The Vexation is part of a sub-group of SMGs that only can spawn with a fixed-element Maliwan barrel. They feature the higher-than-usual elemental damage/second and element chance granted by the Maliwan barrel. These parameters achieve even higher values, if the SMG is equipped with a Maliwan grip.
Despite the low rarity designation of these weapons, their high elemental chance and status effect damage can make them excellent choices for combat until a more suitable (or less common, e.g. legendary) weapon is obtained.
There is a glitch in weapon creation system for this grouping of weapons. Blue rarity weapons have proper textures but color of item card titles is that of Purple rarity. If Colorblind Mode in Video options is turned on, it will read [Purple] instead of [Blue].
Because of this glitch, blue and purple rarity weapons (with the same set of parts) will have identical stats.
The Vexation is obtained randomly from any suitable loot source.
Maya uses a Purple Rarity Vexation in A Meat Bicycle Built for Two short film when she attacks Krieg.