The Rayleigh probability distribution has been used extensively for statistical prediction of ocean waves, responses of ships, and marine structures in a seaway. However, the Rayleigh distribution cannot be used for statistical prediction of non-Gaussian random processes, a typical example of which is ship rolling motion with nonlinear characteristics. To evaluate the statistical properties of the maxima (peak values) of non-Gaussian random processes, this paper discusses generalization of the Rayleigh distribution and its application to practical problems. As examples of application, the problems associated with rolling motion of a vessel stabilized by rudders, responses of a surface effect ship in a seaway, and rolling motion of a ship with nonlinear damping are presented.

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