Extropy-Based Generalized Divergence and Similarity Ratios: Theory and Applications

TL;DR

This paper introduces extropy-based divergence and similarity measures, GESR and GEDR, with theoretical properties, estimators, and applications in lifetime and image data analysis.

Contribution

It proposes new extropy-based divergence and similarity ratios, establishes their properties, and demonstrates their practical applications.

Findings

GESR relates to cosine similarity.

Nonparametric estimators perform well in simulations.

Applications shown in lifetime and image analysis.

Abstract

In this article, we propose two classes of relative information measures based on extropy, viz., the generalized extropy similarity ratio (GESR) and generalized extropy divergence ratio (GEDR), that measure the similarity and discrepancy between two probability distributions, respectively. Definitions of GESR and GEDR are proposed along with their fundamental axioms, properties, and some measures satisfying those axioms are also introduced. The relationship of GESR with the popular cosine similarity is also established in the study. Various properties of GESR and GEDR, including bounds under the proportional hazards model and the proportional reversed hazards model, are derived. Nonparametric estimators of GESR are defined, and their performance is evaluated using simulation studies. Applications of the GESR in lifetime data analysis and image analysis are also demonstrated in this study.