FISHERY BULLETIN: VOL. 74, NO. 3 



T.ABLK 6.-Reported and estimated days on grounds and estimation error rates. 



statement 



Pr{-n< e <fi) = $ju. 



defines these calculated values. Here, e is the error 

 coefficient (Equation 4.0), ju is an arbitrary limit of 

 acceptable error, and ^jx is the likelihood of € being 

 within the interval -ju to +ju. By substitution (i.e., t 

 = U'-f)/f) and reduction of terms: 



Pr( 



f 



1-iU 



■/ 



f 



1-fX 



) = <I>/x 



Bounds on points estimates can therefore be 

 calculated: 



upper limit = /". 



lower limit = f. 



1 

 l + /i 



and values of Oju from Table 5 can be used to 

 approximate the likelihood that the reported days 

 fished (f) will fall within the interval. For example, 

 if estimator III calculated days fished to be 100, it 

 may be stated that there is a 0.945 probability that 

 the reported value of days fished is within the 

 interval 67 to 200, i.e.. 



100 



100 



^^^-:o:^>/='rr5:499) = 0.945. 



It is important to note, however, that the figures in 

 Table 5 were computed directly from the 

 frequency distributions of error rates of estimates 

 made in the past (i.e., 1971-73). Therefore, estima- 

 tion bounds may be correctly approximated on 

 future point estimates only if it is assumed that 

 future distributions of error coefficients are cor- 

 rectly represented by these past performance 

 data. 



Of the methods presented, estimator I (based on 

 the ratio between days fished as reported and 

 sighted days-on-grounds) and estimator III (based 

 on the probability of a day fished given that it was 

 not observed) exhibited the least error. Estimator 

 III was consistently most accurate (especially in 

 the last 2 yr) although the difference between the 

 two is small. This estimator may be expected to 

 calculate days fished to within *0.50 approximate- 

 ly 95% of the time. Estimator I has value in that it 

 does not require sophisticated analysis of over- 

 flight data (only the numbers of sightings and 

 numbers of flights are needed) and is less likely 

 than other estimators to produce error coefficients 

 greater than 0.50. It may be expected to produce 

 estimates within *0.50, 90% of the time. 



Estimator II, based on the probability of a day 

 on grounds if it was not sighted, was consistently 

 the poorest of the three. Its poor performance is 

 likely the result of insufficient instances of 

 reported days on grounds. These parameters allow 

 computations of P{G/N) and K, on which the 

 estimate is based. In the case where complete data 

 was available (GDR), eff'ort was estimated very 

 well by estimator II and, in fact, the error 

 coefficient did not exceed 0.42. A similar estimator 

 also based on P{G/N), however, produced accept- 

 able calculations of days on grounds for all coun- 

 tries that were within *0.50 of the reported value 

 in approximately 80% of all cases. 



Estimation error can result from sources which 

 are known to have occurred in the past and are, 

 therefore, of a magnitude predictable by the 

 proposed methods for approximating probability 

 limits on point estimates. The probabilities of 

 fishing {P{F) =f/{V-At)) from data in Table 1 were 

 found to be highly correlated with the PiF/N) 



512 



