The first part of the paper deals with the mathematical properties of the Rayleigh distribution, including but not limited to the density function, the moment generating function, the maximum likelihood estimator, confidence intervals, and the bivariate Rayleigh distribution. The second part deals with applications of the Rayleigh distribution to the analysis of the responses of marine vehicles to wave excitation. These applications are illustrated with regard to ocean waves, short-and long-term bending moment responses of a ship, and the "target problem" applied to the relationship between wind speed, wave height, and stress.

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