## 3 Statistical Analysis
### Daily Values
#### 3.2.3 Daily Radiation Indices
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & & & & \\ \hline
**Month** & **N** & **Mean** & **StDev** & **CV(\%)** & **Min** & **Q1** & **MedianQ3** & **Max** & **Mean** & **StDev** & **CV(\%)** & **Min** & **Q1** & **MedianQ3** & **Max** \\ \hline
1 & 31 & 0.434 & 0.226 & 52.03 & 0.029 & 0.276 & 0.423 & 0.657 & 0.784 & 0.252 & 0.172 & 68.26 & 0.011 & 0.109 & 0.202 & 0.406 & 0.561 \\
2 & 28 & 0.59 & 0.208 & 35.20 & 0.003 & 0.455 & 0.657 & 0.742 & 0.849 & 0.39 & 0.171 & 43.86 & 0.001 & 0.241 & 0.437 & 0.520 & 0.627 \\
3 & 31 & 0.495 & 0.208 & 42.04 & 0.038 & 0.383 & 0.543 & 0.649 & 0.818 & 0.324 & 0.172 & 53.28 & 0.010 & 0.200 & 0.357 & 0.452 & 0.622 \\
4 & 30 & 0.548 & 0.213 & 38.89 & 0.052 & 0.423 & 0.528 & 0.75 & 0.846 & 0.367 & 0.181 & 49.17 & 0.023 & 0.239 & 0.371 & 0.542 & 0.639 \\
5 & 31 & 0.694 & 0.098 & 14.10 & 0.428 & 0.615 & 0.709 & 0.78 & 0.802 & 0.485 & 0.088 & 18.23 & 0.251 & 0.416 & 0.502 & 0.566 & 0.586 \\
6 & 30 & 0.728 & 0.093 & 12.81 & 0.415 & 0.694 & 0.737 & 0.794 & 0.856 & 0.501 & 0.099 & 19.68 & 0.226 & 0.451 & 0.521 & 0.568 & 0.628 \\
7 & 31 & 0.781 & 0.04 & 5.08 & 0.672 & 0.761 & 0.793 & 0.808 & 0.846 & 0.541 & 0.039 & 7.30 & 0.451 & 0.510 & 0.549 & 0.568 & 0.604 \\
8 & 31 & 0.776 & 0.052 & 6.75 & 0.657 & 0.741 & 0.787 & 0.818 & 0.855 & 0.535 & 0.054 & 10.17 & 0.404 & 0.496 & 0.547 & 0.578 & 0.627 \\
9 & 30 & 0.69 & 0.063 & 9.06 & 0.464 & 0.677 & 0.700 & 0.724 & 0.777 & 0.458 & 0.054 & 11.89 & 0.263 & 0.451 & 0.463 & 0.490 & 0.526 \\
10 & 31 & 0.674 & 0.125 & 18.49 & 0.313 & 0.601 & 0.696 & 0.779 & 0.837 & 0.433 & 0.108 & 24.88 & 0.159 & 0.365 & 0.452 & 0.522 & 0.582 \\
11 & 30 & 0.448 & 0.231 & 51.62 & 0.004 & 0.282 & 0.559 & 0.628 & 0.770 & 0.251 & 0.159 & 63.10 & 0.001 & 0.106 & 0.293 & 0.382 & 0.517 \\
12 & 31 & 0.507 & 0.246 & 48.48 & 0.001 & 0.372 & 0.594 & 0.713 & 0.794 & 0.297 & 0.173 & 58.23 & 0.000 & 0.176 & 0.331 & 0.476 & 0.537 \\ \hline
**Year** & 365 & 0.614 & 0.205 & 33.33 & 0.001 & 0.523 & 0.691 & 0.761 & 0.856 & 0.403 & 0.165 & 41.02 & 0.000 & 0.309 & 0.454 & 0.527 & 0.639 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Descriptive statistics of the daily fraction of direct to global radiation (\(K_{B}\)) and daily direct transmittance (\(K_{BT}\)). Figure 28: (**a**) relation between \(K_{D}\) and \(K_{T}\); and (**b**) relation between \(K_{D}\) and \(\sigma\). Figure 29 shows the relationships between \(K_{B}\) and \(K_{T}\), \(K_{B}\) and \(\sigma\), as well as between \(K_{B}\) and \(K_{D}\). Similar equations were developed for \(K_{BT}\) and other radiation indices. The cubic equations of the above relationships have the following form:  
\[K_{B}=0.160-1.656*K_{T}+6.150*K_{T}^{2}-3.704*K_{T}^{3}R^{2}=0.837 \tag{46}\]  
\[K_{B}=0.00004+1.310*\sigma-1.187*\sigma^{2}+0.714*\sigma^{3}R^{2}=0.880 \tag{47}\]  
\[K_{B}=0.923-1.071*K_{D}+0.252*K_{D}^{2}-0.127*K_{D}^{3}R^{2}=0.978 \tag{48}\]  
\[K_{BT}=0.117-1.142*K_{T}+3.104*K_{T}^{2}-0.930*K_{T}^{3}R^{2}=0.911 \tag{49}\]  
\[K_{BT}=0.0048+0.428*\sigma+0.0017*\sigma^{2}+0.175*\sigma^{3}R^{2}=0.894 \tag{50}\]  
\[K_{BT}=-0.0023+0.277*K_{B}+0.714*K_{B}^{2}-0.214*K_{B}^{3}R^{2}=0.979 \tag{51}\]