Abstract <p>This paper proposes five bootstrap confidence intervals (CIs) for the parameter in the Iwueze distribution, a single-parameter mixture distribution combining the exponential and gamma distributions. The bootstrap CI using the normal approximation, percentile bootstrap CI, basic bootstrap CI, bootstrap-t CI, and bias-corrected and accelerated (BCa) bootstrap CI are introduced and evaluated through simulation studies and application to real datasets. The effectiveness of these methods is assessed in terms of the empirical coverage probability (ECP) and average width (AW) of the CIs in several situations. Through Monte Carlo simulations, the BCa bootstrap method was found to be the most reliable, providing accurate ECPs and making it a strong choice for situations where precise interval estimation is essential. On the other hand, the normal approximation method, though it produces narrower intervals, tends to have less accurate coverage, particularly with smaller sample sizes. This highlights the need to choose the method that best fits the specific goals of the study. Applying these methods to a real-world dataset further confirms their usefulness, offering dependable tools for statistical analysis. This research adds valuable insights to the field by improving the understanding of bootstrap techniques for the Iwueze distribution and offering practical advice on selecting methods to enhance the accuracy of statistical results.</p>

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Confidence Intervals for the Iwueze Distribution Parameter Using Bootstrap Techniques: Methodology and Application

  • Wararit Panichkitkosolkul,
  • Mohammad Mastak Al Amin,
  • Andrei Volodin

摘要

Abstract

This paper proposes five bootstrap confidence intervals (CIs) for the parameter in the Iwueze distribution, a single-parameter mixture distribution combining the exponential and gamma distributions. The bootstrap CI using the normal approximation, percentile bootstrap CI, basic bootstrap CI, bootstrap-t CI, and bias-corrected and accelerated (BCa) bootstrap CI are introduced and evaluated through simulation studies and application to real datasets. The effectiveness of these methods is assessed in terms of the empirical coverage probability (ECP) and average width (AW) of the CIs in several situations. Through Monte Carlo simulations, the BCa bootstrap method was found to be the most reliable, providing accurate ECPs and making it a strong choice for situations where precise interval estimation is essential. On the other hand, the normal approximation method, though it produces narrower intervals, tends to have less accurate coverage, particularly with smaller sample sizes. This highlights the need to choose the method that best fits the specific goals of the study. Applying these methods to a real-world dataset further confirms their usefulness, offering dependable tools for statistical analysis. This research adds valuable insights to the field by improving the understanding of bootstrap techniques for the Iwueze distribution and offering practical advice on selecting methods to enhance the accuracy of statistical results.