The Edgeworth's form of a cumulative expansion of the probability density
function (PDF) of surface elevation expand the maximum wave
height distribution to predict the occurrence probability of freak waves.
This study investigated the enhancement of the occurrence probability of
freak waves due to the fourth order moment of surface elevation, kurtosis, change and found that the nonlinear effects on the occurrence probability of a freak wave linearly depends on kurtosis for
a small number of waves
.
The statistical theory was compared with field data, and freak waves
were sometimes appear when not expected by the Rayleigh theory but they were predicted by the proposed theory.
and 