Abstract
The Longuet–Higgins distribution is a classical joint probability distribution of wave periods and amplitudes still being used for comparison against current approaches in coastal engineering and other applications. However, comparisons are carried out against the theoretical distribution rather than against jointly simulated values. Some formulae to implement the generation of jointly distributed wave amplitudes and periods is unavailable. A practical approach is proposed in this study to cope with this issue. Expressions for the marginal and conditional cumulative distribution functions of the Longuet–Higgins distribution based on the error function, not reported in the literature, are provided. Resulting simulations are in good agreement with the theoretical distributions. It is concluded that the developed equations are formal distributions based on probability theory, that the proposed method leads to adequate simulated values of jointly distributed wave heights and periods and that it is easy to implement in current software and suitable for engineering applications.
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