Talk:Hellinger distance

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I'm not sure that the measure λ needs to be a probability measure. If someone knows for sure that this is not required, please change it.Skbkekas (talk) 20:25, 4 April 2009 (UTC)[reply]

The formula for the Hellinger distance between two normal distributions appears to be incorrect. Could someone more competent than me check it? 88.109.209.42 (talk) 11:33, 7 June 2009 (UTC)[reply]

I checked the Hellinger distance for the two normals. It is correct. It was just the square root for it. I corrected all of them to be squared Hellinger distances and make sense with the rest of the article. —Preceding unsigned comment added by 130.236.58.84 (talk) 15:52, 8 June 2010 (UTC)[reply]

The latter example of using the Lebesgue measure is in contradiction with the requirement that &lambda needs to be a probability measure. Probably the requirement is incorrect... --Kaba3 (talk) 18:07, 11 February 2012 (UTC)[reply]

If lambda is not a probability measure then I believe you will not have invariance with respect to it of the Hellinger distance. In general, this invariance does not hold, as can be seen by a trivial example with a two outcome state space equipped with the discrete topology (and corresponding sigma algebra), and different non-probability measures used as lambda. — Preceding unsigned comment added by 70.22.231.68 (talk) 16:56, 13 November 2012 (UTC)[reply]

Has somebody a reference to the relation of the Hellinger distance to the Bhattacharyya coefficient? I found an article which has a proof (http://www.cse.yorku.ca/~kosta/CompVis_Notes/bhattacharyya.pdf), but a more well-respected source would be better — Preceding unsigned comment added by 87.77.5.80 (talk) 14:39, 29 May 2013 (UTC)[reply]

This: (http://arxiv.org/abs/1201.0418, http://arxiv.org/pdf/1201.0418.pdf) paper seems to be published in as an article in a journal (CoRR) (http://dblp.uni-trier.de/rec/bibtex/journals/corr/abs-1201-0418) und shows on page 2 the relation. — Preceding unsigned comment added by 87.77.5.80 (talk) 11:26, 30 May 2013 (UTC)[reply]

I just went through a long web search in order to find the original article where the Hellinger distance is introduced. It appears that another name for the Hellinger distance seems to be the Jeffreys-Matusita metric. Jeffrey is also written Jeffries, which seems to be a mistake, since it refers to H Jeffeys (https://fr.wikipedia.org/wiki/Harold_Jeffreys). An original article about the Jeffreys-Matusita metric again was not found anywhere on the internet, until I found this (http://projecteuclid.org/euclid.aoms/1177728422) and this (http://rspa.royalsocietypublishing.org/content/186/1007/453.short). So I really wonder where from does the "Hellinger distance" come ??? And is it even appropriate to use this term instead of Jeffreys-Matusita metric ? — Preceding unsigned comment added by 194.214.230.194 (talk) 17:59, 15 April 2016 (UTC)[reply]