Statistical Test of the Distribution of Sea Surface Deflection

A. P. J. Abrahamse Erasmus University, Rotterdam, The Netherlands

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J. van Heteren Rijkswaterstaat, Ministry of Public Works and Transport, Delft, The Netherlands

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A. P. Roskam Rijkswaterstaat, Ministry of Public Works and Transport, The Hague, The Netherlands

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J. Bouman Erasmus University, Rotterdam, The Netherlands

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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 χ2-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.”

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 χ2-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.”

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