On a unification of divergences by means of information amounts (Q1373696)

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.