# Talk:Hellinger distance

WikiProject Statistics (Rated Start-class, Low-importance)

This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.

Start  This article has been rated as Start-Class on the quality scale.
Low  This article has been rated as Low-importance on the importance scale.

WikiProject Mathematics (Rated Start-class, Low-priority)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Low Priority
Field: Probability and statistics

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)

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)

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)

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)

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)

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)

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)

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)