## 5 Estimation and Simulations
### Simulation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{n} & \multirow{2}{*}{**Est.**} & \multicolumn{4}{c}{**Set I: \(\delta\) = 0.5, \(\beta\) = 2.4, \(\alpha\) = 3.6**} & \multicolumn{4}{c}{**Set II: \(\delta\) = 3.2, \(\beta\) = 2.7, \(\alpha\) = 3.8**} \\ \cline{3-8}  & & **MLE** & **MSE** & **Bias** & **MLE** & **MSE** & **Bias** \\ \hline \multirow{4}{*}{600} & \(\delta\) & 0.733 & 0.883 & 0.233 & 3.185 & 1.644 & \(-\)0.015 \\ \cline{2-8}  & \(\hat{\beta}\) & 2.444 & 0.064 & 0.044 & 2.674 & 0.059 & \(-\)0.026 \\ \cline{2-8}  & \(\hat{\alpha}\) & 3.559 & 0.144 & \(-\)0.042 & 3.881 & 0.201 & 0.081 \\ \hline \multirow{4}{*}{700} & \(\delta\) & 0.719 & 0.804 & 0.219 & 3.221 & 1.529 & 0.021 \\ \cline{2-8}  & \(\hat{\beta}\) & 2.443 & 0.061 & 0.043 & 2.686 & 0.054 & \(-\)0.014 \\ \cline{2-8}  & \(\hat{\alpha}\) & 3.553 & 0.132 & \(-\)0.048 & 3.866 & 0.191 & 0.065 \\ \hline \multirow{4}{*}{800} & \(\delta\) & 0.679 & 0.678 & 0.179 & 3.124 & 1.415 & \(-\)0.076 \\ \cline{2-8}  & \(\hat{\beta}\) & 2.439 & 0.054 & 0.039 & 2.671 & 0.051 & \(-\)0.029 \\ \cline{2-8}  & \(\hat{\alpha}\) & 3.569 & 0.118 & \(-\)0.030 & 3.892 & 0.172 & 0.052 \\ \hline \multirow{4}{*}{900} & \(\delta\) & 0.712 & 0.669 & 0.162 & 3.222 & 1.211 & 0.022 \\ \cline{2-8}  & \(\hat{\beta}\) & 2.448 & 0.051 & 0.037 & 2.690 & 0.043 & \(-\)0.009 \\ \cline{2-8}  & \(\hat{\alpha}\) & 3.555 & 0.116 & \(-\)0.045 & 3.850 & 0.137 & 0.040 \\ \hline \multirow{4}{*}{1000} & \(\delta\) & 0.675 & 0.600 & 0.145 & 3.208 & 1.052 & 0.008 \\ \cline{2-8}  & \(\hat{\beta}\) & 2.437 & 0.048 & 0.027 & 2.691 & 0.036 & \(-\)0.009 \\ \cline{2-8}  & \(\hat{\alpha}\) & 3.568 & 0.106 & \(-\)0.032 & 3.849 & 0.118 & 0.039 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{n} & \multirow{2}{*}{**Est.**} & \multicolumn{4}{c}{**Set III: \(\delta\) = 1.2, \(\beta\) = 3.3, \(\alpha\) = 4.5**} & \multicolumn{4}{c}{**Set IV: \(\delta\) = 1.5, \(\beta\) = 3.9, \(\alpha\) = 4.6**} \\ \cline{3-8}  & & **MLE** & **MSE** & **Bias** & **MLE** & **MSE** & **Bias** \\ \hline \multirow{4}{*}{25} & \(\delta\) & 1.941 & 4.911 & 0.994 & 2.397 & 4.383 & 0.969 \\ \cline{2-8}  & \(\hat{\beta}\) & 3.467 & 0.757 & 0.356 & 4.136 & 0.579 & 0.236 \\ \cline{2-8}  & \(\hat{\alpha}\) & 4.386 & 0.522 & \(-\)0.105 & 4.508 & 0.453 & \(-\)0.092 \\ \hline \multirow{4}{*}{50} & \(\delta\) & 1.880 & 4.354 & 0.843 & 2.404 & 4.113 & 0.903 \\ \cline{2-8}  & \(\hat{\beta}\) & 3.416 & 0.439 & 0.236 & 4.079 & 0.398 & 0.179 \\ \cline{2-8}  & \(\hat{\alpha}\) & 4.390 & 0.490 & \(-\)0.075 & 4.426 & 0.493 & \(-\)0.174 \\ \hline \multirow{4}{*}{75} & \(\delta\) & 1.850 & 3.834 & 0.741 & 2.206 & 3.476 & 0.736 \\ \cline{2-8}  & \(\hat{\beta}\) & 3.414 & 0.304 & 0.167 & 4.047 & 0.319 & 0.147 \\ \cline{2-8}  & \(\hat{\alpha}\) & 4.394 & 0.486 & \(-\)0.114 & 4.477 & 0.424 & \(-\)0.123 \\ \hline \multirow{4}{*}{100} & \(\delta\) & 1.846 & 3.539 & 0.680 & 2.224 & 3.408 & 0.723 \\ \cline{2-8}  & \(\hat{\beta}\) & 3.417 & 0.234 & 0.116 & 4.028 & 0.269 & 0.128 \\ \cline{2-8}  & \(\hat{\alpha}\) & 4.386 & 0.465 & \(-\)0.109 & 4.453 & 0.417 & \(-\)0.147 \\ \hline \multirow{4}{*}{200} & \(\delta\) & 1.577 & 2.338 & 0.377 & 1.971 & 2.353 & 0.471 \\ \cline{2-8}  & \(\hat{\beta}\) & 3.361 & 0.136 & 0.061 & 3.966 & 0.149 & 0.066 \\ \cline{2-8}  & \(\hat{\alpha}\) & 4.477 & 0.358 & \(-\)0.023 & 4.522 & 0.313 & \(-\)0.078 \\ \hline \multirow{4}{*}{300} & \(\delta\) & 1.613 & 2.059 & 0.329 & 1.908 & 1.849 & 0.374 \\ \cline{2-8}  & \(\hat{\beta}\) & 3.359 & 0.112 & 0.044 & 3.971 & 0.114 & 0.045 \\ \cline{2-8}  & \(\hat{\alpha}\) & 4.438 & 0.329 & \(-\)0.041 & 4.527 & 0.267 & \(-\)0.071 \\ \hline \end{tabular}
\end{table} 
Table 3: SRs of the NGLog–Weib distribution for Set III and Set IV. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{n} & \multirow{2}{*}{**Est.