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 pi, qi are the probabilities assigned to the point i, for i = 1, ..., n, and is the Bhattacharya coefficient.
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