Comparison of three different methods of moments for derivation of probability distribution parameters

Abstract

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of their response to wave loading is a minimum requirement for the efficient probabilistic analysis of these structures. Even if the structural system can be assumed to be linear, due to nonlinearity of the wave loading mechanism and also due to the intermittency of wave loading on members in the splash zone, the response is often non-Gaussian. The (conventional) method of moments is one of the methods which is frequently used to determine the parameters of the adopted probability model from a simulated or measured record of response. However, when higher order moments (e.g. 3rd or 4th order moments) are required for the derivation of distribution parameters, the parameter values obtained from this method show considerable scatter due to sampling variability. The purpose of this investigation was to compare the efficiency of the conventional form of the method of moments with two alternative forms of the method, i.e. with linear and the (new) low-order methods of moments. As a method of demonstration, the three different methods of moments have been applied to symmetric Pierson–Holmes distributions. The results show that in most cases the sampling variability of the parameter values determined from the two alternative forms of the method of moments is much smaller than their corresponding values derived from the conventional method of moments.