On some Properties of Tsallis Hypoentropies and Hypodivergences

Kurzfassung/Abstract

Both the Kullback-Leibler and the Tsallis divergence have a strong
limitation: if the value zero appears in probability distributions,
it must appear in the same positions for the sake of significance.
In order to avoid this limitation in the framework of Shannon
statistics, Ferreri introduced in 1980 hypoentropy: "such conditions
rarely occur in practice". The aim of the paper is to extend
Ferreri's hypoentropy to the Tsallis statistics. We introduce the
Tsallis hypoentropy and the Tsallis hypodivergence and describe
their mathematical behavior. Fundamental properties, like nonnegativity,
monotonicity, the chain rule and subadditivity, are established.