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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 S n − 1 {\displaystyle S^{n-1}} obtained by projecting the probability simplex on the sphere by the transformation p i ↦ p i , i = 1 , … , n {\displaystyle p_{i}\mapsto {\sqrt {p_{i}}},\ i=1,\ldots ,n}.