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Fishery Bulletin 98(3) 



density function in the case of nonzero catches (i.e. delta 

 lognormal model) than in the case when both zero and 

 positive catches are included (i.e current general linear 

 model). Thus, if departures from the assumed distribution 

 produced biased lognormal estimates, certainly the cur- 

 rent general linear model would be more prone to these 

 biases than the delta lognormal model. 



As stated by Pennington ( 1991 ) in his response to Myers 

 and Pepin's (1991) article, the assumed lognormal data 

 were contaminated with data from distributions that gen- 

 erated extremely small values, close to zero, which in a log- 

 arithmic scale become large negative values. These large 

 negative values then biased estimates of the mean. In the 

 case of the bycatch database this is not a problem because 

 the smallest positive bycatch CPUE values are in most 

 cases greater than 0.05. 



Another point to consider when comparing the delta 

 lognormal model and the current general linear model is 



the variance associated with the estimated bycatch. Smith 

 ( 1988) described an exact variance for the delta lognormal 

 distribution estimates. He also pointed out that the effi- 

 ciency of the delta lognormal variance is a function of the 

 sample size, the proportion of zero observations, and the 

 variance within the nonzero observations. The variance of 

 bycatch estimates are, however, restricted to the variance 

 from the general linear model or the delta lognormal model 

 because the shrimping effort multiplier is assumed to be 

 exactly known (Nichols et al.-i . Thus to compare true stan- 

 dard errors of bycatch estimates, one would require the 

 variance of the shrimping effort and calculate an overall 

 variance through a mathematical approach such as the 

 delta method or use resampling techniques such as boot- 

 strapping procedures. Because point estimates of bycatch 

 are more frequently used in stock assessments of affected 

 species rather than the confidence intervals, the present 

 analysis focused on the point estimates of bycatch. 



