User blog comment:Plexioth- xD/Monster Hunter 3 Ultimate/@comment-3095304-20130326010549/@comment-1837917-20130326033822

There should be armours that give you increased chance of extra items in the Quest Rewards, using the "Luck" skill. I'm pretty sure the Jaggi Mask gives you Good Luck. It's a bit of an odd skill, but it can help you out if you need to get some more materials or rare drops.

If you're talking specifically about an armour that increases the chance of a monster drop being a rare item (as in, when they drop a shiny), there is no such skill.