Abstract
The distribution of maxima during a given time interval is of interest in many applications in risk analysis. Within the framework of stationary Gaussian processes, several theoretical results considering asymptotics from different aspects have been derived for this distribution. In this note, we review results from the theory and study the accuracy of these approximations by exemplifying with a model for wave heights from oceanography. It turns out that for high values and the time periods normally encountered for buoy measurements, care should be taken in use of approximation based on the Gumbel distribution.
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Acknowledgements
The author is grateful to Prof. Igor Rychlik, Lund University, for fruitful discussion and the anynomous referees for their valuable suggestions.
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Rydén, J. A note on asymptotic approximations of distributions for maxima of wave crests. Stoch Environ Res Ris Assess 20, 238–242 (2006). https://doi.org/10.1007/s00477-005-0018-1
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DOI: https://doi.org/10.1007/s00477-005-0018-1