Why is there no name for the precision of the negative class in the assessment of a binary classifer?

Question

In the assessment of a binary classifier, we know that specificity is the recall of the negative class.
So there are clear names for both flavors of recall.

Then looking at precision, I can't help but wonder why there isn't an analogous version for the negative class, ala

tn / (tn + fn)

It seems useful to ask, "of all the sample predicted as negative, how many are really negative?" so you'd think that metric would have it's own name. Is there something obvious I'm missing?

Answer 1

Actually there's a name for it: negative predictive value .