Uniform Estimate Experiment

Description and Use

The experiment is to generate a random sample X₁, X₂, ..., X_n of size n from the uniform distribution on (0, a). The distribution density is shown in blue in the graph, and on each update, the sample density is shown in red. On each update, the following statistics are recorded:

U = 2M where M = (X₁ + X₂ + ЗЗЗ + X_n) / n (the sample mean).
V = (n + 1)X_(n) / n where X_(n) = max{X₁, X₂, ..., X_n} (the n'th order statistic).
W = (n + 1)X₍₁₎ where X₍₁₎ = min{X₁, X₂, ..., X_n} (the first order statistic).

Each statistic is a point estimator of a. On each update, the empirical bias and mean square error of each estimator are recorded in the second table. The parameters a and n can be varied with scroll bars.

This applet illustrates the topics and concepts in the list below. Click on the links to learn more about the mathematical theory.

Instructions for Downloading and Installing

Click on the link below to download the Java archive file:

UniformEstimateExperiment.jar (48 KB)

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.UniformEstimateExperiment.class" archive="UniformEstimateExperiment.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.

Metadata

Type

Java Applet

Keywords

probability
statistics
uniform distribution
point estimation
mean square error
bias

Version

August, 2003

Browser Requirements

Support for the Java 2 runtime environment (version 1.4 or later). Click on the icon to download the appropriate plug-in.

Authors

Kyle Siegrist
Dawn Duehring

Copyright

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.

Related Resources

If you are interested in the Java source code or the Java documentation and object model for this applet, please visit UniformEstimateExperiment in the Object section of the Library.