The third order information measure: a valid measure of information

Abstract

In this paper, we formulated a hierarchy of information measure starting from the basic information measure (e.g. Shannon entropy), q-valued entropies (e.g. Tsallis entropy) to other information measures formulated that enable the researchers to have a generalization that can generate other forms of information measures. It was also proven that the third order information measure is a valid measure of information by satisfying the Khinchin axioms. Aa probability distribution was also derived using the Maximum Entropy Principle which gives it a possible statistics to model.