542 
Fishery Bulletin 96(3), 1998 
Table 2 
Fishing power differences imposed on the simulated data. 
Catch ratio: 
nonstandard 
to standard 
Catch ratio: 
larger to 
smaller 
0.50 
Nonstandard vessel is 
2.00 
0.57 
half as efficient 
1.75 
0.67 
1.50 
0.71 
1.40 
0.77 
1.30 
0.80 
1.25 
0.83 
1.20 
0.87 
1.15 
0.91 
1.10 
0.95 
1.05 
1.00 
Identical fishing power 
1.00 
1.05 
1.05 
1.10 
1.10 
1.15 
1.15 
1.20 
1.20 
1.25 
1.25 
1.30 
1.30 
1.40 
1.40 
1.50 
1.50 
1.75 
1.75 
2.00 
Nonstandard vessel is 
twice as efficient 
2.00 
Goddard and Zimmermann 1 ). If the rare, large ob- 
servations typical of survey CPUEs are chance oc- 
currences rather than the consequence of a fishing 
power difference, then a preferred estimator would 
be insensitive to them. The nonparametric Kappen- 
man estimator has this property. Wilderbuer (1988) 
compared five FPC estimators (the ratio of means, 
the simple multiplicative model [Robson, 1966], the 
additive nested AN OVA, the multiplicative nested 
ANOVA, and the beta distributed index [Fanning, 
1984]) and found all to have wide variability about 
the estimate of fishing power, indicating a sensitiv- 
ity to rare large CPUEs. Wilderbuer et al. ( 1998 ) have 
extended this work to include the Kappenman esti- 
mator and have found it to have an estimation error 
equal to or lower than the others. For the A-distribu- 
tion, s determines heaviness of the right tail of the 
distribution. When the A-distribution is more sym- 
metric in appearance and less heavy-tailed, all of the 
estimators reviewed by Wilderbuer (1988) may be 
reasonably well-behaved. When the A-distribution 
becomes skewed to the right and the magnitude of 
the rare, large observations becomes quite high, the 
insensitivity of the Kappenman estimator results in 
lower estimation error. 
The arithmetic mean was used as the estimator 
for mean CPUE because it is unbiased. Any biases 
JD 
ctJ 
JD 
O 
□I 
CPUE (kg/ha) 
Figure 2 
Histograms of catch-per-unit-of-effort (CPUE) data 
for flathead sole and walleye pollock overlayed by 
the probability density function for the A-distri- 
bution. The histograms are expressed as densities 
rather than as frequencies. The parameters speci- 
fying the A-distribution were estimated from the 
data in the histograms. The walleye pollock dis- 
tribution is truncated to show reasonable detail. 
Not shown are the two most extreme values, 
1,118.5 kg/ha and 2,906.8 kg/ha. 
observed in the means estimated in the simulations 
would then be due to systematic error in the data 
caused by fishing power differences. Also, the arith- 
metic mean has been argued to be the best estima- 
tor of mean CPUE (Myers and Pepin, 1990; Smith, 
1990) and is commonly used (e.g., Harrison, 1992; 
Weinberg, et al. 1994; Goddard and Zimmermann 1 ). 
The issue of design-based versus model-based es- 
timation (Smith, 1990) is raised in the choosing of 
the arithmetic mean to estimate mean CPUE even 
though the data are simulated with a probability 
model that has known optimal estimators. Design- 
based estimation is followed here because that is the 
strategy employed in the analysis of the Bering Sea 
trawl surveys. A probability model is assumed in 
these examples solely to provide a parameter value 
for estimating the MSE. In a similar vein, it would 
seem that the question of relative efficiency could be 
