What is Tivoli Management Statistics?  There's an icon for it on the bottom
button bar on my screen at work.

The area at the right hand end of the taskbar is called the system
tray. Programs running "in the background" (that is, without a window
open) on your computer can display small icons there to allow you to
interact with them.

Because you can see a Tivoli icon in your taskbar, it is likely that
the Tivoli Management Framework is installed on your computer. Using
Tivoli Enterprise products, system administrators can perform tasks
like these on thousands of networked systems:

* Manage user and group accounts 
* Deploy new or upgrade existing software 
* Inventory existing system configuration 
* Monitor the resources of systems either inside or outside the Tivoli
environment
* Manage Internet and intranet access and control 
* Manage third-party applications 

You can read about the many capabilities of Tivoli software at
www.tivoli.com.

You may be concerned that there are privacy implications in
administrators having access to your computer in this way. You are
right to be concerned. It is most likely that the Tivoli tools are
being using to manage and support your computer, not to monitor your
work. However, the only to be sure about the way that Tivoli is used
in your organisation is to ask your manager.

On the Tivoli.com site, I found this under the category "Tivoli
Management Solution for Exchange V1.1 Master Document List":

http://www.tivoli.com/support/public/Prodman/public_manuals/td/exchange/mse.zip/en_US/HTML/StatBld/start.htm