Generalized Arithmetic and Geometric Mean Divergence Measure and their Statistical Aspects

TL;DR

This paper introduces a generalized divergence measure based on arithmetic and geometric means, explores its connection with Fisher information, and unifies several divergence measures within a single framework.

Contribution

It proposes a new generalized divergence measure with scalar parameters, linking it to Fisher information and unifying existing divergence measures.

Findings

Connection established between generalized AG-divergence and Fisher information

Unified framework for AG-divergence and Jensen-Shannon divergence

Potential applications in statistical experiment comparison

Abstract

Using Blackwell's definition of comparing two experiments, a comparison is made with \textit{generalized AG - divergence} measure having one and two scalar parameters. Connection of \textit{generalized AG - divergence} measure with \textit{Fisher measure of information} is also presented. A unified \textit{generalization of AG - divergence}and\textit{Jensen-Shannon divergence measures} is also presented.