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

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

Automated summary

This paper presents a novel methodology for computing varentropy and varextropy, drawing inspiration from Bayesian nonparametric methods. The approach is implemented using a computational algorithm in R and its effectiveness is demonstrated across various examples. Furthermore, these new estimators are applied to test uniformity in data.