Statistical Test of the Distribution of Sea Surface Deflection

Abstract

Most of the common statistical tests are based upon statistically independent data. Many observations of physical phenomena are statistically dependent, as is indicated by the sample-autocorrelation function. In this paper, a test is presented for observations that are not statistically independent. The test is a modified form of the classical ?2-procedure and is based upon a transformation of the observations to statistically independent data assuming a second-order autoregressive model for describing the autocorrelation of the original observations. The test is applied to wind waves on sea, i.e., for testing on normality and on a ?Gram-Charlier distribution? of sea surface deflection. The results show that the instantaneous values of sea surface deflection during swell conditions satisfy the assumption of a normal distribution and those during sea conditions are approximately normal, though a better approximation is provided by the ?Three-term Gram-Charlier A Series distribution.?