MS&E 321

Stochastic Systems

Some web resources and interesting links

Brownian Motion

Brownian paths 1: Applet simulation of 2 and 1 dimensional Brownian Motion. http://www.ms.uky.edu/~ms.uky.edu/java/stat/brmo.html.
Brownian paths 2: Applet illustrating self-similarity by zooming into a Brownian path. http://www.stat.umn.edu/~charlie/Stoch/brown.html.
The "original" Brownian motion: Applets that simulate the movement of a particle in a fluid, due to collisions with the molecules in the fluid: http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html and http://www.phy.ntnu.edu.tw/java/gas2D/gas2D.html.
Brownian paths 3: Some interesting properties of Brownian paths can be found in Favorite Points, Cover Times and Fractals by Prof. Amir Dembo (Statistics Dept, Stanford) http://www-stat.stanford.edu/~amir/math-232/lnotes.pdf.

Confidence Intervals

Central Limit Theorem

Linear regression

The R project: http://www.r-project.org Free statistical software.
VassarStats: http://faculty.vassar.edu/~lowry/VassarStats.html Web site for statistical computation. Includes simple linear regression applications and batteries of tests.
The SciLab project http://www.scilab.org/ Free scientific software package, similar to Matlab. Includes a statistics toolbox.
Matlab resources: A list of freely available toolboxes for statistical applications in Matlab can be found at http://www.statsci.org/matlab.html.
StatLib: http://lib.stat.cmu.edu/index.php. A system for distributing statistical software, datasets, and information to and from the statistics community.
Java Applets to illustrate concepts and properties of linear regression: http://www.kuleuven.ac.be/ucs/java/version2.0/Content_Regression.htm Includes interactive graphical simulations comparing regression output to underlying "true" model, histograms of error measures and regression output, etc.
Effect of outliers on a regression line: http://www.stat.sc.edu/~west/javahtml/Regression.html Interactive applet to visualize the effect of leverage points on a regression line.

Autoregressive processes

ARfit: A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models: http://www.gps.caltech.edu/~tapio/arfit/
Some links to time series software & sources: http://www.time-series-analysis.com/cms

Queueing theory

Myron Hlynka's Queueing Theory Page: http://www2.uwindsor.ca/~hlynka/queue.html
QNAT: Queueing Network Analysis Tool http://poisson.ecse.rpi.edu/~hema/qnat/
Queueing simulation applets:
- A simulation of a single server queue: http://keskus.hut.fi/~esa/java/queue/I/
- A toy program that lets you build a queueing network and simulate its behavior: http://keskus.hut.fi/~esa/java/queue/II/
Queueing Theory Software: http://www.geocities.com/qtsplus. Excel workbooks that analyze queueing models by analytic, numerical and discrete event simulation techniques.