A type of hat with a narrow brim. Brim is often upturned in the back and downwardly turned in the front. Usually the hat has a band around it for decoration. Hat resembles one that would likely have been worn by a member of the Rat Pack (Sinatra, Martin, Davis, et al). Similar to a fedora, but with a narrower brim.
That stingy you're wearing reminds me of Frank Sinatra.