18 
Fishery Bulletin 1 15(1) 
Table 2 
Values from models fitted to simulated length-at-age data after log-skew-f distribution with constant variance, with asymp- 
totic length (L„) = 59.72, growth rate coefficient (K) = 0.16, theoretical age in years when the length is zero (-to) = 2.5, 
heteroscedasticity(p) = -0.5, and dispersion (cr^) = 0.05 considered by ranging the parameters of skewness (A) and degrees 
of freedom (V) in the set (-3, — l,0)x|3,12,100). 
(^v) 
Model Parameter 
(-3,3) 
(-3,12) 
(-3,100) 
(-1,3) 
(-1,12) 
(-1,100) 
(0,3) 
(0,12) 
(0,100) 
Log-normal (type I) 
Constant 
56.789 
57.568 
57.458 
57.519 
57.790 
57.923 
59.717 
59.665 
59.653 
K 
0.158 
0.157 
0.160 
0.155 
0.161 
0.163 
0.161 
0.164 
0.164 
“^0 
2.603 
2.541 
2.530 
2.652 
2.491 
2.427 
2.430 
2.381 
2.354 
0.004 
0.002 
0.001 
0.006 
0.002 
0.002 
0.011 
0.003 
0.003 
Log-normal (type II) 
Constant 
56.797 
57.578 
57.456 
57.595 
57.810 
57.938 
59.739 
59.635 
59.640 
K 
0.157 
0.157 
0.160 
0.154 
0.161 
0.163 
0.160 
0.164 
0.164 
“^0 
2.606 
2.545 
2.529 
2.684 
2.502 
2.435 
2.445 
2.377 
2.351 
0.004 
0.002 
0.001 
0.006 
0.002 
0.002 
0.011 
0.003 
0.003 
Log-skew-^ 
Constant 
56.570 
57.179 
57.346 
57.395 
57.965 
57.859 
59.809 
59.614 
59.654 
K 
0.160 
0.161 
0.161 
0.160 
0.159 
0.163 
0.153 
0.163 
0.163 
”^0 
2.521 
2.453 
2.501 
2.515 
2.518 
2.460 
2.644 
2.403 
2.373 
d 
0.003 
0.003 
0.003 
0.003 
0.004 
0.003 
0.003 
0.004 
0.004 
A 
-3.842 
-3.627 
-3.266 
-1.375 
-1.683 
-1.718 
-0.472 
-0.885 
-1.224 
V 
3.626 
16.640 
18.471 
3.640 
11.739 
17.457 
3.130 
13.739 
16.752 
Log-skew-i 
Exponential 
56.886 
57.651 
57.520 
57.645 
57.801 
58.059 
59.993 
59.624 
59.700 
K 
0.158 
0.156 
0.159 
0.155 
0.161 
0.160 
0.153 
0.163 
0.162 
2.490 
2.510 
2.491 
2.590 
2.473 
2.490 
2.640 
2.403 
2.372 
p 
-0.125 
-0.121 
-0.126 
-0.107 
-0.117 
-0.144 
-0.135 
-0.069 
-0.049 
d 
0.005 
0.005 
0.004 
0.006 
0.006 
0.006 
0.005 
0.005 
0.005 
A 
-3.517 
-3.528 
-2.917 
-1.196 
-1.713 
-1.458 
-0.249 
-0.545 
-1.126 
V 
3.217 
11.846 
15.961 
3.296 
10.977 
15.346 
2.804 
12.430 
15.929 
Log-skew-t 
Power 
56.929 
57.645 
57.495 
57.691 
57.829 
58.049 
59.951 
59.610 
59.705 
K 
0.155 
0.155 
0.159 
0.153 
0.160 
0.160 
0.153 
0.163 
0.162 
-h 
2.570 
2.553 
2.512 
2.635 
2.503 
2.487 
2.647 
2.403 
2.382 
p 
-0.023 
-0.021 
-0.020 
-0.021 
-0.023 
-0.025 
-0.022 
-0.007 
-0.003 
d 
0.004 
0.004 
0.003 
0.005 
0.005 
0.004 
0.004 
0.004 
0.004 
A 
-3.702 
-3.670 
-3.075 
-1.291 
-1.778 
-1.585 
-0.342 
-0.863 
-1.198 
V 
3.341 
13.131 
17.094 
3.476 
11.855 
16.640 
2.940 
13.372 
16.574 
Results 
Simulations 
To assess the effect of error distribution in the VBGF 
parameters, length-at-age data were simulated from a 
log-skew-t distribution with a constant variance and 
the estimated growth parameters of Contreras-Reyes et 
al. (2014) (see the Comparisons and selection of models 
section). Different cases were evaluated by considering 
a range for A and v in the set of l-3,-l,0}x{3,12,100) 
(Table 2). This procedure permits assessment of the 
closeness of estimates in absence and presence of skew- 
ness and heavy-tailed simulated data. Each simulation 
considered 30,000 realizations. For A= -3, estimates of 
indicated the largest differences with real values, 
and the smaller differences were reported in K and -^o- 
The largest differences of v for estimated and simu- 
lated data were produced for v = 100 (which approxi- 
mates the log-skew-normal distribution) and for A= 0 
(which approximates the log-normal distribution). The 
log-skew-^ model presented estimates similar to the 
initial parameters A= -1 and v = 12. 
Modeling data from southern blue whiting 
In the case of the parameters of error distribution, the 
posterior estimates are small values because of the 
application of the log-transformation, and the v poste- 
rior estimates are smaller than 15, indicating the pres- 
ence of extreme values (Table 3). In these models, the 
shape parameters A are close to -1, indicating a non- 
