Support for the
Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate
plug-in.Object Library > Applets > Finite Order Statistic Experiment
The experiment consists of selecting n balls at random (without replacement) from a population of N balls, numbered from 1 to N. For i = 1, 2, ..., n, the i'th smallest number in the sample, X(i) (the i'th order statistic), is recorded on each update. For a selected k, the distribution and moments of X(k) are shown in the blue in the distribution graph and are recorded in the distribution table. When the simulation runs, the empirical distribution and moments of X(k) are shown in red in the distribution graph and are recorded in the distribution table. The parameters N, n, and k can be varied with scroll bars. You may have to undock the toolbar to make all of the controls visible.
This experiment is primarily useful for illustrating the distribution and moments of the order statistics from a random sample, without replacement, from 1, ..., N. These order statistics can be used to construct estimators of N, some of which have been used in famous applications. The estimators vary widely in quality and thus can be used to illustrate topics from point estimation. Finally, like many other experiments, this one illustrates discrete random variables and various forms of the law of large numbers. For a more detailed mathematical analysis, see
Click on the link below to download the Java archive file:
To add the applet to your web page, insert the following in the html file, at the point where you want the applet to appear:
<applet code="edu.uah.math.experiments.FiniteOrderStatisticExperiment.class"
archive="FiniteOrderStatisticExperiment.jar" width="600" height="400"></applet>
The jar file and the html file must be in the same folder.
This width and height dimensions are simply suggestions and can be varied. Generally, components such as graphs and tables expand and contract proportionally, while components such as buttons, scrollbars, dice, and coins are fixed in size.
Support for the
Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate
plug-in.Copyright © 2001-2003 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.
If you are interested in the Java source code or the Java documentation and object model for this applet, please visit FiniteOrderStatisticExperiment in the Object section of the Library.