In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909.[1][2]
It is sometimes called the Jeffreys distance.[3][4]
- ^ Nikulin, M.S. (2001) [1994], "Hellinger distance", Encyclopedia of Mathematics, EMS Press
- ^ Hellinger, Ernst (1909), "Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen", Journal für die reine und angewandte Mathematik (in German), 1909 (136): 210–271, doi:10.1515/crll.1909.136.210, JFM 40.0393.01, S2CID 121150138
- ^ "Jeffreys distance - Encyclopedia of Mathematics". encyclopediaofmath.org. Retrieved 2022-05-24.
- ^ Jeffreys, Harold (1946-09-24). "An invariant form for the prior probability in estimation problems". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 186 (1007): 453–461. Bibcode:1946RSPSA.186..453J. doi:10.1098/rspa.1946.0056. ISSN 0080-4630. PMID 20998741. S2CID 19490929.
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