Yes, it is possible to access your AwStats directly through your domain name.
However, doing this requires you to add a script to your site and configure it. In other words you need to manually install AwStats for under your account for example in a sub-folder. However our recommendation is to keep Stats for your domain names private and access them via cPanel.
cPanel is easy to work with when you have the right host to support you. If you need a reliable partner to help you manage your website with cPanel, check out our cPanel hosting services!