On a unification of divergences by means of information amounts
type: Item
instance of: scholarly article
title: On a unification of divergences by means of information amounts
zbMATH Open document ID: 0920.62008
DOI: 10.1016/S0034-4877(97)81468-1
author: Manabu Miyata
author: Masashi Yamada
author: Tomoaki Kawaguchi
published in: Reports on Mathematical Physics
publication date: 1999-09-06T00:00:00Z
review text: The paper is based on the idea that any \textit{dissimilarity measure} between two \textit{probability distributions} depends either on the difference or on the quotient of the density functions associated with these distributions. Then, on the basis of this key idea, the concept of \textit{discriminating amount} associated with the \textit{divergence} of probability distributions is presented, and several types of discriminating amounts are distinguished: Renyi's one and a unifying family. Jeffrey's invariant of the Renyi discriminating amount is considered to symmetrize it. This symmetrical measure is later employed to obtain some distances to present the notion of \textit{Renyi's infinitesimal discriminating amount}. A similar study is developed for the unified discriminating amount. Local properties on the statistical parameter space, as well as connections between the introduced and the reviewed measures are examined.
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 1091062
zbMATH Keywords: discriminating amount
zbMATH Keywords: dissimilarity measure
zbMATH Keywords: divergence
reviewed by: M. Ángeles Gil
MaRDI profile type: Publication
cites work: Q5564905
cites work: Q3476111
cites work: On Information and Sufficiency
cites work: Entropy differential metric, distance and divergence measures in probability spaces: A unified approach
cites work: On the relation between the statistical divergence and geodesic distance
full work available at URL: s0034-4877(97)81468-1
OpenAlex ID: W2015218855
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description: scientific article; zbMATH DE number 1091062