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On weighted version of dynamic residual inaccuracy measure using extropy in order statistics with applications in model selection

Author

Listed:
  • Majid Hashempour

    (University of Hormozgan)

  • Morteza Mohammadi

    (University of Zabol)

  • Osman Kamari

    (University of Human Development)

Abstract

This paper introduces novel weighted inaccuracy measures for order statistics, leveraging the concept of extropy. We thoroughly investigate various properties of these measures and extend the framework to a weighted dynamic residual version. It is demonstrated that this measure distinctly characterizes the distribution function. Notably, we establish that the weighted extropy of the parent random variable corresponds to the average value of the weighted inaccuracy measure, highlighting the significance of the weighted aspect as a key innovation of this study. We propose a nonparametric kernel estimation approach for the introduced measure, with simulation results showing that the kernel estimator achieves optimal performance. Bandwidth selection is conducted using cross-validation for cumulative distribution function estimation and the normal reference method for probability density function estimation. Finally, we showcase the practical application of the proposed measure in model selection.

Suggested Citation

  • Majid Hashempour & Morteza Mohammadi & Osman Kamari, 2025. "On weighted version of dynamic residual inaccuracy measure using extropy in order statistics with applications in model selection," Statistical Papers, Springer, vol. 66(4), pages 1-28, June.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:4:d:10.1007_s00362-025-01696-9
    DOI: 10.1007/s00362-025-01696-9
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    References listed on IDEAS

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    1. Narayanaswamy Balakrishnan & Francesco Buono & Maria Longobardi, 2022. "On weighted extropies," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(18), pages 6250-6267, September.
    2. Qiu, Guoxin, 2017. "The extropy of order statistics and record values," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 52-60.
    3. Guoxin Qiu & Kai Jia, 2018. "Extropy estimators with applications in testing uniformity," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 182-196, January.
    4. Qiu, Guoxin & Jia, Kai, 2018. "The residual extropy of order statistics," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 15-22.
    5. Majid Hashempour & Morteza Mohammadi, 2024. "On dynamic cumulative past inaccuracy measure based on extropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(4), pages 1294-1311, February.
    6. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
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