nonparametric conventional method (sometimes called the correlation method, or the 
Blackman-Tukey, BT method), and the spectra were compared with the ones obtained by 
the parametric method. From these comparisons, we can get an idea of the characteristics 
of the parametric method. Although they could have very steep peaks, the spectra from 
the parametric method are smooth, and are free from the erroneous smoothing (blurning) 
effect of spectral windows in the nonparametric method. They are differently effected by 
the statistical fluctuations of sample estimation that come from the finiteness of discrete 
data. 
Examples of results obtained by applying this parametric method to the analysis of 
seakeeping data for marine vehicles and structures were also given to demonstrate the 
usefulness of this approach in this field. 
This author concludes that although this parametric approach is not the ultimate 
method of course, it is very promising, gives reliable results, and offers a supplement to 
the nonparametric method explained in Part I. The nonparametric method is, in a sense, a 
method for estimating infinite or very large number of parameters from finite data, or for 
estimating their spectrum or correlation functions. The parametric method on the other 
hand is a method for estimating a finite number of parameters for the same purpose. 
The characteristics of a dynamic system, which is usually assumed to be determinis- 
tic, must be approximated by a finite number of parameters because the system is usually 
governed by equations of motions with a certain finite number of parameters. The types 
and also the order of parametric models are closely related with the order of the equations 
of motions, so the parametric method can be presumed to be more reasonable in the anal- 
ysis of response characteristics. 
In Parts I and I, the processes were assumed to be linear. In Part III, the method for 
treating a nonlinear process was summarized and several methods, such as the lineariza- 
tion method, the perturbation method, and the Voltera expansion method (polyspectra 
method), were reviewed and the relations of these methods to each other were described. 
Then, in relation to the probability distribution of the extreme amplitudes of nonlinear 
processes, the application of the Fokker—Planck equation and some examples appearing 
recently in naval architecture were introduced. The probability distribution of extremes of 
nonlinear response process were also related to the higher order frequency response func- 
tions, and can be connected through the cumulant expressions. The general relations of 
these functions were summarized. The achievements of J. F. Dalzell on the application of 
polyspectra and in the derivation of the probability distributions of extremes of seakeep- 
ing data were introduced at length. At the end of Part III, as an extension of the model 
fitting approach treated in Part II, a few trials on nonlinear parametric models proposed 
by several statisticians were introduced. Some of these trials look promising and are still 
under active development. However, as has been concluded in Chapter 14, we need more 
experience with such applications. 
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