Hi,

$P_1$, $P_2$, $P_3$ are probability distributions defined on the same support.

Knowing that $H(P_1) < H(P_2) < H(P_3)$, can we compare $D_{KL}(P_2,P_1)$ and $D_{KL}(P_3,P_1)$ ?

(H is the Shannon Entropy and $D_{KL}$ is the Kullback–Leibler divergence)

Thank you.