 
        if (e == 0) {
  	return base; 
        }
      
        // Use linear interpolation between 0 and 1 like C4.5 does
        return base + e * (addErrs(N, 1, CF) - base);
      }
      
      // Use linear interpolation at the high end (i.e. between N - 0.5
      // and N) because of the continuity correction
      if (e + 0.5 >= N) {
  
        // Make sure that we never return anything smaller than zero
        return Math.max(N - e, 0);
      }
  
      // Get z-score corresponding to CF
      double z = Statistics.normalInverse(1 - CF);
  
      // Compute upper limit of confidence interval
      double  f = (e + 0.5) / N;
      double r = (f + (z * z) / (2 * N) +
  		z * Math.sqrt((f / N) - 
  			      (f * f / N) + 
  			      (z * z / (4 * N * N)))) /
        (1 + (z * z) / N);
  
      return (r * N) - e;
    }
    
    /**
     * Returns the revision string.
     * 
     * @return		the revision
     */
    public String getRevision() {
      return RevisionUtils.extract("$Revision: 1.9 $");
    }
  }
  