Confidence Intervals for the Parameter of the Juchez Distribution and Their Applications

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, and bias-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 Waldtype 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.