On relative weighted entropies with central moments weight functions

TL;DR

This paper analyzes relative weighted entropy using central moments weight functions, compares it with standard entropy in Gaussian cases, and introduces a weighted deviance information criterion for statistical model assessment.

Contribution

It introduces a new analysis of relative weighted entropy with central moments weights and proposes a weighted deviance information criterion for model evaluation.

Findings

Weighted relative entropy differs from standard entropy in Gaussian cases.

Comparison of weighted and standard entropy highlights differences in information measures.

Proposed weighted deviance information criterion aids in statistical model selection.

Abstract

Following [1], the aim of this paper is to analyze the relative weighted entropy involving the central moments weight functions. We compare the standard relative entropy with the weighted case in two particular forms of Gaussian distributions. As an application, the weighted deviance information criterion is proposed.