## 4 Results and Discussion
### Comparative Study of Probability-Distribution-Function-Based WSP Models
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**RMSE**} \\ \hline
**Model** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **t = 7** & **Average** \\ \hline WEB & 4.42 & 3.007 & 3.92 & 3.9 & 2.6 & 1.75 & 2.07 & 3.10 \\ WEBS & 1.5 & 1.6 & 2.2 & 1.5 & 2.4 & 1.7 & 2.2 & 1.82 \\ WEBSEC & 0.17 & 0.7 & 1.2 & 1.3 & 0.4 & 0.7 & 0.4 & 0.70 \\ RYM & 4.42 & 3.007 & 3.92 & 3.9 & 2.6 & 1.75 & 2.07 & 3.10 \\ RYMS & 0.53 & 2.04 & 1.03 & 7.06 & 1.35 & 1.09 & 2.84 & 2.28 \\ RYMSEC & 0.36 & 1.66 & 1.97 & 0.23 & 0.606 & 1.64 & 0.77 & 1.03 \\ \hline \multicolumn{6}{c}{**MAPE**} \\ \hline
**Model** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **t = 7** & **Average** \\ WEB & 0.05 & 1.28 & 1.77 & 2.22 & 2.49 & 2.48 & 2.54 & 1.83 \\ WEBS & 0.94 & 3.03 & 5.56 & 0.2 & 0.1 & 2.47 & 2.9 & 2.17 \\ WEBSEC & 2.07 & 0.26 & 1.39 & 0.411 & 0.84 & 1.69 & 1.44 & 1.16 \\ RYM & 0.05 & 1.28 & 1.76 & 2.24 & 2.48 & 2.47 & 2.54 & 1.83 \\ RYMS & 0.91 & 1.63 & 0.29 & 4.29 & 8.11 & 2.8 & 0.6 & 2.66 \\ RYMSEC & 0.2 & 2.29 & 1.65 & 0.06 & 0.07 & 1.06 & 0.59 & 0.85 \\ \hline \multicolumn{6}{c}{**MAPE**} \\ \hline
**Model** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **t = 7** & **Average** \\ WEB & 0.05 & 1.28 & 1.77 & 2.22 & 2.49 & 2.48 & 2.54 & 1.83 \\ WEBS & 0.94 & 3.03 & 5.56 & 0.2 & 0.1 & 2.47 & 2.9 & 2.17 \\ WEBSEC & 2.07 & 0.26 & 1.39 & 0.411 & 0.84 & 1.69 & 1.44 & 1.16 \\ RYM & 0.05 & 1.28 & 1.76 & 2.24 &The results from Tables 2-5 imply that for all the regions, the error-corrected simulated probability-distribution-based model is more accurate than the general probability-distribution-based model and the simulated probability-distribution-based model. In the South Plains region of Texas, the error-corrected model can improve the general Weibull-based model to achieve a MAPE as low as 15%, RMSE as low as 1.5, and MAE as low as 1.5. In the Southern Texas Offshore region, the error-corrected model can improve the general Weibull-based model to achieve a MAPE as low as 17%, RMSE as low as 1.49, and MAE as low as 1.5. In the West Virginia Hills region, the error-corrected model can improve the general Rayleigh-based model to achieve a MAPE as low as 9%, RMSE as low as 0.85, and MAE as low as 0.85. Similarly, in the Arizona Hills region, the error-corrected model can improve the general Rayleigh-based model to achieve a MAPE as low as 30%, RMSE as low as 1.03, and MAE as low as 1.03. The results show that for the South Plains Texas region and Southern Offshore Texas region, the Weibull-based model gives better results. In contrast, for the West Virginia Hills and Arizona Hills region, the Rayleigh-based model gives a better result. Therefore, it can be concluded that the wind distribution of the first two regions, i.e., South Plains TX and Southern Offshore region, can be more accurately described using the Weibull probability density function than the Rayleigh probability distribution function. In contrast, for the last two regions, i.e., West Virginia Hills and Arizona Hills region, wind distribution can be accurately described using the Rayleigh probability distribution function. Hence, the wind speed prediction model based on the probability distribution function also depends on how accurately that model describes the region's wind speed.