On weighted residual varextropy: characterization, estimation and application

Li Zhang; Bin Lu; Li Zhang; Bin Lu

doi:10.3934/math.2025509

AIMS Mathematics

2025, Volume 10, Issue 5: 11234-11259. doi: 10.3934/math.2025509

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Research article

On weighted residual varextropy: characterization, estimation and application

Li Zhang ¹,
Bin Lu ^{2
,
,}

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2.
Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China

Received: 26 February 2025 Revised: 30 April 2025 Accepted: 07 May 2025 Published: 16 May 2025
MSC : 62G05, 94A17

In recent years, the study of variability in uncertainty measures has gained significant interest in information theory. In this context, the concept of varextropy has been introduced and investigated by several researchers. This paper focuses on the study of weighted varextropy and introduces weighted residual varextropy, presenting a thorough examination of their theoretical properties. Specifically, we investigate the impact of monotonic transformations on these measures and derive various bounds. Additionally, we analyze the application of weighted varextropy within coherent systems and proportional hazard rates models. A non-parametric kernel-based method is introduced to estimate weighted (residual) varextropy, and the estimators' consistency and asymptotic normality are given. Finally, the effectiveness of this estimation method is demonstrated through simulations as well as analysis of a real-world data set, illustrating its potential applications in uncertainty analysis.
- variability measures,
- weighted residual varextropy,
- proportional hazard rates model,
- non-parametric estimation
Citation: Li Zhang, Bin Lu. On weighted residual varextropy: characterization, estimation and application[J]. AIMS Mathematics, 2025, 10(5): 11234-11259. doi: 10.3934/math.2025509

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Abstract

In recent years, the study of variability in uncertainty measures has gained significant interest in information theory. In this context, the concept of varextropy has been introduced and investigated by several researchers. This paper focuses on the study of weighted varextropy and introduces weighted residual varextropy, presenting a thorough examination of their theoretical properties. Specifically, we investigate the impact of monotonic transformations on these measures and derive various bounds. Additionally, we analyze the application of weighted varextropy within coherent systems and proportional hazard rates models. A non-parametric kernel-based method is introduced to estimate weighted (residual) varextropy, and the estimators' consistency and asymptotic normality are given. Finally, the effectiveness of this estimation method is demonstrated through simulations as well as analysis of a real-world data set, illustrating its potential applications in uncertainty analysis.

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