A dynamic residual measure of inaccuracy based on varextropy

Abstract

In this paper, we introduce a variance-based inaccuracy measure for order statistics based on the concept of varextropy. The proposed measure provides a framework for quantifying the variability of the inaccuracy function between an order statistic and its parent distribution. We establish a transformation property of the proposed measure under strictly increasing differentiable transformations. We establish theoretical upper and lower bounds for this measure. We further develop a dynamic residual version of the proposed inaccuracy measure and establish characterization results for the underlying distribution. Furthermore, we derive bounds for the dynamic residual inaccuracy measures based on extropy and varextropy. Finally, a nonparametric estimator of the proposed measure is developed and applied to real data to assess the goodness-of-fit of candidate distributions and facilitate model selection. 1.

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BibTeX RIS

BibTeX

@misc{goodarzi2026dynamic,
  title = {{A dynamic residual measure of inaccuracy based on varextropy}},
  author = {Faranak Goodarzi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13855},
  eprint = {2609.13855},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13855},
  note = {CC BY-NC-SA 4.0},
}

RIS

TY  - UNPB
TI  - A dynamic residual measure of inaccuracy based on varextropy
AU  - Faranak Goodarzi
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13855
UR  - https://arxiv.org/abs/2609.13855
AB  - In this paper, we introduce a variance-based inaccuracy measure for order statistics based on the concept of varextropy. The proposed measure provides a framework for quantifying the variability of the inaccuracy function between an order statistic and its parent distribution. We establish a transformation property of the proposed measure under strictly increasing differentiable transformations. We establish theoretical upper and lower bounds for this measure. We further develop a dynamic residual version of the proposed inaccuracy measure and establish characterization results for the underlying distribution. Furthermore, we derive bounds for the dynamic residual inaccuracy measures based on extropy and varextropy. Finally, a nonparametric estimator of the proposed measure is developed and applied to real data to assess the goodness-of-fit of candidate distributions and facilitate model selection. 1.
ER  -

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