Entropy and F-divergence construction using the Einstein sum

Abstract

Starting from the Einstein sum and considering the real parameter a ∈ (1, ∞), we define the function f : [0, ∞) → (−∞, ∞) with the formula. Using the function f, the following formulas for entropy Hf and f-divergence Df are constructed, where P = (p1, p2, . . . , pn) and Q = (q1, p2, . . . , qn) are two discrete probabilities distributions.