## 6 Simulation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \((\mathbf{n},\mathbf{m})\) & **Scheme** & \(\mathbf{p}\) & **PPs** & **PPs** \\ \hline \multirow{3}{*}{(45,30)} & \multirow{3}{*}{\(V_{1}\)} & 3 & 0.5487 & \((-1.4254,0.8255)\) \\  & & 7 & 1.4205 & \((-0.5458,2.9171)\) \\  & & 10 & 2.2475 & \((2.2112,2.6621)\) \\ \hline \multirow{3}{*}{(45,30)} & \multirow{3}{*}{\(V_{2}\)} & 3 & 0.5972 & \((-0.4371,2.6985)\) \\  & & 7 & 1.3989 & \((0.3967,3.1084)\) \\  & & 10 & 2.2601 & \((1.2117,3.1575)\) \\ \hline \multirow{3}{*}{(42,25)} & \multirow{3}{*}{\(V_{3}\)} & 3 & 0.6666 & \((-0.5030,0.8077)\) \\  & & 7 & 1.5834 & \((1.3446,2.0823)\) \\  & & 10 & 2.2819 & \((1.3769,2.7395)\) \\ \hline \multirow{3}{*}{(42,25)} & \multirow{3}{*}{\(V_{4}\)} & 3 & 0.4173 & \((-0.8854,1.3781)\) \\  & & 7 & 1.3503 & \((1.2718,2.4466)\) \\  & & 10 & 2.3137 & \((1.1238,2.3024)\) \\ \hline \multirow{3}{*}{(35,20)} & \multirow{3}{*}{\(V_{5}\)} & 3 & 0.4638 & \((-0.8409,6.6454)\) \\  & & 7 & 1.3803 & \((1.0270,3.0104)\) \\  & & 10 & 2.5017 & \((2.0111,3.0394)\) \\ \hline \multirow{3}{*}{(35,20)} & \multirow{3}{*}{\(V_{6}\)} & 3 & 0.5590 & \((-0.6948,2.1087)\) \\  & & 7 & 1.3765 & \((1.3211,2.6564)\) \\  & & 10 & 2.5290 & \((2.4362,3.0446)\) \\ \hline \multirow{3}{*}{(25,15)} & \multirow{3}{*}{\(V_{7}\)} & 3 & 0.8869 & \((0.4629,0.9623)\) \\  & & 7 & 1.2162 & \((-0.9793,1.8674)\) \\  & & 10 & 2.3599 & \((2.1350,4.0407)\) \\ \hline \multirow{3}{*}{(25,15)} & \multirow{3}{*}{\(V_{8}\)} & 3 & 0.7029 & \((0.5576,2.0648)\) \\  & & 7 & 1.4934 & \((1.3333,0.3181)\) \\  & & 10 & 2.4397 & \((2.0893,3.0897)\) \\ \hline \multirow{3}{*}{(18,11)} & \multirow{3}{*}{\(V_{9}\)} & 3 & 0.5261 & \((0.3264,1.1449)\) \\  & & 7 & 1.4039 & \((0.8403,3.1833)\) \\  & & 10 & 2.2299 & \((2.2221,2.8448)\) \\ \hline \multirow{3}{*}{(18,11)} & \multirow{3}{*}{\(V_{10}\)} & 3 & 0.4196 & \((-0.6409,1.5666)\) \\  & & 7 & 1.4171 & \((1.0248,2.8736)\) \\ \cline{1-1}  & & 10 & 2.4701 & \((1.1667,2.5096)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Point Predictions (PPs) and 95% Prediction Intervals (PIs). The predictions are generated based on the values of \(y_{3}\), \(y_{7}\), and \(y_{10}\) (collectively referred to as \(y_{p}\)), utilizing a future dataset of size \(K=10\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\((\mathbf{n},\mathbf{m})\)} & **Scheme** & \multicolumn{2}{c}{**ACIs**} & \multicolumn{2}{c}{**HPD**} \\ \cline{3-6}  & & **AL** & **CP** & **AL** & **CP** \\ \hline \multirow{2}{*}{(45,30)} & \multirow{2}{*}{\(V_{1}\)} & 2.1636 & 0.7682 & 1.0595 & 0.8872 \\  & & 1.1655 & 0.7656 & 1.0395 & 0.9367 \\ \hline \multirow{2}{*}{(45,30)} & \multirow{2}{*}{\(V_{2}\)} & 2.3394 & 0.7849 & 0.0515 & 0.8834 \\  & & 1.7577 & 0.8874 & 1.0566 & 0.6837 \\ \hline \multirow{2}{*}{(42,25)} & \multirow{2}{*}{\(V_{3}\)} & 2.0246 & 0.9442 & 0.8070 & 0.7878 \\  & & 2.4179 & 0.7250 & 0.7243 & 0.9276 \\ \hline \multirow{2}{*}{(42,25)} & \multirow{2}{*}{\(V_{4}\)} & 1.6523 & 0.7135 & 0.9373 & 0.8765 \\  & & 2.2842 & 0.9160 & 0.5214 & 1.0472 \\ \hline \multirow{2}{*}{(35,20)} & \multirow{2}{*}{\(V_{5}\)} & 2.5520 & 0.7181 & 0.5298 & 0.8027 \\  & & 1.9482 & 0.7973 & 0.5524 & 0.9058 \\ \hline \multirow{2}{*}{(35,20)} & \multirow{2}{*}{\(V_{6}\)} & 1.8121 & 0.7410 & 0.9959 & 0.8625 \\  & & 1.7446 & 0.7843 & 0.7257 & 0.8592 \\ \hline \multirow{2}{*}{(25,15)} & \multirow{2}{*}{\(V_{7}\)} & 1.9155 & 0.7293 & 0.0014 & 0.7849 \\  & & 2.1602 & 0.7468 & 0.6998 & 0.9901 \\ \hline \multirow{2}{*}{(25,15)} & \multirow{2}{*}{\(V_{8}\)} & 1.8895 & 0.7697 & 0.6682 & 0.7958 \\  & & 1.7537 & 0.8029 & 0.8605 & 0.4644 \\ \hline \multirow{2}{*}{(18,11)} & \multirow{2}{*}{\(V_{9}\)} & 2.5341 & 0.8386 & 0.6161 & 0.8216 \\  & & 2.0619 & 0.7564 & 0.6915 & 0.7681 \\ \hline \multirow{2}{*}{(18,11)} & \multirow{2}{*}{\(V_{10}\)} & 2.1427 & 0.8070 & 0.7953 & 0.7851 \\  & & 1.9152 & 0.8186 & 1.2948 & 0.7192 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: 95% Interval estimations for \(\alpha\) and \(\lambda\).