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Extreme value analysis of Baltic Sea water levels

REF. DATE:23 October 2015 CREATED/MODIFIED: 27 October 2015 45 views No Comment

WaterlevelAn intense week researching on Extreme Value Analysis (EVA). Extracting relevant information from big time series of water level data. Quite interesting, learning a lot – at Institute of Cybernetics, University of Tallinn.

     Classical statistics focus on the average behavior of the stochastic process (central limit theorem). On the other hand, EVA focus on extreme and rare events (Fisher-Tippett theorem). The main distribution in EVA is the so-called The GEV cumulative distribution function is given by \begin{equation*} F(x, \theta):=\left\{\begin{array}{ll} \exp\left(-\left(1+\frac{x-L}{C}S\right)^{-1/S}\right) & \mbox{ if } S\neq0,\\ \exp\left(-\exp\left(-\frac{x-L}{C}\right)\right) & \mbox{ if } S= 0, \end{array}\right. \end{equation*} where $\theta:=(L,C,S)$ is the set of three parameters: $L$ (location), $C$ (scale), $S$ (shape). Notice that, in the statistical literature, such parameters are denoted by $\mu$, $\sigma$, $\gamma$, and, in the hydrologic literature, it is common to parametrize the above distribution using instead $\bar{\gamma}=-S$ or $\alpha=-1/S$.

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