Partial Duration Series with Log-Normal Distrubuted Peak Values

Abstract

The T-Year estimate in a partial duration (PD) series with log-normal distributed pesk exceedances is analysed in case of parameter estimation by means of the maximum likelihood method and the method of moments, respectively. Approximate expressions for bias and variance of the T-year estimate are developed, and it is hereby found that the sample variance of the log-normal distribution parameters is the main reason for the uncertainty of the T-year estimate, whereas the sample variance of the intensity of the process is of minor importance. Providing smaller bias (in absolute terms) and smaller variance the maximum likelihood method is found to be superior to the method of moments. The two methods produce bias of different signs, positive bias in case of maximum likelihood estimation and negative in case of estimation by method of moments. The variance expression in case of maximum likelihood estimation is to some extent wave heights. The purpose of the investigation was to assess the 50-year significant wave height on the basis of 17 years of hindcasted wave data together with the standard deviation of the estimate.