Location, dispersion, and asymmetry variability of the probability distribution of the maximum wave height from a set of N individual wave heights are examined in terms of the spectral peakedness and the duration of the sea states through the use of robust statistical parameters. The capability of various empirical and theoretical models to reproduce the observed features is also explored. The study is based on the analysis of numerically simulated Gaussian wave records with given target spectra to fulfill the long duration and stationarity jointly required conditions, seldom found in nature. Results indicate a clear dependence of the probability distribution structure and location on the record length and the spectral narrowness. Furthermore, it is observed that theoretical models based on the statistical independence of individual waves in a sea state and the knowledge of its population distribution assumptions are not able to characterize the structure and variations induced by these factors on the empirical distribution. However, the observed features can be reproduced by a simple empirical model depending on the sample quartiles
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