FISHERY BULLETIN: VOL. 85, NO. 2 



APPENDIX A. Derivation of Vartot 



For a fixed age subsampling, substituting rij = n/L into Equa- 

 tion (2), the Var(p,) is 



Var(p,) = ^ 



L I J q,j (1 - Qi^ Ij {q,j - p,y 

 n N 



(A.l) 



Applying Equation (3), 



Vartot = J. Var(p,) 



1=1 



L Ij q,j (1 - q,j) Ij iq,j - Pj)^ 



n 



N 



A L 



A L 



1 I [L if g, (1 - g,)] I I [i, (9y - py)2] 



i=l j=l 



i=l i=l 



+ 



n 



N 



n N 



which is Equation (4). 



For a random age subsampling, substituting n-^ = n Ij into Equa- 

 tion (2) and applying Equation (3), the Vartot is 



A L 



Vartot = X X 



i=i j=i 



h<iij{'^ - Qij) h (g^; ~ P')^ 



n 



iV 



.4 L 



A L 



I I [/, g, (1 - g,^)] I I [^, (g,;^ - p,)2] 



t=l i=l 



w 



i=l J=l 



AT 



fel ^ ^2 



which is Equation (5). 



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