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

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.