^"' (^k) = ^ • ^(k) * '' 



(9) 



7-1, 



If the plot of F"'{k/n + 1) with Y/j^x approximates a straight line with 

 slope A and intercept B then the proposed theoretical distribution is ac- 

 cepted. Sometimes more than one of the possible distributions will yield a 

 straight line fit. In this case, the better of these is usually that which 

 best fits the upper tail of the function Fj^ . However, some subjective 

 judgment is required in such cases. 



10. The quantity known as the return period, R , is defined to be the 

 mean value of the random number of observations preceding and including the 

 first exceedence of a specified wave threshold x . In terms of the cumula- 

 tive probability function and the Poisson model parameter u 



" = uci -'f(x)1 <'«' 



Another useful measure is the nonencounter probability, NE(x) , or the prob- 

 ability that for a design life L the largest wave condition is less than or 

 equal to x in value. For the Poisson model 



NE(x) = exp (=jj (11) 



Note that if L = R then 



NE(x) = 0.37 



Thus the probability of encountering a condition larger than the R year re- 

 turn period condition in R years is 0.63. This demonstrates the misleading 

 nature of the return period in that during R years, there is a 63 percent 

 chance of encountering an R year extreme condition. Care should be taken 

 when using return period as the only criterion for extremal prediction. 



Extremal Plotting 



11. A computer software package called EXPLOT was developed at the US 

 Army Engineer Waterways Experiment Station (WES) on the Honeywell DPS1 system 

 to plot the formula given in Equation 9. The plotting was performed for each 



12 



