Did you have a look at "Piwik" (http://piwik.org/)? They want to become a real open source google analytics alternative, you can install it on your own server in minutes..
You can track page views either by including some javascript generated by piwik (its more or less the same as google analytics) or by directly calling the api from php-code (didnt try that though).
We run it in production for a few month now together with google analytics and it works pretty good. Tracking results seem to be pretty much the same for both (Piwik ~ 5%+).
I've checked piwik an seems to be quite similar with AWStats. I wonder if there is another one more specific to EzPublish which we can use to analyze the ez publish log files not apache one.