On a unification of divergences by means of information amounts
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.
scientific article; zbMATH DE number 1091062