Rarity
Part of speech: noun
Definition: A rare object. A measure of the scarcity of an object.
Example sentence: When I grew up in India, telephones were a rarity. In fact, they were so rare that elected members of Parliament had the right to allocate 15 telephone lines as a favor to those they deemed worthy. If you were lucky enough to be a wealthy businessman or an influential journalist, or a doctor or something, you might have a telephone.
Infrequency
Part of speech: noun
Definition: The characteristic of being infrequent; rarity; irregularity; scarcity.