On Triangular Inequality of the Discounted Least Information Theory of Entropy (DLITE)

TL;DR

This paper introduces DLITE, a new entropy-based measure that quantifies differences between probability distributions and proves its metric properties, including the triangle inequality.

Contribution

The paper proves the triangular inequality for DLITE's cube root and provides alternative proofs for other key metric properties.

Findings

DLITE satisfies the triangle inequality.

DLITE acts as a metric distance between distributions.

Proofs establish DLITE's theoretical soundness as a metric.

Abstract

The Discounted Least Information Theory of Entropy (DLITE) is a new information measure that quantifies the amount of entropic difference between two probability distributions. It manifests multiple critical properties both as an information-theoretic quantity and as metric distance. In the report, we provide a proof of the triangular inequality of DLITE's cube root ($\sqrt[3]{DL}$), an important property of a metric, along with alternative proofs for two additional properties.