  Comparative convexity is a generalization of convexity relying on abstract
notions of means. We define the Jensen divergence and the Jensen diversity from
the viewpoint of comparative convexity, and show how to obtain the generalized
Bregman divergences as limit cases of skewed Jensen divergences. In particular,
we report explicit formula of these generalized Bregman divergences when
considering quasi-arithmetic means. Finally, we introduce a generalization of
the Bhattacharyya statistical distances based on comparative means using
relative convexity.
