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Abstract <p>The zero-inflated two-parameter Rayleigh distribution is formulated as a mixture model that incorporates both excess zeros and positive observations, where the zero component is governed by a binomial process and the nonzero values follow a two-parameter Rayleigh distribution. This study develops several approaches for constructing confidence intervals for its parameters. The techniques examined include the percentile bootstrap, generalized confidence intervals, standard confidence intervals, Bayesian credible intervals, and the Bayesian highest posterior density (HPD) interval. To compare the performance of these interval estimation methods, a Monte Carlo simulation study is carried out, focusing on two key criteria: coverage probability and expected interval width. Simulation results reveal that the Bayesian HPD approach consistently provides superior performance relative to the other methods considered. The proposed procedures are subsequently illustrated by constructing confidence intervals for the distribution parameters using actual COVID-19 mortality data from Myanmar recorded between February and April.</p>

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Bayesian Credible Interval for Parameters of Zero-inflated Two-Parameter Rayleigh Distribution

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • Sasipong Kijsason,
  • Sa-Aat Niwitpong,
  • Suparat Niwitpong

摘要

Abstract

The zero-inflated two-parameter Rayleigh distribution is formulated as a mixture model that incorporates both excess zeros and positive observations, where the zero component is governed by a binomial process and the nonzero values follow a two-parameter Rayleigh distribution. This study develops several approaches for constructing confidence intervals for its parameters. The techniques examined include the percentile bootstrap, generalized confidence intervals, standard confidence intervals, Bayesian credible intervals, and the Bayesian highest posterior density (HPD) interval. To compare the performance of these interval estimation methods, a Monte Carlo simulation study is carried out, focusing on two key criteria: coverage probability and expected interval width. Simulation results reveal that the Bayesian HPD approach consistently provides superior performance relative to the other methods considered. The proposed procedures are subsequently illustrated by constructing confidence intervals for the distribution parameters using actual COVID-19 mortality data from Myanmar recorded between February and April.