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Fishery Bulletin 98(2) 



Appendix 



The detection probability by depth (p„(2 ) I was defined 

 as the proportion by which the mean values ofSNR^ 

 exceed the threshold, TNR (Eq. 16). Strictly speak- 

 ing, one should define the detection probability as 

 the expected probability that each signal exceeds the 

 threshold. The expectation would be computed by 

 integrating over the pdf of mean SNR^. For a lognor- 

 mal distribution of mean SNR,, we would have 



PJz) = \Pis> TNR I SNR^ )lognormal (SNR^ idSNR^ 

 = {\1-^(TNR-SNR,)] , ^ 



exp 



-0.5 



( ln(SNR^)-^^ 

 [ o 



2 \ 



diSNR, ), 



(20) 



where 



SNR 



= the signal-noise-ratio which 

 follows normal iSNRz, 1); 

 and 



= a lognormal random vari- 



2K(y SNR, 



able with mean;/^ = In (A) + 

 £(ln(.r))-2a2; and 

 standard deviation a = SD( ln(.v ) ) where .v is the pack- 

 ing density. 



Our exercise indicated that both detection probabil- 

 ities from Equations 16 and 20 were very similar. 

 Equation 16, although an approximation, was used in 

 our computation because of its simplicity. 



