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<sub>i</sub>, q<sub>i</sub> 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 obtained by projecting the probability simplex on the sphere by the transformation .
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