\ell(\mu, \sigma, \xi ; z)=-n \log \sigma-\left(1+\frac{1}{\xi}\right) \sum_{i=1}^{n} \log \left(1+\xi \frac{z_{i}-\mu}{\sigma}\right)-\sum_{i=1}^{n}\left(1+\xi \frac{z_{i}-\mu}{\sigma}\right)^{-1 / \xi}