## 2 Characterization of Wind-Solar Power Generation for Earth Regions
### The Renewable Resources
At the same time, ambient temperature finds its best distribution by normal distribution [43]. So, these three distributions were evaluated. After estimating the parameters of the distributions using the maximum likelihood method (MLE) via the fitdist function in MATLAB (MatLab R2023a), a comprehensive assessment of the fit and goodness of fit for each variable (solar irradiance, wind speed, and temperature) was conducted, as summarized in Table 2. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) for each fitted distribution were calculated to validate the choice of probability distributions. These criteria were used to compare the selected models (Beta, Weibull, and normal). The chosen models consistently demonstrated lower AIC and BIC values, confirming their suitability for representing the observed data, with the best fits being the beta distribution for solar irradiance, the Weibull distribution for wind speed, and the normal distribution for temperature. Figure 2: Summary of the main steps to be followed in applying the BEPU methodology. Once the PDFs are fitted to the historical data, the synthetic datasets are generated by randomly sampling from these distributions. A random parameter \(k_{i}\) is selected and applied consistently across all 52 weeks of the year from the fitted PDFs, multiplied by the maximum registered value for each week across the complete dataset from 2001 to 2023. Finally, a synthetic dataset that spans 8760 h, representing the availability of renewable sources, is obtained. This process can be repeated the desired number of times, such as the number of runs or assessments. As mentioned before, [PERSON]'s formula yields a number of 93. This artificial dataset accurately simulates the variability and probability of renewable energy sources. It preserves the statistical properties of historical data, including mean, variance, and distribution shape. By incorporating stochastic elements, the approach reflects the unpredictable nature of renewable energy generation, enabling a robust evaluation by simulating a wide range of potential scenarios. In Figure 3, the synthetic curves illustrate the natural intermittency and variability of renewable energy sources, particularly solar irradiance and wind speed, represented in blue. While a deterministic approach can assess renewable energy availability over a year--using registered values and/or historical data, depicted in red in Figure 3--incorporating multiple scenarios for wind speed, solar irradiance, and temperature enables a more comprehensive analysis. This probabilistic approach considers a wider range of possibilities, offering a complete understanding of the variability and uncertainty associated with renewable energy generation. \begin{table}
\begin{tabular}{c c c} \hline AIC values; & AIC values; & AIC values; \\ Beta: \(-11.8591\) & Beta: \(-32.3662\) & Beta: \(-134.8166\) \\ Weibull: 73.6683 & Weibull: \(-41.2643\) & Weibull: \(-158.4579\) \\ Normal: 73.7159 & Normal: \(-32.6231\) & Normal: \(-172.264\) \\ BIC values: & BIC values: & BIC values: \\ Beta: \(-6.0935\) & Beta: \(-26.6006\) & Beta: \(-129.0359\) \\ Weibull: 79.4339 & Weibull: \(-35.4987\) & Weibull: \(-152.6772\) \\ Normal: 79.4815 & Normal: \(-26.8575\) & Normal: \(-166.4833\) \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of the best-fit distributions for solar, wind, and temperature resources.