Abstract:
A statistical description of the sea surface is necessary for solving a wide range of fundamental and applied problems. One of the main components of this description is modeling the probability density function of sea surface elevations.
The paper considers two approaches to calculating the parameters of the probability density function in the form of a two-component Gaussian mixture. The first is based on the
use of an incomplete system of Pearson equations, which is due to the fact that when
measuring sea waves, the fifth statistical moment is usually not determined. Within the
framework of the second approach, an additional empirical relationship between the third
and fifth statistical moments is used to close the system of Pearson equations. It is shown
that the first approach is preferable, since it makes it possible to construct the probability
density function in almost all ranges of measured statistical moments of the third and
fourth orders. Taking into account the fifth statistical moment significantly limits the area
in which solutions of the considered system of equations exist.
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