On a sum form functional equation emerging from statistics and its applications

Abstract

In this paper, we obtain the general solutions of a sum form functional equation arising from the expected value of a discrete random variable. The significance of its general solutions in reference to entropies emerging from information theory and diversity index has been discussed.

Keywords

• additive mapping
• bounded mapping
• linear mapping
• logarithmic mapping
• the entropies of type (α β)
• diversity index
• expectation of a discrete random variable