Do you mean the hybrid parrot or the 'true' parrot cichlid (Hoplarchus Psittacus)? Though I don't know for sure I would expec the true parrot to live for 8-15 years in line with similar cichlids. The man made parrot fish I would expect to live slightly shorter at 7-10 years probably (if a deformity doesn't kill it first - my views on the parrot cichlid creeping in there ). Though like I said, I'm not 100% sure but these sound like good estimates to me.
I too dont like the cultavated parrot cichlid, but we have 100's at work and some are well over 5 years old now. some are known to be nearly 10 years old but we dont know any any older that that.