The supposed wave condition has the most significant effect on the result of the statistical estimation of the wave induced variable of a ship. It is the general case of the theoretical estimation of the wave induced variable of a ship in a given sea zone to suppose the observed wave statistics of the weather ships or voluntary ships in the sea zone. Authors researched the data of wave observation of 62 voluntary ships in the North Pacific Ocean during 3 years (1976-78). It was clarified that the wave conditions encountered by them had remarkably wide scatter band in comparison with that of random samples from the same population. To investigate the cause of the wide scatter band, authors research statistical character of wave and wind conditions observed on 35 voluntary ships in the above sea zone during 6 years (197681), wave condition on 9 weather ships in the North Atlantic Ocean for 18 years, and records wind measurement at 5 weather stations in Japan for 20 years. From the above statistical study, it is made clear that the newly analysed wave and wind records have also the similar wider scatter band. Authors deduced from the result that such variable as wave-and wind in ocean have the basic character in which the sample distribution shows a different distribution from that of random samples from usual population having a given distribution with constant parameters. Authors study on the probabilistic model of population which can describe this special sample distribution, and introduce a population having a complex distribution with parameters which are not constant but stochastic variables, too. The distribution of the above observed wave heights is described by assuming them as sample values from the population with a complex log-normal distribution with a constant standard deviation and a mean which is described by a normal distribution. From the study of the sample distribution of wave conditions encounterd by ships, it is evaluated that the coefficient of variation of the extreme wave condition encountered by a ship during her life time in a given sea zone may be nearly 15% in maximum, and the value for larger ship will increase. This means the coefficient of the extreme value of wave induced variables of the ship has also nearly the same value. This value is larger than that usualy supposed in the case of reliability of strength of ship structure.