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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年4月17日

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  • Majid Hashempour,
  • Morteza Mohammadi,
  • Osman Kamari

摘要

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.