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<p>In the study of statistical inference, researchers often face two types of errors: those arising from insufficient information, inaccurate information, or a combination of both. Inaccuracy measures serve as valuable tools for addressing these challenges. The analysis of system inactivity time plays a crucial role in reliability data evaluation. This research extends the concept of the past inaccuracy measure to a bivariate framework, focusing on errors in predicting a bivariate random process and exploring its properties. Additionally, we generalize this measure to conditionally specified models, referred to as conditional past inaccuracy measures, and investigate their characteristics. For cases where the densities of random variables are unknown, we propose a non-parametric kernel estimator for their estimation. This study also introduces a kernel estimator for the measure and examines its asymptotic properties. To demonstrate the practical relevance of this measure, we provide numerical illustrations in real-world scenarios.</p>

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On Bivariate Dynamic Past Inaccuracy Measure

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • K. V. Viswakala,
  • E. V. Gijo,
  • E. I. Abdul Sathar

摘要

In the study of statistical inference, researchers often face two types of errors: those arising from insufficient information, inaccurate information, or a combination of both. Inaccuracy measures serve as valuable tools for addressing these challenges. The analysis of system inactivity time plays a crucial role in reliability data evaluation. This research extends the concept of the past inaccuracy measure to a bivariate framework, focusing on errors in predicting a bivariate random process and exploring its properties. Additionally, we generalize this measure to conditionally specified models, referred to as conditional past inaccuracy measures, and investigate their characteristics. For cases where the densities of random variables are unknown, we propose a non-parametric kernel estimator for their estimation. This study also introduces a kernel estimator for the measure and examines its asymptotic properties. To demonstrate the practical relevance of this measure, we provide numerical illustrations in real-world scenarios.