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The evaluation on ship roll motion in seas has attracted many, researchers in the field of science and engineering in the case of either deterministic or random excitation because overlarge motion will be a potential threat to the good and life on the ship.For the case of random excitation, most efforts have been devoted to the moments of responses under continuous Gaussian white noise excitation.The probability density function (PDF) of response has been less addressed and other types of excitation are scarcely investigated (i.e..discrete Poisson white noise).