It has been recognized the potential of Extreme Value Theory in estimating and assessing statistical models for tail-related wave height measurements. Focusing solely on the tail of the underlying distribution through the consideration of both extreme and intermediate order statistics, three testing procedures are applied so as to determine the choice of the extreme model which more adequately describes the largest significant wave heights that occurred at Figueira da Foz, Portugal, from 1958 up to 2001. On the basis of the results yielded by these alternative tests of hypothesis, inferences are established about the tail behavior of the underlying distribution, namely about whether it decays exponentially fast and if it has finite endpoint or not. The statistical choice of extreme domains proved to be a fundamental step preceding the estimation of extreme characteristics since it provided, for instance, a way of distinguishing upon several estimation methods the most adequate to adopt within the present setting. The fact that the extreme value index γ of any distribution with at most moderately heavy tails (with γ ≤ 0) remains the same under integer-power transformations plays a prominent role in the analysis of the data.

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