Re: Hellinger Distance

From: mdshafri (mdshafri_at_yahoo.com)
Date: 02/16/05 

Date: 16 Feb 2005 12:50:26 -0500

How to set the range of d value to represent the measurement.
We could be set 0 for no changes between two discrete distributions C
and H. What happen if the value of C far much bigger than H.
Please anybody advice me !!

On 19 Apr 1997 13:46:35 -0500, Herman Rubin wrote:
>In article <335237AD.59E2@dcs.rhbnc.ac.uk>,
>Peter Burge <peteb@dcs.rhbnc.ac.uk> wrote:
>>Please could someone give me a reference for a measure
>>known as the Hellinger Distance between two
>>discrete distributions C and H. In Latex,
>
>>d=\sum_{i=0}^{K} (\sqrt{C_{i}} - \sqrt{H_{i}})^{2}
>
>>This expression may be lacking additional terms.
>
>It is not lacking any terms. For general measures, although
>it is not likely to be of much use unless they are finite,
>it is
>
> d = \int (sqrt(dF) - sqrt(dG))^2.
>
>That this is well-defined can be seen by using as a base
>measure H = F + G. It is the supremum of the discrete
>versions obtained by using finite partitions.
>
>The real introduction of this into mathematics was by
>Kakutani, who gives credit to Hellinger in a footnote.
>--
>This address is for information only. I do not claim that these
views
>are those of the Statistics Department or of Purdue University.
>Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette
IN47907-1399
>hrubin@stat.purdue.edu Phone: (765)494-6054 FAX:
(765)494-0558