## 3 Results and Discussion  
### Obtained Results  
Table 6 shows the DNI PDFs for each month and for each city. The cities have been sorted according to their own climatic zone shown in Table 2.  
In this case, the predominant PDF is the extreme value for all zones except for the cities in zone 5, where the logarithmic PDF prevails. The gamma PDF is the least predominant among all the distributions, with an occurrence that is not significant at zone 1. In zone 4, there are no occasions where the PDF is bimodal, while for the rest of the zones, there are few instances when the bimodality is present and a kernel PDF is assigned. \begin{table}
\begin{tabular}{c c c} \hline
**Distribution Name** & **PDF [f(x)]** & **CDF [F(x)]** \\ \hline Beta & \(\frac{x^{-1}(1-x)^{\beta-1}}{B(p,q)}\) & \(\frac{\int_{0}^{x}\left(p^{-1}(1-x)^{\beta-1}dt\right)}{B(p,q)}\) \\ \hline Chi-square & \(\frac{\exp(-x/2)x^{\frac{\beta}{2}-1}}{2^{\alpha/2}\Gamma\left(1/2\right)}\) & \(\frac{\gamma\left(\frac{\beta}{2},\frac{\beta}{2}\right)}{\Gamma\left(\frac{ \beta}{2}\right)}\) \\ \hline Exponential & \(\frac{1}{\beta}\exp\left(-\frac{x-\mu}{\beta}\right)\) & \(1-\exp(-x/\beta)\) \\ \hline Extreme value & \(\frac{1}{\beta}\exp\left(\frac{x-\mu}{\beta}\right)\exp\left(-\exp\left( \frac{x-\mu}{\beta}\right)\right)\) & \(1-e^{-e^{x}}\) \\ \hline Gamma & \(\frac{x^{(-1)}\exp\left(-x\right)}{\Gamma\left(\gamma\right)}\) & \(\frac{\int_{0}^{x}\left(p^{-1}\exp\left(-t\right)dt\right)}{\Gamma\left( \gamma\right)}\) \\ \hline Lognormal & \(\frac{\exp\left(-\left(\frac{\left(\mu\left(\frac{x-\mu}{\alpha}\right) \right)^{2}}{2\alpha^{2}}\right)\right)}{\left(x-\beta\right)\
u\sqrt{2\pi}}\) & \(\Phi\left(\frac{\ln\left(x\right)}{\sigma}\right)\) \\ \hline Normal & \(\frac{\exp\left(-\frac{x-\mu^{2}}{2\alpha^{2}}\right)}{\sigma\sqrt{2\pi}}\) & \(\int_{-\infty}^{x}\frac{\exp\left(-x^{2}/2\right)}{\sqrt{2\pi}}\) \\ \hline Rayleigh & \(\frac{x}{\sigma^{2}}\exp\left(-\frac{x^{2}}{2\alpha^{2}}\right)\) & \(1-\exp\left(-\frac{x^{2}}{2\alpha^{2}}\right)\) \\ \hline T-distribution & \(\frac{1}{2}\left[\frac{1}{2}+\left(\frac{x}{\alpha}\right)^{-\frac{1}{2}} \right]\) & \(\frac{1}{2}\left[\frac{1}{2}+\left(\frac{x}{\alpha}\right)^{-\frac{1}{2}} \right]sgn(t)\) \\ \hline Weibull & \(\frac{\gamma}{4}\left(\frac{x-\mu}{\alpha}\right)^{\gamma-1}\exp\left(-\left( \frac{x-\mu}{\alpha}\right)^{\gamma}\right)\) & \(1-\exp(-(x^{\gamma}))\) \\ \hline \end{tabular}
\end{table} 
Table 5: Distributions considered with their respective PDF and CDF. Source: own elaboration based on [69; 70; 71]. The same information presented in Table 6 is depicted at Figure 9, in order to graphically show the percentage that a certain PDF appears in each of the zones. From Figure 9, it can be seen that certain PDFs appear more often in some zones, while in other zones, they do not appear, stating the great location-dependent radiation characterization. Figure 10 displays examples of the PDF fitting test results. The histograms of the data samples for the month of October in Nador, the month of December in Kenitra and the month of March in Tetouan are shown along with the characterization of the adjusted extreme value, normal and kernel PDFs, respectively. The results show a good performance of the test for PDF fitting.