The highest value of wave height and its frequency at each wave period interval of a supposed wave condition have the most significant effect on the theoretically estimated extreme of wave induced variable of a ship. Regarding the supposed wave statistics as a result of a random sampling from the population which has no upper limit value of wave height, it is to be expected that the ship has chances to meet far more severe surface conditions than the extreme surface condition in the supposed wave statistics. From the above viewpoint, to estimate the extreme by supposing a wave condition means to regard wave height distribution which has no upper limit as a distribution truncated at an upper limit value. In this case, the distribution of parameter R of short-term distribution of the response variable is also truncated at an upper limit value, which corresponds to the value of wave height. Thus, the theoretical prediction of the extreme may be an under estimation. Authors study on the distribution of R of actual ships. Applying two mathematical models which describe the distribution approximately, the reduction of the extreme by truncating the distribution is investigated. From the result of calculation of the extreme of wave bending moments on the North Atrantic (by Walden), it is clarified that the erorr ranges from 2 to 7% and changes by ship size. The erorr range also changes according to the sample size of original wave observation of the supposed wave condition. So it is desirable that the numbers of observation of such wave statistics are more than 1 × 10⁵ in order to get a reliable result. In the first report of this paper, application of corrected maximum wave height in each wave period interval was suggested. It is made clear that the extreme on the corrected wave condition may have higher reliability than that on the original wave condition, in this paper.