西南交通大学学报 JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY 第 59 卷 第 2 期 2 0 2 4 年 4 月 Available online at http://jsju.org Vol. 59 No. 2 April 2024 © 2024 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/ ). Open Access Article https://doi.org/10.35741/issn.0258-2724.59.2.23 Research article Mathematics CONFIDENCE INTERVALS FOR THE KOMAL DISTRIBUTION PARAMETER AND THEIR APPLICATIONS 科马尔分佈參數的信賴區間及其應用 Wararit Panichkitkosolkul a, b, *, Benjamas Tulyanitikul a , Wanwarat Anlamlert a a Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Pathum Thani, Thailand b Research Unit in Mathematical Sciences and Applications, Thammasat University, Thailand * Corresponding author: warаrit@mathstat.sci.tu.аc.th. Received: January 10, 2024 ▪ Reviewed: February 6, 2024 ▪ Accepted: March 13, 2024 ▪ Published: April 30, 2024 Abstract This paper aims to propose four confidence intervals (CIs) for parameter estimation of the Komal distribution, a robust model used in lifetime data analysis. This study proposed likelihood-based, Wald- type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap CIs and evaluated them through Monte Carlo simulation studies and application to a real dataset. The efficacy evaluation of these confidence intervals considered their empirical coverage probability (CP) and expected length (EL), which offer insights into their performance in different circumstances. In addition, we have derived the explicit formulation of the Wald-type CI formula, simplifying its computation. The results show that when the sample size is small, such as 10, 20, or 30, the bootstrap-t and BCa bootstrap CIs produce CPs less than 0.95. However, as sample sizes increase, the CPs of all CIs tend to converge toward the nominal confidence level of 0.95. The parameter values also impact the CP. At low parameter values, the CPs are close enough to the nominal confidence level, with the likelihood-based and Wald-type CIs achieving CPs of approximately 0.95. However, the CPs for the bootstrap-t and BCa bootstrap CIs tend to lower coverage at higher parameter values with small sample sizes. Application to engineering data, resulting in outcomes corresponding to those obtained from the simulation, confirmed the efficacy of the confidence intervals. Keywords: confidence interval, Komal distribution, likelihood, Wald, bootstrap 摘要 本文旨在提出用於科马尔分佈參數估計的四個置信區間，科马尔分佈是一種用於壽命資料分