  Jizba-Arimitsu entropy (also called hybrid entropy) combines axiomatics of
R\'enyi and Tsallis entropy. It has many common properties with them, on the
other hand, some aspects as e.g., MaxEnt distributions, are completely
different from the former two entropies. In this paper, we demonstrate the
statistical properties of hybrid entropy, including the definition of hybrid
entropy for continuous distributions, its relation to discrete entropy and
calculation of hybrid entropy for some well-known distributions. Additionally,
definition of hybrid divergence and its connection to Fisher metric is also
discussed. Interestingly, the main properties of continuous hybrid entropy and
hybrid divergence are completely different from measures based on R\'enyi and
Tsallis entropy. This motivates us to introduce average hybrid entropy, which
can be understood as an average between Tsallis and R\'enyi entropy.
