values are found in The Handbook of Mathematical Functions (Abramowitz and 

 Stegun 1972). 



For a chi square with 5-degrees of freedom (n = 4) 



Pr^X4 ^ 0.711) = 0.95 



Prfxl ^ 1.064) = 0.90 



and by means of linear interpolation 



Pr(x4 ^ 0.928) = 0.92 



Since the computed statistic is small compared to 92 percent of all possible 

 chi square values, it is concluded that the Poisson assumption is valid. This 

 result will be instrumental in defining such quantities as return period and 

 nonencounter probability in the following sections of this report. 



Extremal Theory 



8. There are several theoretical probability distributions that have been 

 successfully used in the fitting and subsequent extrapolation of extreme wave 

 conditions. These are the Extremal or Fisher-Tippett Type I distribution, the 

 Lognormal distribution, the Log Extremal distribution, and the Weibull 

 distribution. These distributions have cumulative probability functions as 

 listed in Table 4. 



Table 4 

 Extremal Models 



Extremal Type I : 



F(x) = exp |-exp H^ ^^ ( (3) 



< X < 



(Continued) 



10 



