I was able to get my hands on mangosteen, a dark purple fruit that is grown in Southeast Asia that is hard to find in the United States. It's got a hard shell on the outside that feels like a very unripe avocado with a very flat and sturdy stem. It's been sitting in my fruit bowl for about a week and the firmness has not changed and I don't smell any fragrance. How do I know if it's ripe enough to eat? 
Generally, mangosteens are harvested when they are ripe as they don't tend to ripen once picked. 