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The delta-Rayleigh distribution comprises a mixture of zero and non-negative values following the Rayleigh distribution. Percentiles are practical tools for describing skewed data and are widely used in several fields. The purpose of this study is to construct confidence intervals for different percentiles of the delta-Rayleigh distributions using generalized confidence interval (GCI), normal approximation (NA), method of variance estimates recovery (MOVER), percentile bootstrap confidence interval (PBCI), and Bayesian methods. Monte Carlo simulations were conducted to evaluate the performance of these methods using coverage probabilities and average widths. The results indicate that the GCI method outperformed others. For a real-world data application, we utilized a dataset on CO concentration to assess the performance of the presented methods.

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Confidence Intervals for the Difference Between the Percentiles of the Delta-Rayleigh Distributions

  • 会议论文

  • 发表日期：

    2026年

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  • Nerisa Thornsri,
  • Sa-Aat Niwitpong,
  • Suparat Niwitpong

摘要

The delta-Rayleigh distribution comprises a mixture of zero and non-negative values following the Rayleigh distribution. Percentiles are practical tools for describing skewed data and are widely used in several fields. The purpose of this study is to construct confidence intervals for different percentiles of the delta-Rayleigh distributions using generalized confidence interval (GCI), normal approximation (NA), method of variance estimates recovery (MOVER), percentile bootstrap confidence interval (PBCI), and Bayesian methods. Monte Carlo simulations were conducted to evaluate the performance of these methods using coverage probabilities and average widths. The results indicate that the GCI method outperformed others. For a real-world data application, we utilized a dataset on CO concentration to assess the performance of the presented methods.