## 5 Simulation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & **Gamma Prior** & **Quasi-Density Prior (\(m=0.5\))** & **Quasi-Density Prior (\(m=1\))** \\ \cline{3-8} \(n\) & \(t\) & \(R(t)\) & \(\hat{R}_{SEL}(t)\) & \(\hat{R}_{SEL}(t)\) & \(\hat{R}_{SEL}(t)\) & \(\hat{R}_{SEL}(t)\) \\ \hline  & 0.5 & 0.89442719 & 0.87140372 & 0.87026485 & 0.87612504 & 0.87922039 & 0.88161397 & 0.88458424 \\  & 1.0 & 0.70710678 & 0.66263949 & 0.67697393 & 0.68941180 \\  & 1.5 & 0.55470020 & 0.50540811 & 0.524308878 & 0.54016925 \\  & & (0.00097336) & (0.01977326) & (0.01509506) \\
10 & 2.0 & 0.44721360 & 0.40146574 & 0.42221176 & 0.43920878 \\  & & (0.00140592) & (0.02012684) & (0.01540660) \\  & 3.0 & 0.31622777 & 0.28199122 & 0.30315901 & 0.31998567 \\  & & (0.001689686) & (0.015833323) & (0.01214109) \\  & 4.0 & 0.24253563 & 0.21790019 & 0.23821225 & 0.25407353 \\  & & (0.00200895) & (0.01167751) & (0.00894554) \\  & & 0.00112645 & 0.01398495 & 0.01068517 \\  & 0.5 & 0.89442719 & 0.88797084 & 0.89003636 & 0.89173440 \\  & & (0.00016410) & (0.00349479) & (0.003029019) \\  & 1.0 & 0.70710678 & 0.69349769 & 0.69843747 & 0.70253490 \\  & & (0.00089375) & (0.01778125) & (0.01640886) \\  & 1.5 & 0.55470020 & 0.53946625 & 0.54590884 & 0.55130046 \\
30 & 2.0 & 0.44721360 & (0.0014 \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & & \multicolumn{2}{c}{**Gamma Prior**} & \multicolumn{2}{c}{**Quasi-Density Prior (\(m=0.5\))**} & \multicolumn{2}{c}{**Quasi-Density Prior (\(m=1\))**} \\ \cline{3-10} \(n\) & \(t\) & \(R(t)\) & \(R(t)\) & \(R_{QEL}(t)\) & \(R_{QEL}(t)\) & \(R_{QEL}(t)\) & \(R_{QEL}(t)\) & \(R_{QEL}(t)\) \\ \hline  & 0.5 & 0.89442719 & 0.87177507 & 0.87174935 & 0.87652719 & 0.88071209 & 0.88457977 & 0.88601588 \\  & & & (0.00103479) & (0.00103636) & (0.00089526) & (0.00226954) & (0.00024260) & (0.00167339) \\  & 1.0 & 0.70710678 & 0.65688460 & 0.65635514 & 0.66872637 & 0.67756936 & 0.68713813 & 0.68996808 \\  & & & (0.00578756) & (0.00586942) & (0.00578980) & (0.01242161) & (0.00151643) & (0.00932654) \\  & 1.5 & 0.55470020 & 0.49419175 & 0.49239579 & 0.51012950 & 0.51968885 & 0.53318154 & 0.53555167 \\  & & & (0.00954473) & (0.00902351) & (0.01108011) & (0.02033247) & (0.00279849) & (0.01558087) \\
10 & 2.0 & 0.44721360 & 0.38620110 & 0.38287256 & 0.40383561 & 0.41200643 & 0.42802265 & 0.4289254 \\  & 3.0 & 0.01829660 & (0.01161192) & (0.01433154) & (0.02315430) & (0.00350127) & (0.0180180230) \\  & 3.0 & 0.31622777 & 0.26245327 & 0.25649611 & 0.28039597 & 0.28457583 & 0.30337980 & 0.30095278 \\  & & & (0.00999489) & (0.01142056) & (0.01630101) & (0.02182261) & (0.00376708) & (0.01763912) \\  & 4.0 & 0.24253563 & 0.19679374 & 0.18908714 & 0.21379666 & 0.21461880 & 0.23470551 & 0.22960587 \\  & & & (0.00824171) & (0.00997375) & (0.01575132) & (0.01843233) & (0.00348225) & (0.01531750) \\ MISE & & & 0.00757222 & 0.00830592 & 0.01069151 & 0.01640548 & 0.00255135 & 0.01293829 \\ \hline \end{tabular}
\end{table} 
Table 4: The Bayesian estimates under the QEL function and \(\alpha=2\) and \(\beta=0.5\), with their MSEs shown in brackets. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & & \multicolumn{2}{c}{**Gamma Prior**} & \multicolumn{2}{c}{**Quasi-Density Prior (\(m=0.5\))**} & \multicolumn{2}{c}{**Quasi-Density Prior (\(m=1\))**} \\ \cline{3-10} \(n\) & \(t\) & \(R(t)\) & \(R(t)\) & \(R_{QEL}(t)\) & \(R_{QEL}(t)\) & \(R_{QEL}(t)\) & \(R_{QEL}(t)\) & \(R_{QEL}(t)\) \\ \hline  & 3.0 & 0.31622777 & 0.25327911 & 0.22265381 & 0.27034802 & 0.24807910 & 0.28649631 & 0.26363066 \\  & 4.0 & 0.24253563 & 0.18698475 & 0.15444508 & 0.20294492 & 0.17647134 & 0.21762876 & 0.19003693 \\  & & & (0.01032390) & (0.01903242) & (0.01365523) & (0.03073922) & (0.01817177) & (0.02759084) \\ MISE & & & 0.00884199 & 0.01387377 & 0.00976299 & 0.02529274 & 0.01267967 & 0.02124077 \\  & 0.5 & 0.89442719 & 0.8876716 & 0.88