2023/05/01 by Shital Saha, Saha, Shital, Suchandan Kayal +1
Decision Sciences · Mathematics · #FOS: Mathematics #Multi-Criteria Decision Making #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2305.00852
openalex publication_date 2023/05/01 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28
In information theory, it is of recent interest to study variability of the uncertainty measures. In this regard, the concept of varentropy has been introduced and studied by several authors in recent past. In this communication, we study the weighted varentropy and weighted residual varentropy. Several theoretical results of these variability measures such as the effect under monotonic transformations and bounds are investigated. Importance of the weighted residual varentropy over the residual varentropy is presented. Further, we study weighted varentropy for coherent systems and weighted residual varentropy for proportional hazard rate models. A kernel-based non-parametric estimator for the weighted residual varentropy is also proposed. The estimation method is illustrated using simulated and two real data sets.