Analog claims to be "The most popular logfile analyser in the world". This is a bold claim but they say they can back it up. It certainly is a very popular and long-standing stats package, recommended by many server geeks.
Analog displays a lot of information on a single page, similar to AWStats. On the plus side the page includes a great deal of useful information. On the downside the layout is a bit raw and the graphs are a little clunky. It's not really the most user-friendly presentation.
If you yearn for prettier graphics and better layout, your server admin can install Report Magic (www.reportmagic.org) which works with Analog to provide much better-looking reports.
Server admins like Analog because it's fast and efficient, and is able to handle huge loads.
I have used Analog as a back-up stats package for a number of years and overall it's a fine package. The stats are very detailed and I've never had any problems with it. It just lacks a bit in the style department, and doesn't provide the advanced display options of some other applications.