# Topp-Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data
## 5 Simulation
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**First Combination**} & \multicolumn{3}{c}{**ML**} & \multicolumn{3}{c}{**MPS**} & \multicolumn{3}{c}{**Bayesian**} \\ \hline \(\lambda\) & **n** & & **RB** & **MSEr** & **LACI** & **RB** & **MSEr** & **LACI** & **RB** & **MSEr** & **LCCI** \\ \hline \multirow{6}{*}{0.6} & \multirow{6}{*}{30} & \(\alpha\) & 0.5590 & 0.2732 & 1.7321 & 0.1053 & 0.1775 & 1.6392 & 0.3274 & 0.1398 & 1.1151 \\  & & \(\beta\) & 0.1203 & 0.7663 & 3.4215 & \(-\)0.0980 & 0.2442 & 1.9244 & 0.0753 & 0.1159 & 1.2911 \\  & & \(\theta\) & 0.7338 & 6.2504 & 7.9380 & 0.1212 & 0.9189 & 3.6374 & 0.2537 & 1.6512 & 4.3075 \\  & & \(\lambda\) & 0.3275 & 0.1739 & 1.4427 & 0.0594 & 0.0747 & 1.0626 & 0.2622 & 0.0982 & 0.7599 \\ \cline{2-11}  & & \(\alpha\) & 0.5217 & 0.1971 & 1.4090 & 0.1017 & 0.1266 & 1.3764 & 0.2279 & 0.0912 & 0.9666 \\  & & \(\beta\) & \(-\)0.1170 & 0.3119 & 2.1839 & \(-\)0.0919 & 0.1483 & 1.4949 & 0.0483 & 0.0626 & 1.0571 \\  & & \(\theta\) & 0.5274 & 3.7303 & 6.3455 & 0.0638 & 0.5940 & 2.9812 & 0.1550 & 0.9555 & 3.2180 \\  & & \(\lambda\) & 0.2829 & 0.1035 & 1.0716 & 0.0486 & 0.0487 & 0.8417 & 0.2037 & 0.0634 & 0.5619 \\ \cline{2-11}  & & \(\alpha\) & 0.5051 & 0.1140 & 0.8791 & 0.0923 & 0.0598 & 0.8492 & 0.1554 & 0.0322 & 0.6493 \\  & & \(\beta\) & \(-\)0.0971 & 0.0702 & 0.8203 & \(-\)0.0916 & 0.0474 & 0.7690 & \(-\)0.0266 & 0.0209 & 0.5862 \\  & & \(\theta\) & 0.3542 & 1.2459 & 3.3828 & 0.0583 & 0.2675 & 1.9763 & 0.0823 & 0.2894 & 1.8616 \\  & & \(\lambda\) & 0.1991 & 0.0232 & 0.3701 & 0.0411 & 0.0116 & 0.3331 & 0.1266 & 0.0214 & 0.2629 \\ \hline \multirow{6}{*}{30} & \multirow{6}{*}{30} & \(\alpha\) & \(-\)0.3465 & 0.3909 & 2.3600 & \(-\)0.1871 & 0.1166 & 1.2902 & 0.2722 & 0.1569 & 1.3391 \\  & & \(\beta\) & 0.4070 & 0.4790 & 2.5440 & 0.1221 & 0.1776 & 1.6305 & \(-\)0.0107 & 0.0946 & 1.1588 \\  & & \(\theta\) & 0.2691 & 2.1451 & 5.3509 & 0.0877 & 0.8827 & 3.6258 & 0.1040 & 2.0391 & 4.1324 \\  & & \(\lambda\) & 0.1716 & 0.7055 & 2.6072 & 0.0834 & 0.4865 & 2.7104 & 0.6100 & 0.6178 & 2.1479 \\ \cline{2-11}  & & \(\alpha\) & \(-\)0.3088 & 0.2280 & 1.7118 & \(-\)0.1726 & 0.0775 & 0.9703 & 0.2377 & 0.1492 & 1.3171 \\  & & \(\beta\) & 0.3988 & 0.3053 & 1.8913 & 0.1206 & 0.1237 & 1.2377 & \(-\)0.0105 & 0.0937 & 1.0953 \\  & & \(\theta\) & 0.0229 & 0.7876 & 3.4767 & \(-\)0.0533 & 0.3438 & 2.2618 & 0.0253 & 0.6873 & 4.1040 \\  & & \(\lambda\) & 0.1708 & 0.4688 & 1.7817 & 0.0789 & 0.2192 & 1.5084 & 0.1632 & 0.3885 & 1.2829 \\ \cline{2-11}  & & \(\alpha\) & \(-\)0.2340 & 0.1448 & 1.3348 & \(-\)0.1528 & 0.0608 & 0.7914 & 0.2133 & 0.1394 & 1.3147 \\  & & \(\beta\) & 0.3963 & 0.1912 & 1.4394 & 0.1130 & 0.0946 & 0.9834 & \(-\)0.0105 & 0.0926 & 1.0638 \\  & & \(\theta\) & \(-\)0.0215 & 0.3284 & 2.2118 & \(-\)0.0495 & 0.1860 & 1.5192 & 0.0248 & 0.2511 & 2.1610 \\  & & \(\lambda\) & 0.1422 & 0.2973 & 1.3326 & 0.0719 & 0.1340 & 0.9922 & 0.1157 & 0.2876 & 1.1344 \\ \hline \end{tabular}
\end{table} 
Table 4: ML, MPS, Bayes estimation methods: RB, MSE, LACI and LCCI at first combination. Figure 4: Heatmaps of MSEr for parameters under different estimation methods.