Report.tex

Fitting our data to the model initially provided \textit{maximum likelihood\footnote{The likelihood for the data given the model is
\begin{equation}
    -m\log(\sigma) - (1 + \frac{1}{\xi})\sum_{i}\left[\log{\left(1 + \xi\left(\frac{z_{i} - \mu}{\sigma}\right)\right)} - \left(1 +         \xi\left(\frac{z_{i} - \mu}{\sigma}\right)\right)^{-\frac{1}{\xi}} \right]\end{equation} 
where $z_{i}$ are the empirical maxima. 
  
The case $\xi = 0$ is treated as the limiting form of $G(z | \mu, \sigma, \xi\rightarrow 0)$. The likelihood is maximised with respect to the parameters $\mu$, $\sigma$, $\xi$.}}
estimates of the parameters....