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烟雨山河 [不良人|尤川](11)
作者:紫微客 阅读记录
$\hat{\mu}$ & 2.2727 & 2.6162 & 2.9056 & 2.9494 \\
$\hat{\sigma}$ & 1.6357 & 1.8062 & 1.9616 & 1.9775 \\
$\hat{\beta}$ & 2.4406 & 1.6247 & 1.1405 & 1.0732 \\
RMSE($\hat{\mu}$) & 1.1067 & 0.6524 & 0.2891 & 0.2104 \\
RMSE($\hat{\sigma}$) & 0.9879 & 0.7912 & 0.4399 & 0.3088 \\
RMSE($\hat{\beta}$) & 3.3107 & 1.1244 & 0.3810 & 0.2601 \\
\hline
\end{tabular}
\end{table}
\begin{table}[!htbp]
\caption{Moment Estimation and RMSE for $\mu$=3, $\sigma$=3, $\beta$=1}
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
$n$ & 50 & 100 & 500 & 1000 \\
\hline
$\hat{\mu}$ & 1.9091 & 2.4243 & 2.8584 & 2.924 \\
$\hat{\sigma}$ & 2.4536 & 2.7092 & 2.9424 & 2.9662 \\
$\hat{\beta}$ & 2.4406 & 1.6247 & 1.1405 & 1.0732 \\
RMSE($\hat{\mu}$) & 1.6601 & 0.9786 & 0.4337 & 0.3156 \\
RMSE($\hat{\sigma}$) & 1.4818 & 1.1868 & 0.6599 & 0.4632 \\
RMSE($\hat{\beta}$) & 3.3107 & 1.1244 & 0.3810 & 0.2601 \\
\hline
\end{tabular}
\end{table}
\begin{table}[!htbp]
\caption{Moment Estimation and RMSE for $\mu$=2, $\sigma$=1, $\beta$=1}
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
$n$ & 50 & 100 & 500 & 1000 \\
\hline
$\hat{\mu}$ & 1.6429 & 1.7982 & 1.9539 & 1.976 \\
$\hat{\sigma}$ & 0.8136 & 0.8876 & 0.9759 & 0.9885 \\
$\hat{\beta}$ & 2.3482 & 1.6643 & 1.1393 & 1.0722 \\
RMSE($\hat{\mu}$) & 0.524 & 0.3342 & 0.1411 & 0.1025 \\
RMSE($\hat{\sigma}$) & 0.4584 & 0.3783 & 0.2059 & 0.1498 \\
RMSE($\hat{\beta}$) & 2.5026 & 1.193 & 0.3803 & 0.256 \\
\hline
\end{tabular}
\end{table}
\begin{table}[!htbp]
\caption{Moment Estimation and RMSE for $\mu$=1, $\sigma$=1, $\beta$=1}
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
$n$ & 50 & 100 & 500 & 1000 \\
\hline
$\hat{\mu}$ & 0.6429 & 0.7982 & 0.9539 & 0.976 \\
$\hat{\sigma}$ & 0.8136 & 0.8876 & 0.9759 & 0.9885 \\
$\hat{\beta}$ & 2.3482 & 1.6643 & 1.1393 & 1.0722 \\
RMSE($\hat{\mu}$) & 0.524 & 0.3342 & 0.1411 & 0.1025 \\
RMSE($\hat{\sigma}$) & 0.4584 & 0.3783 & 0.2059 & 0.1498 \\
RMSE($\hat{\beta}$) & 2.5026 & 1.193 & 0.3803 & 0.256 \\
\hline
\end{tabular}
\end{table}
\begin{table}[!htbp]
\caption{MLE and RMSE for $\mu=3, \sigma=1, \beta=1$}
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
$n$ & 50 & 100 & 500 & 1000 \\
\hline
$\hat{\mu}$ & 2.9971 & 3.0004 & 3.0001 & 3.0000 \\
$\hat{\sigma}$ & 1.0018 & 1.0363 & 1.0504 & 1.0640 \\
$\hat{\beta}$ & 1.0889 & 1.0549 & 1.0600 & 1.0694 \\
RMSE($\hat{\mu}$) & 0.0192 & 0.0063 & 0.0010 & 0.0005 \\
RMSE($\hat{\sigma}$) & 0.1344 & 0.0855 & 0.0851 & 0.0933 \\
RMSE($\hat{\beta}$) & 0.1740 & 0.0894 & 0.0852 & 0.0936 \\
\hline
\end{tabular}
\end{table}
\begin{table}[!htbp]
\caption{MLE and RMSE for $\mu=3, \sigma=1, \beta=2$}
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
$n$ & 50 & 100 & 500 & 1000 \\
\hline
$\hat{\mu}$ & 3.1030 & 3.0461 & 3.0008 & 2.9988 \\
$\hat{\sigma}$ & 1.0354 & 1.0108 & 1.0034 & 1.0022 \\
$\hat{\beta}$ & 1.8206 & 1.9197 & 1.9822 & 1.9888 \\
RMSE($\hat{\mu}$) & 0.1500 & 0.0868 & 0.0242 & 0.0145 \\
RMSE($\hat{\sigma}$) & 0.1342 & 0.0834 & 0.0468 & 0.0345 \\
RMSE($\hat{\beta}$) & 0.2594 & 0.1818 & 0.1066 & 0.0744 \\
\hline
\end{tabular}
\end{table}
\begin{table}[!htbp]
\caption{MLE and RMSE for $\mu=3, \sigma=1, \beta=3$}
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
$n$ & 50 & 100 & 500 & 1000 \\
\hline
$\hat{\mu}$ & 3.4092 & 3.2893 & 3.1199 & 3.0734 \\
$\hat{\sigma}$ & 1.4339 & 1.3088 & 1.1104 & 1.0622 \\