GEV:
The level of return associated with a probability = the threshold whose probability of exceeding is . corresponds to a return period of :
GPD:
With the same manner we have:
= the threshold whose probability of exceeding is
.
corresponds to a return period of
:![z^{GEV}_{p} = G^{-1}_{\xi}(1-p) = \left \{ \begin{array}{l} \mu -[1 - \lbrace- \log (1-p) \rbrace^{-\xi} ] \frac{\sigma}{\xi} \quad if \quad \xi \neq 0 \\ \quad \\ \mu - \sigma \log( - \log(1-p)) \quad if \quad \xi = 0 \end{array} \right.](../res/eq31.png)
![z^{GPD}_{p} = H^{-1}_{\sigma , \xi}(1-p) = \left \{ \begin{array}{l} \mu -\frac{\sigma}{\xi} [1 - (1-p)^{\xi}] \quad if \quad \xi \neq 0 \\ \quad \\ \mu - \sigma \log( 1-p) \quad if \quad \xi = 0 \end{array} \right.](../res/eq32.png)
