Metric used in probability and statistics
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.