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 S n − 1 obtained by projecting the probability simplex on the sphere by the transformation p i ↦ p i ,   i = 1 , … , n .

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