Mathematics and Statistics Vol. 12(3), pp. 256 - 269
DOI: 10.13189/ms.2024.120306
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Confidence Intervals for the Parameter of the Juchez Distribution and Their Applications

Patchanok Srisuradetchai ¹, Wararit Panichkitkosolkul ^1,2,*
1 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Thailand
² Research Unit in Mathematical Sciences and Applications, Thammasat University, Thailand

ABSTRACT

This paper presents four types of confidence intervals (CIs) for parameter estimation of the Juchez distribution, a robust model in the domain of lifetime data analysis. The likelihood-based, Wald-type, bootstrap-t, andbias-corrected and accelerated (BCa) bootstrap confidence intervals are proposed and evaluated through simulation studies and application to real datasets. The effectiveness of these methods is assessed in terms of the empirical coverage probability (CP) and average length (AL) of the confidence intervals, providing an understanding of their performance under various conditions. Additionally, we derive the Wald-type CI formula in explicit form, making it readily calculable. The results show that when the sample size is small, such as 10, 20, or 30, the bootstrap-t and BCa bootstrap methods produce CPs less than 0.95. However, as sample sizes increase, the CPs of all methods tend to converge towards the nominal level of 0.95. The parameter values also affect the CP. At low values of the parameter, the CPs are quite close to the ideal, with both the Wald-type and likelihood-based methods achieving a CP of approximately 0.95. However, at higher parameter values with small sample sizes, the CPs for the bootstrap-t and BCa bootstrap methods tend to have lower coverage.

KEYWORDS
Confidence Interval, Bootstrap, Lifetime Distribution, Wald, Likelihood

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Patchanok Srisuradetchai , Wararit Panichkitkosolkul , "Confidence Intervals for the Parameter of the Juchez Distribution and Their Applications," Mathematics and Statistics, Vol. 12, No. 3, pp. 256 - 269, 2024. DOI: 10.13189/ms.2024.120306.

(b). APA Format:
Patchanok Srisuradetchai , Wararit Panichkitkosolkul (2024). Confidence Intervals for the Parameter of the Juchez Distribution and Their Applications. Mathematics and Statistics, 12(3), 256 - 269. DOI: 10.13189/ms.2024.120306.