From what I understand of the system (Steve can give you a more complete answer), Brazilian Jiu Jitsu doesn't award you your first colored belt ranking (blue) until you've demonstrated that you have a solid grasp of the fundamentals, and can apply them effectively. Essentially, this is the equivalent of the black belt in most other Ju Jutsu systems that use such a definition.
Someone who has his purple belt in BJJ would be the equivalent of either an advanced Shodan or an early Nidan in other Ju Jutsu systems, and is eligible to run his own dojo.
Brown belts in BJJ are the equivalent of an experienced Nidan, and closer to being an advanced Nidan equivalent in other Ju Jutsu systems.
Someone who has his black belt (Shodan) in BJJ would be the equivalent of a Sandan in other Ju Jutsu systems. That's not a rank that is given out very easily.