Bhattacharyya angle

In statistics, Bhattacharyya angle, also called statistical angle, is a measure of distance between two probability measures defined on a finite probability space. It is defined as
where "p""i", "q""i" are the probabilities assigned to the point "i", for "i" = 1, ..., "n", and
is the Bhattacharya coefficient.
The Bhattacharya distance is the geodesic distance in the orthant of the sphere formula_3 obtained by projecting the probability simplex on the sphere by the transformation formula_4.
This distance is compatible with Fisher metric. It is also related to Bures distance and fidelity between quantum states as for two diagonal states one has