The third and best method of estimating k is the maximum likelihood 

 method. Scores, Z, are computed from trial values of k until Z=0: 



A x 

 Z = E ( T > - N log e {1 + (x/fc)} (3) 



k + x 



where A^. = accumulated frequency in all units containing 

 more than x organisms 



All three estimates of k were calculated for total CPUE, as well as 

 for selected shore-zone species CPUE. Further, by using the estimates 

 of k in the probability distribution function, 



P = & + * " *>• • £ (4) 



X x!(k - 1)! q k 



where R = p/q 

 p = x/k 

 q = 1 + p 



the expected frequency of samples containing x organisms was calculated. 

 A chi-square statistic: 



X 2 = ((F x ~ P x ) 2 > (5) 



Px 

 where F x = actual frequency of x organisms 



was used to test if the seine data did in fact fit a negative binomial 

 distribution. 



In order to estimate the adequacy of the seine program, the variances 

 of the log.. n (CPUE + 1) data were used to determine the sample size 

 required to detect specified differences for different alpha and beta 



42 



