Higher moments of weighted integrals of non-Gaussian fields

In general, the exact probability distribution of a definite integral of a given non-Gaussian random field is not known. Some information about this u nknown distribution can be obtained from the 3rd and 4th moment of the inte gral. Approximations to these moments can be calculated by discretizing the integral and replacing the integrand by third-degree polynomials of correl ated Gaussian Variables which reproduce the first four moments and the corr elation function of the field correctly. The method described (see Ditlevse n O, Mohr G, Hoffmeyer P. Integration of non-Gaussian fields. Probabilistic engineering mechanics, 1996) based on these ideas is discussed and further developed and used in a computer program which produces fairly accurate ap proximations to the mentioned moments with no restrictions put on the weigh t function applied to the field and the correlation function of the field. A pathological example demonstrating the limitations of the method is given . (C) 1998 Published by Elsevier Science Ltd. All rights reserved.