*Principal Component Analysis and Artificial Intelligence Approaches for Solar… DOI: http://dx.doi.org/10.5772/intechopen.102925*


#### **Table 1.**

*Solar irradiation data.*


#### **Table 2.**

*Meteorological data.*


#### **Table 3.** *Supplemental data.*

variables to make them more normal is common when dealing with such data. The Box-Cox and Yeo-Johnson transformations (YJT) are two well-known methods for this. Yeo and Johnson (2000) improved the Box-Cox transformation to create a oneparameter family that can transform both positive and negative variables [10]. YJT is defined by Eq. (1):

$$\mathcal{Y}^{(\lambda)} = \begin{cases} \frac{(\mathbf{y}+\mathbf{1})^{\lambda}-\mathbf{1}}{\lambda} & \lambda \neq \mathbf{0} \text{ and } \mathbf{y} \ge \mathbf{0} \\\\ \ln\left(\mathbf{y}+\mathbf{1}\right) & \lambda = \mathbf{0} \text{ and } \mathbf{y} \ge \mathbf{0} \\\\ \frac{-\left(\left(-\mathbf{y}+\mathbf{1}\right)^{2-\lambda}-\mathbf{1}\right)}{2-\lambda} & \lambda \neq \mathbf{2} \text{ and } \mathbf{y} < \mathbf{0} \\\\ \ln\left(-\mathbf{y}+\mathbf{1}\right) & \lambda = \mathbf{2} \text{ and } \mathbf{y} < \mathbf{0} \end{cases} \tag{1}$$

This transformation is ideal for correcting left and right skew when *λ >* 1 and *λ <* 1 respectively, whereas when *λ* ¼ 1, the linear connection is established.
