probabilities that the samples could have been picked from a 
normal distribution were 30 in 100, and 50 in 100. There were 
two cases in which Chi Square was very large. 
The skewness of the histogram of the surface records is 
one way in which 7)(t) does not follow a Gaussian distribution. 
A second way in which the distribution will not be Gaussian 
comes from the fact that equation (7.34) yields a finite probabi- 
lity for very high crests and very low troughs. For low waves, 
this finite but very small probability is not important. The 
Gaussian distribution is only a statistical ideal; for example, 
it predicts men twenty feet high from a population with a five 
foot mean and a variance of one foot. In short, all statistical 
theory must be used with judgment. Actual wave heights cannot 
exceed a certain value since the crests will break. It is to 
be expected that for high seas the histograms will be both skewed 
and chopped off at the extremes. The effect of breaking ina 
complex irregular sea surface is again a non-linear problem and 
cannot be treated by the methods under study. 
Figure 14 shows consequently that actual wave records very 
closely approximate the requirement that 7) (t) have a Gaussian 
distribution of the amplitudes. Berkoff and Kotig [1951] have 
commented on the fact that certain symmetry requirements for 
(tt) are not met in actual wave records. This failure is a 
consequence of the actual non-linearity of the problem, but 
again the departure from the Gaussian case is small. 
This fact is indeed fortunate. The theory of the statis- 
tical analysis of functions of the form of equation (7.1) in 
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