The Hellinger distance is a metric between statistical distributions obtained from their square roots. For discrete probability
mass functions 
and 
on the same set, its usual normalization is
 |
The sum 
is called Hellinger affinity, so
. The distance is 0 for identical distributions and 1 when their nonzero probabilities occur on disjoint
sets of outcomes. For the binary laws 
and 
with 
, one has 
(Anantharam et al. 2017).
