Statistical distance

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 pi, qi 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 (Wikipedia).

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Orthant | Statistics | Hellinger distance | Bhattacharyya distance | Bures metric | Probability