It is important to note that a wave record and the
spectrum derived from it are only samples of the sea
state (see Section 1.3.4). As with all statistical estimates,
we must be interested in how good our estimate is,
and how well it is likely to indicate the true state. There
is a reasonably complete statistical theory to describe
this. We will not give details in this Guide but refer the
interested reader to a text such as Jenkins and Watts
1.3.8 Wave parameters derived from the
spectrum
A wave spectrum is the distribution of wave energy (or
variance of the sea surface) over frequency (or wavelength
or frequency and direction, etc.). Thus, as a
statistical distribution, many of the parameters derived
from the spectrum parallel similar parameters from any
statistical distribution. Hence, the form of a wave spectrum
is usually expressed in terms of the moments* of
the distribution (spectrum). The nth-order moment, mn,
of the spectrum is defined by: