Conditions for the existence of a generalization of Rényi divergence

08/11/2020

∙

by   Rui F. Vigelis, et al.

∙

0

∙

share

We give necessary and sufficient conditions for the existence of a generalization of Rényi divergence, which is defined in terms of a deformed exponential function. If the underlying measure μ is non-atomic, we found that not all deformed exponential functions can be used in the generalization of Rényi divergence; a condition involving the deformed exponential function is provided. In the case μ is purely atomic (the counting measure on the set of natural numbers), we show that any deformed exponential function can be used in the generalization.