Kitada and Tezuka Survey designs for estimating recreational fishery catch 



231 



iHn-l) ^ 



where Q = V C,^, / n. 



W'jl'" = Q'"wj(. In general, season-permit and day-permit 

 (7) anglers fish in the same location; therefore we assumed 



the same mean body weight for both kinds of anglers. 

 The samples for estimating C/. and iv f, are independent; 

 therefore the variances are estimated by using Goodman's 

 (1960) formula: 



Estimation for day-permit anglers We estimated the catch 

 of day-permit anglers separately. The notations for day- 

 permit anglers catch estimation are as follows: 



D = total number ofday-permits sold through the season 



(known); 

 Dj^ = total number of day-permits sold in k th month 



(known); 

 dj. = total number of day-permit anglers who returned 

 logbooks in kth month; 

 Rl''' = catch rate of A'th month for day-permit anglers; 

 Cjf' = total catch by day-permit anglers in ^th month (to 

 be estimated). 



The estimator of total number of fish caught by day-per- 

 mit anglers in A'th month is 



v(w,j = v(w;;') + v(wi" 



(14) 



where ViWl"') = W^V(C'^-") + cf V(JZ7,, ) + V(C'^")V{UJ^ ) 

 and V(Wl'") = ZZvfV(Ci'" ) + C','"''V{W, ) + V(C['' ' )V{Ui, ). 



The mean body weight offish in Ath month is estimated 

 from a sui-vey of individual body weights (u\^, of /,, fish 

 caught on the fishing grounds). The estimator for Ath 

 month and its variance estimator are 



and ViUJ^ ' = Z !li ' "' * ' '"^^ '" / (/* (4 - !>)■ 



Cl'"=DX''\ 



(8) 



where the catch rate for day-permit anglers, estimated by 

 the sample mean, is 



The total fishing days in Ath month is estimated as the 

 sum of the fishing days estimates of the season-permit an- 

 glers and the day-permit anglers by 



K'" 



^ d,: 



(9) 



The variance estimator of Cj/' is (Cochran, 1977, p. 26, 

 from Eq. 2.20): 



nCl'"}= D-iViRi'"} ^ ^^'A-c^^) |-(C,, - R,'^)\ 



d,id, 



(10) 



Total monthly catch of season- and day-permit anglers The 



total catch by season- and day-permit anglers in ^th 

 month is Q, which is estimated by 



C,=Cl'' + C['". 



(11) 



Mj.f. =M^+Di^ 



(15) 



and the variance is estimated by V(M.,.i.) = N'-ViMi^) be- 

 cause Di is known. 



Estimation of annual catch 



Method 1 (based on monthly estimates) The annual catch 



is estimated by summing monthly catch estimates over 

 the entire fishing season (A' months). The point estimator 



c=£Q=£cr+|;ci'"=c-+c"^'. 



(16) 



These two total estimates are obtained from independent 

 samples (season- and day-permit anglers); therefore the 

 variance is estimated by adding the variances: 



V(C.) = V(C,") + V{CY 



(12) 



When the same sample of anglers reports catches through- 

 out the season, the sampling is not independent in each 

 month, and monthly catch estimates are auto-correlated. 

 Taking this correlation into account, the variance estima- 

 tor is 



The total catches in weight in kth month are estimated by 

 using the mean body weight of the species in ^th month ( w f^) 

 estimated from the survey of individual body weights by 



W,=W-' + <'=C,i^, 



(13) 



where VV^~ and W^'^'are the total catches in weight for sea- 

 son- and day-permit anglers, given by W"^" = C^'W^ and 



V(C) = V(C'") + V(C'") 



= XV(Cr') + 2;^c7v(Cr,Ci^') 



K 



K 



(17) 



+^v(c,'")+2^cov(c;'",c;^'). 



