Munro: Correcting relative fishing power differences in trawl survey data 
541 
power difference the more likely that correct- 
ing it will improve error in mean CPUE. For 
the range of the relative fishing power differ- 
ence for which correction increases (becomes 
worse), the MSE will be called the “noncor- 
rection region.” The two ranges of the relative 
fishing power difference for which correcting 
reduces (improves) the MSE will be referred to 
collectively as the “correction region.” 
This procedure has four critical elements: 
simulating the CPUE data, the estimator of 
FPC, the estimator of mean CPUE, and the 
sample size in each simulation. The CPUE data 
(kilograms per hectare) were simulated with the 
A-distribution. The A-distribution has been pro- 
posed as an appropriate distribution for data 
that include the value 0.0 and that are heavily 
skewed to the right (Pennington, 1983; McCon- 
naughey and Conquest, 1992). The probability 
density function for the A-distribution has pa- 
rameters p, the probability of an observation 
with the value 0.0, and p and a, the conven- 
tional defining parameters of the lognormal dis- 
tribution, which are the population mean and 
standard deviation of the log-transformed ele- 
ments, respectively (Aitchison and Brown, 
1957). The parameters for this distribution were 
calculated with CPUE data for flathead sole 
( Hippoglossoides elassodon ) and walleye pollock 
( Theragra chalcogramma ) collected in the 1992 
eastern Bering Sea survey (Table 1; Fig. 2). 
These two species were chosen to illustrate 
cases of moderate and extreme skewness to the 
right. The mechanism for imposing a fishing 
power difference is also part of simulating each 
survey. In these examples the relative differ- 
ence was applied by multiplying each CPUE 
from the nonstandard vessel by a ratio that rep- 
resented the true mean nonstandard CPUE 
over the true mean standard CPUE. Two-hun- 
dred surveys were simulated at each of twenty 
preselected fishing power differences (Table 2). 
In each simulated survey, half of the data were 
selected to represent the standard vessel and 
the fishing power difference was imposed on the 
other half of the data, representing the non- 
standard vessel. The sample sizes in two of the 
simulations were based on the number of ob- 
servations used to calculate the parameters of 
the A-distribution: 149 per vessel for pollock and 
144 per vessel for flathead sole. The third simulation 
was based on 50 observations per vessel for flathead 
sole. The smaller sample size is similar to the number 
of tows made in the larger strata of the annual Bering 
Sea survey (Goddard and Zimmermann 1 ). 
-1 
LU 
Z> 
Q_ 
O 
c 
a 
<D 
uncorrected data 
corrected data 
E 
o 
LU 
c n 
5 
correction 
region 
noncorrection 
region 
correction 
region 
i 
0.6 
r 
1.0 
i 
1.4 
Fishing power difference 
Figure 1 
The noncorrection region that emerges from plotting mean square 
error of mean CPUE against the fishing power difference imposed 
on the simulated data. “Uncorrected data” refers to the scenario 
where mean CPUE was estimated without correcting the fishing 
power difference. “Corrected data” refers to the scenario where 
mean CPUE was estimated after correcting the fishing power 
difference. 
Table 1 
The A-distribution parameters and fishing power correction fac- 
tors estimated from the 1992 Bering Sea survey data. Sample 
sizes are different because different vessels represented the “stan- 
dard” vessel for each species. 
Walleye pollock 
(Theragra 
chalcogramma ) 
Flathead sole 
( Hippoglossoides 
elassodon ) 
A-distribution parameters 
p (fraction of zeros) 
0.0336 
0.1042 
p (mean of log nonzeros) 
3.3590 
1.5859 
o (SD of log nonzeros) 
2.1194 
1.4985 
Number of observed 
CPUEs used to compute 
parameters 
149 
144 
Estimated fishing power 
correction (FPC) factor 
1.32 
0.76 
The Kappenman estimator of the ratio of scale 
parameters (Kappenman, 1992) was used to estimate 
the FPC in each simulated survey. Inordinately large, 
rare observations are typical of trawl survey CPUE 
data (Koeller and Smith, 1983; Weinberg et al., 1994; 
