Bayesian Estimation of Variance-Based Information Measures and Their Application to Testing Uniformity

Entropy and extropy are emerging concepts in machine learning computer science. Within the past decade, statisticians have created estimators for these measures. However, associated variability metrics, specifically varentropy varextropy, received comparably less attention. This paper presents a novel methodology computing drawing inspiration from Bayesian nonparametric methods. We implement this approach using computational algorithm R demonstrate its effectiveness across various examples. Furthermore, new applied to test uniformity data.