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.[1]

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

See also

References

  1. Bhattacharya, Anil Kumar (1943). "On a measure of divergence between two statistical populations defined by their probability distributions". Bulletin of the Calcutta Mathematical Society. 35: 99–109.
This article is issued from Wikipedia - version of the 5/28/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.