/*
Copyright (C) 2001 Kyle Siegrist, Dawn Duehring
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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
package distributions;
/**This class models the distribution of the maximum value of a symmetric random walk on the interval
[0, n].*/
public class WalkMaxDistribution extends Distribution{
//Paramters
private int steps;
/**This general constructor creates a new max walk distribution with a specified time parameter.*/
public WalkMaxDistribution(int n){
setSteps(n);
}
/**This default constructor creates a new walk max distribution with time parameter 10.*/
public WalkMaxDistribution(){
this(10);
}
/**This method sets the time parameter.*/
public void setSteps(int n){
if (n < 1) n = 1;
steps = n;
super.setParameters(0, steps, 1, DISCRETE);
}
/**This method defines the density function.*/
public double getDensity(double x){
int k = (int)Math.rint(x), m;
if ((k + steps) % 2 == 0) m = (k + steps) / 2;
else m = (k + steps + 1) / 2;
return comb(steps, m) / Math.pow(2 , steps);
}
/**This method returns the maximum value of the density function.*/
public double getMaxDensity(){
return getDensity(0);
}
/**This method returns the number ofsteps.*/
public double getSteps(){
return steps;
}
/**This method simulates a value from the distribution.*/
public double simulate(){
int step, max = 0, position = 0;
for (int i = 1; i <= steps; i++){
if (Math.random() < 0.5) step = 1;
else step = -1;
position = position + step;
if (position > max) max = position;
}
return max;
}
}