,
where n is the number of observations in the series, is the standard deviation of a normal distribution prior to exponentiation and is the observed CPUE index value in year tand region g. We used a constant value of 0.3 of all in this analysis. We also used the standard error of each estimate of as an estimate of , an approach that weights the contribution of each year differently based on the precision of the estimate. This alternative made little difference in the overall fits of the model so we retained the constant value of 0.3. This equation was appropriately modified when different grouping of the data were used.
,
is the standard deviation of a normal distribution 
is the observed 
in this analysis. We also used the standard 