Relative and divergence measures based on extropy: dynamic forms and properties

Abstract Extropy-based divergence measures offer distinct advantages over entropy-based counterparts, owing to their mathematical simplicity and enhanced interpretability. Relative extropy by Lad et al . [5] is a symmetric divergence measure between two probability distributions, and Mohammadi et al . [8] introduced the asymmetric divergence between two distributions based on extropy. We further study these measures, their properties, and interrelationships in this article. To address the divergence between truncated lifetime distributions, we define dynamic relative extropy for residual and past lifetime scenarios. Exploring the interrelationships of dynamic cases of relative extropy, extropy divergence, and extropy inaccuracy, we derive some unique properties and characterizations for the exponential distribution. A nonparametric estimator for relative extropy is developed, and its performance is assessed through numerical simulation studies. The practical applicability of relative extropy is used to analyze the divergence in lifetime patterns of mice under a lifetime feeding experiment and the shopping patterns of customers based on age and income groups. Further, the application of relative extropy is also applied to find the dissimilarity between two images.