McConnaughey and Conquest: Comparative trawl-survey estimation based on lognormal theory 



1 13 



value out of 40,000 data points that caused a consider- 

 able increase in the RMSE associated with the AM 

 estimate. It is noteworthy that the magnitude of this 

 simulated density value is in keeping with extreme 

 values observed in the field. Accuracy of GM estima- 

 tion improved dramatically as skewness increased, in 

 contrast to the FM and AM responses wherein accu- 

 racy decreased as skewness increased. 



Deviation of the estimator from the parameter 

 (bias) Overall, the most extreme deviations were as- 

 sociated with the smallest sample sizes; this disparity 

 decreased as sample sizes increased (Fig. 3). GM esti- 

 mates deviated less, stabilized at smaller sample sizes, 

 and, despite the positive bias, converged much more 

 predictably to e MLN than did AM and FM in estimating 

 u. In general, estimates of u oscillated about the para- 

 metric value and converged as sample size increased. 

 The absolute values of the deviations from u are smaller 



for the FM than for the AM method in 17 of the 26 

 cases examined, without an obvious trend related to 

 the skewness of the data. It is noteworthy that esti- 

 mates of u obtained with the AM and FM methods are 

 equivalent when n=2. 



Average length of the interval estimate The aver- 

 age length of the 1000 909c confidence intervals (CIs) 

 calculated for each sample size was consistently shorter 

 for the GM (which only estimates one parameter) than 

 for the intervals of the AM or FM (Fig. 4). Intervals 

 calculated using the FM method were consistently 

 larger than those for the AM method. Overall, the de- 

 gree of difference between the three estimators 

 decreased as sample size increased and as skewness 

 decreased. Average lengths were inordinately large at 

 the smallest sample sizes and decreased rapidly there- 

 after. The average CI length for the GM decreased as 

 skewness increased, in contrast with the behavior of 

 CI lengths for u. 



150 



20 30 



SAMPLE SIZE 



Figure 3 



Comparison of degree of deviation from the parameter (bias; 

 scaled to 0) for the three estimators of central tendency ac- 

 cording to sample size, (a) LOGN (4,2) data representative of 

 coastal population of Cancer magister used for Monte Carlo 

 simulations, (b) LOGN (6,1) data representative of estuarine 

 population of C. magister used for Monte Carlo simulations. 



5,000 



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U 3,000 



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 o> 



LU 



O 2,000 



£ 



LU 



< 1,000 



8,000 



€ 6,000 



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 (3 



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£ 2,000 



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10 



20 



30 



40 



50 



10 



20 30 



SAMPLE SIZE 



40 



50 



Figure 4 



Comparison of average length of 90<7( confidence interval for 

 the three estimators of central tendency according to sample 

 size, (a) LOGN (4,2) data representative of coastal popula- 

 tion of Cancer magister used for Monte Carlo simulations, (b) 

 LOGN (6,1) data representative of estuarine population of C. 

 magister used for Monte Carlo simulations. 



