It has been mentioned so far that the amplitude of random variable in ships has so-called lognormal probability distribution in long term. Actually, it was indicated that there were many data in long-term having such a distribution. However, in some cases, there are some data deviated from such distribution and in these data the forms of distribution curve is concave upward on log-normal probability paper. In this paper, the author attempted to derive the new probability distribution function for random variable in long term by extending the log-normal distribution function. New distribution function is given in equation (7), Furthermore, in this paper, the method of prediction of population distribution function using the data and method of prediction of maximum amplitude available in design stage are explained.