## 3 Interval Estimation
### Bootstrap Confidence Interval
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & & & & & & \\ \hline \multicolumn{1}{c}{\(\eta_{i}\)} & \multicolumn{1}{c}{**C.S**} & \multicolumn{1}{c}{**AL/CP**} & \multicolumn{1}{c}{**ACI**} & \multicolumn{1}{c}{**Logit**} & \multicolumn{1}{c}{**BootCI**} & \multicolumn{1}{c}{**BCI**} & \multicolumn{1}{c}{**HPDCI**} & \multicolumn{1}{c}{**BCI**} & \multicolumn{1}{c}{**HPDCI**} \\ \hline \multirow{3}{*}{} & (\(S_{2}\), \(T_{5}\)) & AL & 0.3293 & 0.3189 & 0.3254 & 0.3234 & 0.3205 & 0.3089 & 0.3065 \\  & CP & 0.9333 & 0.9527 & 0.9473 & 0.9507 & 0.9420 & 0.9633 & 0.9540 \\ \hline \multirow{3}{*}{} & (\(S_{3}\), \(T_{6}\)) & AL & 0.3392 & 0.3279 & 0.3368 & 0.3330 & 0.3296 & 0.3179 & 0.3153 \\  & CP & 0.9273 & 0.9507 & 0.9233 & 0.9560 & 0.9353 & 0.9687 & 0.9587 \\ \hline \multirow{3}{*}{} & (\(S_{4}\), \(T_{4}\)) & AL & 0.3257 & 0.3179 & 0.3239 & 0.3229 & 0.3173 & 0.3081 & 0.3036 \\  & CP & 0.9133 & 0.9447 & 0.9347 & 0.9427 & 0.9307 & 0.9573 & 0.9507 \\ \hline \multirow{3}{*}{} & (\(S_{5}\), \(T_{5}\)) & AL & 0.3163 & 0.3090 & 0.3118 & 0.3134 & 0.3086 & 0.2997 & 0.2955 \\  & CP & 0.9147 & 0.9400 & 0.9340 & 0.9380 & 0.9267 & 0.9507 & 0.9393 \\ \hline \multirow{3}{*}{} & (\(S_{6}\), \(T_{6}\)) & AL & 0.3243 & 0.3168 & 0.3209 & 0.3219 & 0.3162 & 0.3072 & 0.3024 \\  & CP & 0.9127 & 0.9480 & 0.9293 & 0.9453 & 0.9300 & 0.9640 & 0.9553 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._To better compare the effects of the different estimates, in Tables 2-5, we present the simulation results shown in Figure 7 for the point estimates and Figure 8 for the interval estimates. Note that the x-axis sequentially represents 12 different combinations of censoring schemes. In Figure 7, it can be seen that the Bayes estimates performed better in the majority of cases because they had lower MADs and MSEs. However, the Bayes estimate with non-informative priors, where F2 was chosen as the loss function, performed slightly worse. In the Bayes estimate, the informative priors had lower MADs and MSEs than the non-informative priors. In all cases, among the three loss functions, F3 performed the best, followed by F1, and F2 performed the worst. In addition, the performances of the different censoring schemes varied. For \(\eta_{1}\), the censoring scheme (\(S_{2}\), \(T_{5}\)) exhibited the smallest MADs and MSEs, and the censoring scheme (\(S_{3}\), \(T_{6}\)) was the second-best performer. For \(\eta_{2}\), the censoring scheme (\(S_{5}\), \(T_{5}\)) exhibited the smallest MADs and MSEs, and the censoring scheme (\(S_{6}\), \(T_{6}\)) was the second-best performer. Figure 5: Trace plots for \(\eta_{1}\) (**a**) with C.S (\(S_{2}\), \(T_{5}\)), (**b**) with C.S (\(S_{4}\), \(T_{1}\)). Figure 6: Trace plots for \(\eta_{2}\) (**a**) with C.S (\(S_{3}\), \(T_{3}\)), (**b**) with C.S (\(S_{4}\), \(T_{4}\)). average lengths, whereas the BCIs had higher coverage probabilities so they each have their own advantages. In addition, the informative priors outperformed the non-informative priors, as they exhibited both shorter average lengths and higher coverage probabilities. Furthermore, different censoring schemes also performed differently. For \(\eta_{1}\), in terms of average lengths, the censoring scheme that performed the best was (\(S_{2}\), \(T_{5}\)), whereas in terms of coverage probabilities, the censoring scheme that performed the best was (\(S_{4}\), \(T_{4}\)). For \(\eta_{2}\), in terms of average lengths, the censoring scheme that performed the best was (\(S_{5}\), \(T_{5}\)), whereas in terms of coverage probabilities, the censoring scheme that performed the best was (\(S_{2}\), \(T_{5}\)). ### Real Data Example

To illustrate the suitability of the proposed method, a real data set was used.