Estimate Reliability 



14. Methods for computing the reliability of extreme wave condition 

 estimates can be found in various reports and articles (Petrauskas and Aagaard 

 1971, Isaacson and Mackenzie 1981, Borgman 1983). The method given by Bergman 

 requires relatively little computation while the other methods either do not 

 apply to prediction or entail extensive numerical simulations. The method 

 used here has been successfully applied to the extremal analysis of hindcast 

 data on the coast of California (Borgman 1982). 



15. The first step in computing the estimate reliability is to calcu- 

 late an upper bound on the error (standard deviation) o„ from estimating 



r 



the function F(x) from Table U. This upper bound is approximated by the 

 Kolmogorov-Smirnov (KS) limit for the quantity 



|Fr-F(x)| (12) 



for Fp from Equation 7. The KS upper bound is the value D(a,n) such 

 that 



PR 



maxiFp - F(x)| > D(ct,n)J = a 



for a = a small number. In other words, the number D(a,n) is such that the 



maximum absolute difference between the cumulative probability function F(x) 



and its estimated value Fp will be greater than D(a,n) only with small 



probability a . The value D(a,n) is then assumed to represent a Z ,„ x o„ 



0.1 c. r 



error where Z ,„ is the standard normal variate such that Pr(Z < Z ,„) 

 a/2 a/2 



= a/2 ; thus, an approximate value for the error Op, is computed to be 



ap = 5^ (13) 



a/2 



For samples of n > 35 and a = 0.05 an approximate value for D(a,n) 

 given n = 62 is 



D(0.05,n) = ^^ 



yg2 



and 



17 



