Relationships between certain f -divergences

Abstract

We investigate the concavity deficit of the entropy functional. Some properties of the skew-divergence are developed and a “skew” $\chi^{2}$ divergence is introduced. Various relationships between these f - divergences and others are established, including a reverse Pinsker type inequality for the skew divergence, which in turn yields a sharpening on the upper bound for the entropic concavity deficit.